Using simple interest, it is found that:
John paid $12 in interest for the loan.The total amount that he paid the bank was of $887.Simple InterestSimple interest is used when there is a single compounding per time period.
The amount of money after t units of time in is modeled by:
[tex]A(t) = A(0)(1 + rt)[/tex]
In which:
A(0) is the initial amount.r is the interest rate, as a decimal.For this problem, the parameters are given as follows:
A(0) = 875, r = 0.0004273, t = 32.
Hence the amount paid is given by:
A(32) = 875 x (1 + 0.0004273 x 32) = $887.
The amount of interest is given by:
I = 887 - 875 = $12.
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Find the mode for the scores 3,760, 5,200, 8,750, 4,400, 5,250
Which answer choice shows that the set of irrational numbers is not closed under addition? π+(-π)=0
1/2+(-1/2)=0
π+π=2π
1/2+1/2=1
Answer:
(a) π + (-π) = 0
Step-by-step explanation:
You want a counterexample for the statement that irrationals are closed under addition.
Closed setA set is closed under addition if adding members of the set always results in a member of the set.
π + (-π) = 0This shows that adding members of the set can result in a rational number. This is the counterexample you're looking for.
(1/2) + (-1/2) = 0Irrelevant. 1/2 is rational, so is not a member of the set of irrationals.
π + π = 2πAn example of a sum that is an element of the set. This is not a counterexample.
(1/2) +(1/2) = 1Irrelevant. 1/2 is rational, so is not a member of the set of irrationals.
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Which of the following expressions would simplify to be the multiplicative identity?
023.32
023.23
021
0 20
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need help I don't know the answer
The sum of a number and seven is six less than four times the number. Write an algebraic equation and solve to find the number.
Answer:
13/3 or 4.333
Step-by-step explanation:
Let the number be x
the sum of x and 7 is 6 less than 4x, giving the equation: x+7+6 = 4x
Solve:
x+7+6 = 4x
x+13 = 4x
13 = 3x
x = 13/3
Lisa is cutting a 14-inch piece of paper into 0.4-inch strips. How many strips of paper will she have when she is finished?
5.6
35
30
28
Answer:
take 14/0.4the multiply by ten both the denominator and .numerator then simplify by two your final answer will be 35
What is the domain of the relation graphed below?
The domain of the relation shown in the graph is -4 <= x <= 4
How to determine the domain of the relation shown in the graph?The relation on the graph is an ellipse function.
The domain is the set of x values the function can take
From the graph, we have the following x values
This means that the domain of x in the graph is -4 <= x <= 4
Hence, the domain of the relation shown in the graph is -4 <= x <= 4
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NO LINKS! Please help me with this problem
Answer:
x=70, y=55
Step-by-step explanation:
Since the angle "y" and 2x-15 form a straight line, that means the sum of the angles, must be 180 degrees.
So using this we can derive the equation: [tex]y+2x-15=180[/tex]
The next thing you need to know is that the sum of interior angles of a triangle is 180 degrees, so if we add all the angles, we should get 180.
So using these we can derive the equation: [tex]x+2y=180[/tex]
So, in this case we simply have a systems of equations. We can solve this by solving for x in the second equation (sum of interior angles), and plug that into the first equation.
Original Equation:
[tex]x+2y = 180[/tex]
Subtract 2y from both sides
[tex]x = 180-2y[/tex]
Now let's plug this into the first equation
[tex]y+2x-15=180[/tex]
Plug in 180-2y as x
[tex]y+2(180-2y)-15=180[/tex]
Distribute the 2
[tex]y+360-4y-15=180[/tex]
Combine like terms
[tex]-3y + 345 = 180[/tex]
Subtract 345 from both sides
[tex]-3y = -165[/tex]
Divide both sides by -3
[tex]y=55[/tex]
So we can plug this into either equation to solve for x
[tex]x+2y=180[/tex]
Substitute in 55 as y
[tex]x+2(55)=180[/tex]
[tex]x+110=180[/tex]
Subtract 110 from both sides
[tex]x=70[/tex]
Answer:
x = 70°
y = 55°
Step-by-step explanation:
The angle sum theorem and the definition of a linear pair can be used to write two equations in the two unknowns. Those can be solved for the angle values.
Setupx + y + y = 180° . . . . . . angle sum theorem
y + (2x -15) = 180° . . . . definition of linear pair
SolutionWe can use the first equation to write an expression for x that can be substituted into the second equation:
x = 180 -2y
y +(2(180 -2y) -15) = 180 . . . . substitute for x
345 -3y = 180 . . . . . . . . . . . collect terms
115 -y = 60 . . . . . . . . . . . . .divide by 3
y = 55 . . . . . . . . . . . . . . add (y-60)
x = 180 -2(55) = 70
The values of the variables are ...
x = 70°
y = 55°
exterior angle = 125°
The two-way frequency table below shows the preferred communication method of employees at a company, based on years of employment with the company.
Text
Message Instant
Message Phone Call Email Total
0 to 7 years 36 49 8 21 114
8 or more years 12 22 19 43 96
Total 48 71 27 64 210
What percentage of employees with 8 or more years at the company reported that email is their preferred method of communication?
A.
48.84%
B.
20.48%
C.
67.19%
D.
44.79%
Using it's concept, the percentage of employees with 8 or more years at the company reported that email is their preferred method of communication is:
D. 44.79%.
What is a percentage?The percentage of an amount a over a total amount b is given by a multiplied by 100% and divided by b, that is:
P = a/b x 100%
In this problem, there are 96 employees with 8 or more years of experience, of which 43 prefer email, hence the percentage is:
P = 43/96 x 100% = 44.79%.
Hence option D is correct.
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Definition of economic costs Gilberto lives in San Diego and runs a business that sells pianos. In an average year, he receives $701,000 from selling pianos. Of this sales revenue, he must pay the manufacturer a wholesale cost of $420,000; he also pays wages and utility bills totaling $247,000. He owns his showroom; if he chooses to rent it out, he will receive $9,000 in rent per year. Assume that the value of this showroom does not depreciate over the year. Also, if Gilberto does not operate this piano business, he can work as a financial advisor, receive an annual salary of $32,000 with no additional monetary costs, and rent out his showroom at the $9,000 per year rate. No other costs are incurred in running this piano business.
The wholesale cost for the pianos that Tim pays the manufacturer, wages and utility bills that Tim pays are counted as explicit cost. On the other hand, the salary that Tim could earn if he worked as an accountant and the rental income that Tim could earn from renting his showroom fall under implicit cost.
Difference between Implicit Cost and Explicit Cost:
These two expenses, implicit cost and explicit cost, both represent company activity. The connection between cost and business is what distinguishes these two.
An explicit cost is one that the owner bears directly; an implicit cost is one that the owner bears indirectly without paying or utilizing its own resources. However, the organization or corporation takes into account both expenses while making management decisions.
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Solve the system of equations algebraically and create a graphical model.
[tex]3x + 2y = 8 \\ x + 2y = 4[/tex]
Answer: [tex]x=2, y=1[/tex]
Step-by-step explanation:
Subtracting the second equation from the first yields [tex]2x=4 \longrightarrow x=2[/tex].
This means that [tex]y=1[/tex].
So, the solution is [tex]x=2, y=1[/tex]
what is the length of the hypotenuse of a right triangle whose legs have lengths 12 cm and 16 cm?
f(x)=x3 −4x even odd or neither
Answer:
The function would be odd
The answer is neither.
Let's take an odd number and substitute.
f(3) = 3³ - 4(3)f(3) = 27 - 12f(3) = 15 (odd)Now, let's take an even number.
f(4) = 4³ - 4(4)f(4) = 64 - 16f(4) = 48 (even)Since both even and odd numbers are possible, it is neither.
Using your favorite statistics software package, you generate a scatter plot with a regression equation and correlation coefficient. The regression equation is reported as
y
=
−
10.51
x
+
15.05
and the
r
=
−
0.45
.
The proportion of the variation in y that can be explained by the variation in the values of x is 0.2025
How to determine the proportion of the variation in y that can be explained by the variation in the values of x?The complete question requires that we calculate the proportion of the variation in y that can be explained by the variation in the values of x
The given parameters in the question are:
The regression equation is reported as
y = − 10.51x + 15.05
r = − 0.45
Take the square of both sides in the equation r = − 0.45
r^2 = − 0.45^2
Evaluate the squares
r^2 = 0.2025
This represents the proportion of the variation in y that can be explained by the variation in the values of x
Hence, the proportion of the variation in y that can be explained by the variation in the values of x is 0.2025
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What’s the next 3 numbers 0 10 1011 1031 102113 10311213
The next three numbers here would be 0, 10, 1011, 1031, 102113, 10311213, 10411223, 1031221314, 1041222314.
What is a number sequence
The term number sequence is used to refer to the list of numbers that have the relationship of having a linked rule. The number that follows in the sequence has to be worked out from the previous numbers in that particular sequence. You have to follow the particular rule to be able to work out the number that has to follow in the sequence.
For example we have these numbers 1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34 etc. We would have to understand the pattern of numbers that are in the sequence. We can see that there is a difference of 3 between the number that succeeds the previous one in the sequence.
How to get the next values in the sequenceThe first value here is given to be 0
Next we have the 1 0 = 10
The next that we have is 1 0 and 1 1 written as 1011
Next is 1 zero and three one = 1031
We continue to follow the pattern till we arrive at 1041222314. This is where the sequence would then have to stop.
Hence we have to conclude that the next numbers are 10411223, 1031221314, 1041222314.
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What is the range of the function f(x) = 2x^2 + 2 over the interval of -2 ≤ x < 5?
Answer:
10 ≤ f(x) < 52
Step-by-step explanation:
the range is the values of f(x) given by the domain - 2 ≤ x < 5
substitute the end points of the interval into f(x)
f(- 2) = 2(- 2)² + 2 = 2(4) + 2 = 8 + 2 = 10
f(5) = 2(5)² + 2 = 2(25) + 2 = 50 + 2 = 52
then range is 10 ≤ f(x) < 52
if a rectangular piece of metal has 27.75 square inches what is the length and width?
The maximum area of a rectangular piece of metal with perimeter of 27.75 in² has length of 6.9375 in and width of 6.9375 in.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the length and y represent the width. hence:
Perimeter = 2(x + y)
27.75 = 2(x + y)
y = 13.875 - x
Area (A) = xy
A = x(13.875 - x)
A = 13.875x - x²
Maximum area is at A' = 0, hence:
A' = 13.875 - 2x
13.875 - 2x = 0
x = 6.9375
y = 6.9375
The maximum area of a rectangular piece of metal with perimeter of 27.75 in² has length of 6.9375 in and width of 6.9375 in.
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Which statement is not true for goodness-of-fit tests? Question content area bottom Part 1 A. Expected frequencies must be whole numbers. B. Observed frequencies must be whole numbers. C. The observed frequency is found from sample data values. D. The expected frequency is found assuming that the distribution is as claimed.
The statement that is not true for goodness-of-fit tests is: A. Expected frequencies must be whole numbers.
What is Goodness-of-fit tests?Goodness-of-fit tests can be defined as the test conducted to help find out whether the observe value work hand in hand with expected value or the observe value is different from the expected value.
The statement is not true because it is not must for expected frequencies to be whole number despite the fact that expected frequencies are whole numbers.
Therefore the statement that is not true for goodness-of-fit tests is: A. Expected frequencies must be whole numbers.
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An online store sells two types of speaker docks for smartphones. The higher-priced speaker dock sells for $170 and the lower-priced speaker dock sells for $80. Last week the store sold four times as many lower-priced speaker docks as higher-priced speaker docks. Combined sales totaled $4,410. How many lower-priced speaker docks did it sell?
The lower-priced speaker docks and higher-priced speaker docks is 9 and 36 respectively.
AlgebraCost of higher-priced speaker = $170Cost of lower-priced speaker = $80Number of lower-priced speaker = 4xNumber of higher-priced speaker = xHigher-priced speaker = 170 × x
= 170x
Lower-priced speaker = 80 × 4x
= 320x
Total sales = $4,410
170x + 320x = 4,410
490x = 4,410
divide both sides by 490
x = 4,410 / 490
x = 9
So,
Number of lower-priced speaker = 4x
= 4 × 9
= 36
Number of higher-priced speaker = x
= 9
Therefore, the lower-priced speaker docks and higher-priced speaker docks is 9 and 36 respectively.
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50% is what percent of 40%?
Answer:
125%Step-by-step explanation:
[tex] \frac{50}{100} \times 40[/tex][tex] = 125\%[/tex]Find the coordinates of the image point for S(−11, 2) across y = 1.
Answer:
(11,0)
Step-by-step explanation:
Given that a function, g, has a domain of -20 < x < -5 < g(x) <45 and that g(0)= -2 and g(-9)= 6, select the statement that could be true for g.
The given statement that's true about the function is g(-13) = 20 is true for g.
How to illustrate the function?From the information given, the function, g, has a domain of -20 < x < -5 < g(x) <45 and that g(0)= -2 and g(-9)= 6.
Let's analyze the options that are given in the scenario. g(7) = -1. It should be noted that 7 isn't in our domain. Therefore, this isn't possible.
g(-13) = 29
x = 13 is in our domain and 20 is also is in our range. Therefore, this is true for g.
g(0) = 2.
This isn't true because it is given that g(0) = 2
In conclusion, the given statement that's true about the function is g(-13) = 20 is true for g.
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Which expression represents seven less than the product of thirteen times a number, and two squared?
(13x + 22) · 7
7(13x · 22)
7 + 13x + 22
7 + 13x · 22
(13x · 22) − 7
Seven less than the product of thirteen times a number, and two squared is as follows;
(13x × 2²) - 7
How to represent an expression?The expression says seven less than the product of thirteen times a number, and two squared.
Let
the number = x
Hence, the product of thirteen times a number, and two squared is as follows:
13(x)(2²)
Therefore, seven less than the product of thirteen times a number, and two squared is as follows;
(13x × 2²) - 7
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Admission into an amusement park for 4 children
and 2 adults is $116.90. For 6 children and 3 adults,
the admission is $175.35. Assuming a different price
for children and adults, what is the price of the child's
ticket and the price of the adult ticket?
Answer:
A child ticket costs $16.50 and an adult ticket costs $25.45.
It is found that the child ticket costs $16.50 and an adult ticket costs $25.45.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Given that 4 children and 2 adults are $116.90. For 6 children and 3 adults, the admission is $175.35.
Assuming a different price for children and adults,
Let the children are x and the adult is y.
Therefore,
4x + 2y = 116.90
6x + 3y = 175.35
Hence, the child ticket costs $16.50 and an adult ticket costs $25.45.
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-|8-15| what is the answer
Answer:
-7
Step-by-step explanation:
8-15 = -7 but since it's an absolute value, it is 7 and then you add the negative sign in front since it is not in the absolute value.
What is the length of CG?
Answer:
19
Step-by-step explanation:
63÷21=3
21 was multiplied by 3 to get 63
CG by 3 should give 57
Find the inverse of function f. F(c) = 9x + 7
Answer:
(x-7)/9
Step-by-step explanation:
F(c) = 9x + 7
y = 9x + 7 Now switch the y and the x and solve for y
x = 9y + 7 Subtract 7 from both sides
x - 7 = 9y Divide both sides by 9
(x-7)/9
Pls answer these questions ASAP
From the given descriptions and dimensions, we have;
6. 2000 cm²
7. 81 m²
8. a. 138 m²
b. 538 m²
c. 62 cm²
9. $107.25
Which method can be used to calculate the surface areas and cost?6. Type of box = Open box with no lid
Side length of the box = 20 cm
Therefore;
Number of faces of the box, painted = 5
Area of a face of the box = 20² = 400
Area of the surface painted, A = 5 × 400 cm² = 2000 cm²7. Area of the plastic to cover one book, A, is found as follows;
A = 2 × 20 × 15 + 2 × 3 × 15 + 2 × 20 × 3
Which gives;
A = 600 + 90 + 120 = 810The area of plastic needed to cover 1000 books is therefore;
Total area = 1,000 × 810 cm² = 810,000 cm²
Conversion of cm² to m² gives;
1 m² = 10,000 cm²Therefore;
A = 810,000 cm² = 810,000 cm² × 1/10,000 m²/cm² = 81 m²
The area of plastic needed to cover 1000 books is A = 81 m²8. The surface areas are;
a. A = 2 × 3 × 6 + 5 × 6 + 7 × 6 + 2×3×(3+7)/2 = 138
The surface area is 138 m²b. A = 2 × 15 × 5 + 2×(10×5 + (6×8)/2) + 2×8×15 = 538
A = 150 + 148 + 240 = 538
The surface area is 538 m²c. From the congruent marks, we have;
A = 5 × 3 × 3 + 5×1×3 + 2×1×1 = 62
The surface area is 62 cm²9. From the congruent markings, we have;
A = 2 × (1.5 × 1.5 + (1.5 × 1.3)/2) + 5×2×1.5
A = 6.45 + 15 = 21.45
Surface area of a the canvas, A = 21.45 m²
Cost per unit area of the canvas, c = $5
Cost of the canvas for the tent, C, is therefore;
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The average speed of a car on a stretch of interstate is 70 miles per hour. Convert this rate to feet per second.
Answer:
102. 66 feet / SecondStep-by-step explanation:
To do conversion change miles into feet and hour into second.
One foot is 5280 feet
And an hour is 3600sec
70 miles / Hour
70 * 5280feet / 3600 second
369600 feet / 3600seconds
Then simplify
102. 66 feet / Second
Speed given
70mph1 mi=5280ft
1h=3600s
So convert
70×5280ft/3600s7×528ft/36s102.67ft/swhich graph represents -5x+3y is equal to or greater than 9
Answer:
First, transform the given equation into the slope intercept form.
-5x + 3y >= 9
3y >= 5x + 9
y >= 5/3x + 3
Then graph the line y = 5/3x + 3. Draw a solid line with y intercept 3 and slope of 5/3.
Finally, shade everything that is above the line.
Complete each statement describing the transformations you observed for the graph of y = 2x + k.
When the value of k increases, the graph of the function:
When the value of k decreases, the graph of the function:
.
Using translation concepts, it is found that:
When the value of k increases, the graph of the function shifts up.When the value of k decreases, the graph of the function shifts down.What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
The translation y -> y + k represents:
A shift up if k > 0.A shift down if k < 0.Hence:
When the value of k increases, the graph of the function shifts up.When the value of k decreases, the graph of the function shifts down.More can be learned about translation concepts at https://brainly.com/question/4521517
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