The amount of money that he earned in interest is given as follows:
$420.
How to obtain the balance using simple interest?The balance of an account after t years, using simple interest, that is, a single compounding per year, is given by the equation presented as follows:
A(t) = P(1 + rt).
In which the parameters of the equation are explained as follows:
P is the value of the initial deposit.
r is the interest rate, as a decimal.
The interest accrued is given as follows:
I(t) = Prt.
The parameters for this problem are given as follows:
P = 7000, r = 0.02, t = 3.
Hence the total interest is of:
I(3) = 7000 x 0.02 x 3
I(3) = $420.
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What is the slope of the function?
–3
–2
3
4
The slope of the function is equal to: C. 3.
How to calculate the slope of a line?In Mathematics, the slope of any straight line can be determined by using this mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = rise/run
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Substituting the given data points into the slope formula, we have the following;
Slope, m = (4 - 1)/(0 - (-1))
Slope, m = 3/4=1
Slope, m = 3.
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Allison was in an accident cause by her own negligence. She has 50/250 bodily injury insurance. There were 5 people injured in a mini-van and 2 people injured in Allison’s own car. The people injured in the accident sued and 4 were awarded $40,000, 2 were awarded $80,000 and 1 person was awarded $160,000. How much will the insurance company pay?
In this situation, Allison's insurance company will pay a total of $400,000.
Calculate the cost of insurance companyFirst, we need to add up the total amount awarded to the people injured in the accident. This is $40,000 x 4 + $80,000 x 2 + $160,000 x 1 = $400,000.
Next, we need to look at Allison's insurance policy. She has 50/250 bodily injury insurance, which means that the insurance company will pay up to $50,000 per person and up to $250,000 per accident.
Since the total amount awarded is $400,000, the insurance company will only pay the maximum amount allowed per accident, which is $250,000.
Therefore, the insurance company will pay $250,000 and Allison will be responsible for the remaining $150,000.
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What are the three components of research questions?
A research question is an inquiry that a study or research project aims to resolve. Quantitative and Qualitative research questions are the components of questions.
Descriptive research questions are used to determine how the population of the study will react to one or more variables or to describe the factors that the study will evaluate. These questions typically begin with "what."
Comparative research questions aim to identify differences between two or more groups for an outcome variable. These inquiries could possibly be the cause. A comparison between two groups, one in which a certain variable is present and the other in which it is not, may be made, for instance.
Relationship research themes aim to find patterns and interactions between two or more variables. The phrases "association" and "trends," as well as dependent and independent variables, are commonly used in these enquiries.
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Write some examples of interval variables
An interval variable is a type of quantitative variable, where the difference between two values of the variable is meaningful and the values can be ordered.
Examples of interval variables include temperature (in Celsius or Fahrenheit), time (in seconds, minutes, hours, etc.), and dates. You can calculate the difference in temperature between two points, the length of time between two events, or the number of days between two dates. For example, let's say that the temperature outside is 25°C at noon and 29°C at 4 pm. The interval variable is the temperature, and the difference between the two temperatures is 4°C (29°C - 25°C = 4°C). Another example is the length of time between two events. Let's say that Event A began at 1 pm and Event B began at 2 pm. The interval variable is the length of time between the two events and the difference between the two times is 1 hour (2 pm - 1 pm = 1 hour). Finally, let's say that Date A is January 1, 2020 and Date B is January 10, 2020. The interval variable is the number of days between the two dates, and the difference between the two dates is 9 days (January 10,)An interval variable is a type of quantitative variable, where the difference between two values of the variable is meaningful and the values can be ordered.
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if 132=(6x+30) what is the value of x
Answer:
x=17
Step-by-step explanation:
132 + (-30) = (6x+30) + (-30)
132 - 30 =6x + 30 - 30
102 =6x
6x/6 = 102/6
(This step has a picture)
x=17
Find the area. Simply your answer. 3x and x+2
Answer:
4x+2
Step-by-step explanation:
Add common numbers together.
3x + x = 4x
Therefore, the answer is 4x+2.
Hope this helps ^_^
Determine the, LCM, of the following three terms: 3st,4s2,5t2
60 s²t² is the lowest common multiple of 3st, 4s^2, 5t^2
Finding the LCM of expressionsLCM is known as the lowest common multiple. This is the smallest number that is a multiple of both of two numbers is called the least common multiple.
Given the terms 3st, 4s^2, 5t^2
Find the factors
3st = 3 * s * t
4s² = 4 * s * s
5t² = 5 * t * t
The LCM is calculated as thus:
LCM = (3*4*5) * s²t²
LCM = 60 s²t²
Hence the LCM of the terms 3st, 4s^2, 5t^2 is 60 s²t²
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A parallelogram is drawn on a centimetre grid.
Find the area of the parallelogram
Answer: 15
Step-by-step explanation:
Base x Height = Area
What is the LCM of 9 and 27?
Answer: 27
Step-by-step explanation: in order to find out the LCM, you have to list out the multiples of 9 ( 9: 9, 18, 27, 36, etc.) and 27 ( 27: 27, 54, etc). Then you find the least common multiple which in this case is 27.
Jimmy is an accountant who also works part-time as a museum tour guide. Information from his tax worksheet is wages from accounting job, $75,937.84; wages from museum job, $14,937.92; interest, $839.40; and dividends, $123.45. What is Jimmy’s total income?
Jimmy’s total income is $91838.61
How to determine Jimmy's income?
You should understand that total income' refers to the sum of certain incomes (in cash and, in some circumstances, in kind) of the statistical unit during a specified reference period
The given parameters that will help us to determine the income are
wages from accounting job, $75,937.84;interest, $839.40wages from museum job, $14,937.92; dividends, $123.45.Therefore Jimmy's total income is the sum of all the incomes
$(75,937.84 + 839.40 + 14,937.92 + 123.45)
Total income = $91838.61
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I need help with my homework please help
The formulas for the rigid transformations of the figures are listed below:
Case 1: (x, y) → (x - 10, y + 9)
Case 2: (x, y) → (- y, x)
Case 3: (x, y) → (- x, y)
Case 4: (x, y) → (- y, x)
Case 5: (x, y) → (x, - y)
Case 6: (x, y) → (x, y + 10)
How to determine the transformation rule for each case
In this question we find six cases of rigid transformations applied on figures. The most common rigid transformations are listed below:
Translation: (x, y) → (x + a, y + b), where a, b are real numbers.Reflection about x-axis: (x, y) → (x, - y)Reflection about y-axis: (x, y) → (- x, y) Rotation: (x, y) → (x · cos θ - y · sin θ, x · sin θ + y · cos θ), where θ is the angle of rotation.Then, by direct inspection, we derive the following rigid transformations:
Case 1 (Translation)
(x, y) → (x - 10, y + 9)
Case 2 (Rotation)
(x, y) → (x · cos (- 270°) - y · sin (- 270°), x · sin (- 270°) + y · cos (- 270°))
(x, y) → (- y, x)
Case 3 (Reflection about y-axis)
(x, y) → (- x, y)
Case 4 (Rotation)
(x, y) → (x · cos 90° - y · sin 90°, x · sin 90° + y · cos 90°)
(x, y) → (- y, x)
Case 5 (Reflection about x-axis)
(x, y) → (x, - y)
Case 6 (Translation)
(x, y) → (x, y + 10)
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what are the coordinates of the top right corner of the screen?
The coordinates of the top right corner of the screen (1280, 720).
The coordinates usually consist of two or three values, depending on whether you're working with a two-dimensional or three-dimensional system.
To answer your question, we need to know which coordinate system we're using. In this case, we're assuming that we're dealing with a two-dimensional system, which means that we only need to specify two coordinates: the x-coordinate and the y-coordinate.
The top right corner of the screen is located at a specific position that can be determined by measuring the distance from the origin (usually the bottom left corner) to that point. If we assume that the origin is located at (0, 0), then we need to find the x and y values that correspond to the top right corner.
The x-coordinate of the top right corner depends on the width of the screen, which can vary depending on the device you're using. For example, if the width of the screen is 1280 pixels, then the x-coordinate of the top right corner would be 1280.
The y-coordinate of the top right corner also depends on the height of the screen, which again can vary depending on the device. If the height of the screen is 720 pixels, then the y-coordinate of the top right corner would be 720.
Therefore, the resulting coordinates would be (1280, 720).
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20 In a village the number of houses and the number of flats are in the ratio 7:4 the number of flats and the number of bungalows are in the ratio 8: There are 50 bungalows in the village. How many houses are there in the village? 77
The number of houses is there in the village will be 25.
What is the solution to the equation?An answer to a formula is any variable value that fulfills the equal outcomes, that is, it tends to make the Left Hand Side (LHS) and Right Hand Side (RHS) of the formula equal. To solve an equation, you must locate the feasible solution) to that formula.
In a village, the number of houses and the number of flats is in the ratio 7:4 the number of flats and the number of bungalows is in the ratio 8: There are 50 bungalows in the village.
Let 'x', 'y', and 'z' be the number of houses, flats, and bungalows, respectively. Then the equations are given as,
x / y = 7 / 4
y = (4/7)x ...1
y / z = 8 / 6
z = 6y / 8
z = 3x / 7 ...2
x + y + z = 50 ...3
From equations 1, 2, and 3, then we have
x + (4/7)x + (3/7)x = 50
7x + 4x + 3x = 350
14x = 350
x = 25
The number of houses is there in the village will be 25.
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Many sheet materials used in construction, such as plywood or drywall, measure 8 feet by 4 feet. What are these dimensions in inches?
Two friends shop for fresh fruit. Elena buys a watermelon for $8.55 and 5 pounds of cherries. Taniy buys a pineapple for $4.45 and 4 pounds of cherries. Use the variable p to represent the price, in dollars, per pound of cherries. Write and simplify an expression to represent how much more Elena spent.
The expression to represent how much more Elena spent is 4.1 + p.
How to find the expression to represent a situation?Two friends shop for fresh fruit. Elena buys a watermelon for $8.55 and 5 pounds of cherries. Taniya buys a pineapple for $4.45 and 4 pounds of cherries.
Therefore, the expression to represent how much more Elena spent can be represented as follows:
hence,
p = price in dollars, per pound of cherries.
Hence,
amount Elena spent more = 8.55 + 5p - (4.45 + 4p)
amount Elena spent more = 8.55 + 5p - 4.45 - 4p
amount Elena spent more = 8.55 - 4.45 + 5p - 4p
Therefore,
amount Elena spent more = 4.1 + p
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Forty-four percent of the members of the Science Club wear blue shirts. Which of the following is a binomial experiment?
Selecting eight members randomly and recording whether each member is wearing a blue shirt
Selecting eight members randomly and recording the number in the group wearing a blue shirt
Selecting members randomly until one without a blue shirt is chosen
Selecting members randomly until one with a blue shirt is chosen
Option A is correct.
Selecting eight members randomly and recording whether each member is wearing a blue shirt.
A binomial experiment is defined as a statistical experiment which consists of n repeated trials. Only two possible outcomes are possible in each trial- either its a success or a failure. Here the probability of success remains the same on every trial.
Here, in 8 members the person wearing blue will be a success others will be a failure outcome.
Answer:
a
Step-by-step explanation:
Walter deposits $203.77 each month into an annuity account for his child's college fund in order to accumulate a future value of $60,000 in 18 years. How much of the $60,000 will Walter ultimately deposit in the account, and how much is interest earned? Round your answers to the nearest cent, if necessary.
Based on the amount deposited into the account every month, the amount that Andrew will deposit in the account is $72,548.64. The interest earned will be $17,451.36.
What is interest?Interest is the price you pay to borrow money or the cost you charge to lend money. Interest is most often reflected as an annual percentage of the amount of a loan. This percentage is known as the interest rate on the loan.
here, we have,
What amount does Andrew deposit?
This can be found by the formula:
= Amount deposited every month x Number of years x Number of months in a year
= 503.81 x 12 x 12
= $72,548.64
What amount of interest is earned?
This can be found as:
= Future value of amount - Amount deposited
= 90,000 - 72,548.64
= $17,451.36
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A family wants to rent a car to go on vacation. Company A charges $30.50 and 8 cents permile. Company B charges $ 65.50 and 13 cents permile . How much more does Company A charge for x miles than ?
The amount of money Company A charge more for x miles, 35 - 0.05x dollars
What is subtraction?In mathematics, subtraction is an operation which means taking away a few portions of the group or few things from a whole part.
For example, if we take 4 pencils out of 10 then remaining pencils are 6
so this process is called subtraction.
Let's call the number of miles the family wants to travel "x".
The cost for Company A is $30.50 plus 8 cents per mile, so the total cost for Company A is,
30.50 + 0.08x.
The cost for Company B is $65.50 plus 13 cents per mile, so the total cost for Company B is,
65.50 + 0.13x.
To find out how much more Company A charges, we can subtract the cost for Company B from the cost for Company A:
= (30.50 + 0.08x) - (65.50 + 0.13x)
= 35 - 0.05x
So, Company A charges 35 - 0.05x dollars more than Company B for x miles.
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pls help asap!!!
The table shows the proportional relationship between the number of tickets required per game at a carnival.
Games 4 7 10
Tickets 24 42 60
Determine the constant of proportionality.
3
6
16
30
What is the value of 2.7 liters in ounces
One liter is equal to 33.814 ounces, so 2.7 liters is equal to 90.772 ounces. This can be calculated using the following formula, which is multiplying 2.7 by 33.814: 2.7 x 33.814 = 90.772.
To calculate the number of ounces in a given amount of liters, this formula can be used. This can be calculated using the following formula, which is multiplying 2.7 by 33.814: 2.7 x 33.814 = 90.772.This is useful for quickly and accurately converting between liters and ounces, which can come in handy when measuring liquids or other substances. For example, if a recipe calls for 2.7 liters of a certain ingredient, you can easily convert that to ounces using the formula.
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Select the equation that should be used to solve for x. Responses 8x−14+2x+10=90 8 x minus 14 plus 2 x plus 10 is equal to 90 8x−14+2x+10=180 8 x minus 14 plus 2 x plus 10 is equal to 180 8x−14=2x+10 8 x minus 14 is equal to 2 x plus 10 8x−14+2x+10=360 8 x minus 14 plus 2 x plus 10 is equal to 360
The value of x is 9.4 in the equation 8x−14+2x+10=90.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given equation is 8x−14+2x+10=90
Eight times of x minus forteen plus two times of x plus ten equal to ninety.
In the given equation x is the variable
Plus and minus are the operators.
Add the like terms
Ten times of x minus four equal to ninety
10x-4=90
Add 4 on both sides to cancel four on the left hand side.
10x-4+4=90+4
10x=94
Divide both sides by 10
x=94/10
Divide numerator and denominator by 10.
x=9.4
Hence, the value of x is 9.4 in the equation 8x−14+2x+10=90.
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The complete question
Solve the equation 8x−14+2x+10=90
what a unit of measurement equal to one thousand meters?
A unit of measurement equal to one thousand meters is called a kilometer.
The prefix "kilo" means one thousand, so a kilometer is a unit of length in the metric system that is equal to 1000 meters. Kilometers are commonly used to measure longer distances, such as the distance between cities or countries, or the length of a marathon race. In contrast, smaller distances may be measured in meters, centimeters, or millimeters, which are all smaller units of length in the metric system.
a metric measurement of length that is equal to 1,760 yards or 5,280 feet. A thousandth of a liter is the same as a metric unit of capacity. a length measurement in meters that is one-thousandth of a meter. a time interval that is frequently used and equates to 60 seconds and 1/60 of an hour.
The complete question is:-
What word goes with a unit of measurement equal to one thousand meters?
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Write an equation in slope-intercept form of the line with slope −1 that contains the point (5,−2).
A. y = x + 5
B. y = −x + 5
C. y = −x + 3
D. y = −x − 2
Answer:
Below
Step-by-step explanation:
y = mx = b is slope intercept form
m= slope b = y-axis intercept ..... sub in the values given
-2 = (-1)(5) + b shows b = 4
y = -x + 3
The side lengths of a triangle are 6, 8, and 10. Is this a right triangle?
OA. Yes, because 62 +82 > 10².
B. No, because 62 +82 # 10².
C. Yes, because 62 +82 = 10².
OD. No, because 6 + 8 + 10.
SUBMIT
Is this a right triangle: C. Yes, because 6² + 8² = 10².
What is the triangle inequality theorem?In Euclidean geometry, the Triangle Inequality Theorem states that the sum of any two sides of a triangle must be greater than or equal (≥) to the third side of the triangle.
Mathematically, the Triangle Inequality Theorem is represented by this mathematical expression:
b - c < n < b + c
Where:
n, b, and c represent the side lengths of this triangle.
By applying Pythagorean theorem, the possible side lengths of the triangle's third side is given by:
10² = 6² + 8²
100 = 36 + 64
100 = 100 (True).
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5,694 x 5 PLEASE HELP MEEEE!!!!!!!
Answer:
5,694 x 5 = 28,470Step-by-step explanation:
You're welcome
The budget for a project on voting trends includes $3200 for hiring undergraduate students, graduate students, and faculty members to conduct interviews on the day before an election. Each undergraduate student will conduct 30 interviews for $100. Each graduate student will conduct 32 interviews for $150. Each faculty member will conduct 33 interviews for $200. No more than 20 interviewers can be hired.
(a) How many of each type of interviewer should be hired in order to maximize the number of interviews?
(b) What is the maximum number of interviews?
To increase the number of interviews, it should be recommended that 0 undergraduate students, 16 graduate students, and 4 faculty members be hired. There can be a maximum of 644 interviews by statistics
Simplex Method:In 1947, George Dantzig invented an algorithm that allows us to take a system of equations and find its maximum or minimum values that make the equations most efficient. This method is used in linear programming to determine optimization.
If n = the number of interviews, then let x = the number of undergraduate students hired, y = the number of graduate students employed, z = the number of faculty members hired.
Maximization of n = 30x + 32y + 33z
The limitations are: x + y + z 20; 100x + 150y + 200z 3200; and 0;
The answer is 644 because x = 0, y = 16, z = 4.
To increase the number of interviews, it should be recommended that 0 undergraduate students, 16 graduate students, and 4 faculty members be hired. There can be a maximum of 644 interviews by statistics given.
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Graph the linear system and tell how many solutions it has. If there is exactly one solution, estimate the solution and check it algebraically.
Answer:
There is exactly one solution: (3, 1)
Step-by-step explanation:
To graph these equations, you need to change them to slope intercept form:
x + y = 4 in slope intercept form is y = -x + 4 (subtract x frok both sides).
x - y = 2 in slope intercept form is y = x - 2 (subtract x from both sides then divide both sides by -1)*.
Now, all you have to do is graph both and find the point they cross at (the solution) which is (3, 1).
* = y can never be negative, which is why you divide by a -1 after subtracting x.
Hope this helps!
factor help pleaseeeee
Answer:
(6x+8y)(6x-8y)
Step-by-step explanation:
See attached worksheet.
The angle of depression from the top of Pike’s Peak, at an altitude of 14,000 feet, to the city of Colorado Springs is 8o. The horizontal distance from the city to the peak is 58,000 feet. Find the altitude of Colorado Springs.
Answer:
[tex]\mbox{\large \boxed{\textsf{5, 849 \;feet}}}[/tex]
Step-by-step explanation:
See figure for information pertaining to this explanation
The figure is self explanatory
The triangle ABC forms a right triangle with the vertical leg of length 14000-h and horizontal length of 58000
The angle opposite side 14000 - h = 8°
By the tangent formula
[tex]\tan 8^\circ = \dfrac{AB}{AC} = \dfrac{14000-h}{58000}[/tex]
Switching sides,
[tex]\dfrac{14000-h}{58000} = \tan 8^\circ[/tex]
[tex]14,000 - h = 58,000 \times \tan 8^\circ\\\\14,000 - h = 8,151.36 \approx 8,151[/tex]
h = 14,000 - 8,151 = 5,849 feet
So the altitude of Colorado Springs is roughly 5,849 feet
This is close to the published value of 6,035 feet. The differences are due to estimate errors in horizontal distance, peak height and angle of depression
If the vertex of the graph of y = −1(x − 2)2 + 3 is (a,b) what is the value of b?
Answer:
the value of b is 3.
Step-by-step explanation:
The vertex of the graph of a parabola in the form y = a(x - h)^2 + k is given by (h, k), where h is the x-coordinate of the vertex and k is the y-coordinate of the vertex.
So in this case, the vertex of the graph of y = -1(x - 2)^2 + 3 is (2, 3), and the value of b is 3.
Answer:
b=3
Step-by-step explanation:
[tex]y=a(x-h)^2+k\\y=-1(x-2)^2+3[/tex]
If we compare the vertex-form equation of a parabola to our given function, we can see the vertex is [tex](2,3)[/tex], which means that b=3.