No, 16x2 40x 25 is not a perfect square trinomial.
What is perfect squares?Perfect squares are numbers that are the result of multiplying a number by itself. Examples of perfect squares include 4, 9, 16, 25, 36, and 49. Perfect squares are also known as "square numbers" or "whole numbers." Perfect squares are not just limited to whole numbers; some decimals and fractions can also be perfect squares.
A perfect square trinomial is an expression of the form a2 + 2ab + b2, where a and b are constants. 16x2 40x 25 does not fit this form, and is therefore not a perfect square trinomial.
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What should be the value of a if the value of 2x² X − a 5 when x 0?
The value of a=0 in a given expression.
what are expression?A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation. Let's examine the writing of phrases. The other number is x, and a number is 6 greater than half of it. In a mathematical expression, this proposition is denoted by the equation x/2 + 6.
Define algebraic expression.An algebraic expression in mathematics is an expression created using variables, constant algebraic numbers, and algebraic operations. A good example of an algebraic expression is 3x2 2xy + c.
If the value of 2x² - a*5 when x = 0 is 0, then we can substitute x = 0 into the equation and solve for a.
So,
[tex]2(0)² - a5 = 0[/tex]
[tex]-a5 = 0[/tex]
[tex]a = 0[/tex]
Therefore, the value of a should be 0.
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Nancy Stone has a small company and has negotiated a special rate for rental cars when she and other employees take business trips. The maximum charge is $45. 00 per day plus $0. 40 per mile. Discounts apply when renting for longer periods of time or during off-peak seasons
A linear inequality that models the total cost of the daily rental c(m) as a function of the total miles driven, m is c(m) ≤ 45 + 0.4 m.
What is linear inequality?
In mathematics, an inequality involving a linear function is referred to as a linear inequality. One of the inequality symbols is found in a linear inequality. In graph form, it displays the non-equal data.
Given:
Nancy Stone has a small company and has negotiated a special rate for rental cars when she and other employees take business trips.
The maximum charge is $45. 00 per day plus $0. 40 per mile.
A linear inequality involves a linear function. It contains one of the symbols of inequality. It exactly looks like a linear equation, with the inequality sign replacing the equality sign.
According to the statement Nancy has negotiated a special rate and the maximum charge is $45.00 per day with the addition of $ 0.40 per mile.
So,
a linear inequality that models the total cost of the daily rental as a function of the total miles driven, m is:
c(m) ≤ 45 + 0.4m
Hence, a linear inequality that models the total cost of the daily rental c(m) as a function of the total miles driven, m is c(m) ≤ 45 + 0.4 m.
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1. Indicate whether the value of each expression is positive or negative.
-3(-6)
(-3)(6)
-(-3)(6)
2(3)(-6)
-2(-3)(-6)
2(-3)(-6)
So we know that if you multiply a negative number by a positive number, you get a negative number. We also know that if you multiply a negative number by a negative number you get a positive number! (Two negatives cancel each other out!)
So going down the list:
(-3)(-6) = positive (two negatives!)
(-3)(6) = negative (one negative, one positive!)
-(-3)(6) = positive (this is because you multiple left to right. because the negative is technically a -1 multiplying the -3, your -3 turns into a +3!)
(2)(3)(-6) = negative
(-2)(-3)(-6) = negative (remember, you multiply in the order of left to right! So multiplying the -2 and -3 gives you a positive. However, the -6 makes that positive number negative!)
(2)(-3)(-6) = positive
I hope this helps!
In a statistics class, a teacher had the students complete an activity in which they grabbed as many bite-sized pretzels as they could with their dominant hand, without crushing them. The teacher then measured their handspan in centimeters. The scatterplot displays the data the teacher collected along with the least-squares regression line. One student with a handspan of 23 cm grabbed 38 pretzels. This point is circled on the graph.
What effect will the circled point have on the y-intercept?
The y-intercept will not change with the addition of this point.
The y-intercept will decrease because the point pulls the least-squares regression line toward it.
The y-intercept will increase because the point pulls the least-squares regression line toward it.
The y-intercept will increase because this point represents an extremely high number of pretzels grabbed with the dominant hand.
answer is B
We can see here that the effect that the circled point will have on the y-intercept is: B. The y-intercept will decrease because the point pulls the least-squares regression line toward it.
What is an intercept?In statistics, an intercept is the value of the dependent variable when the independent variable(s) is equal to zero. It is often represented by the symbol "b" in a linear equation.
For example, a simple linear equation has the form y = mx + b, where "y" is the dependent variable, "x" is the independent variable, "m" is the slope of the line, and "b" is the y-intercept. The y-intercept is the point where the line crosses the y-axis.
We see here that the answer above is the correct answer.
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HELP PLEASE! 100PTS!
You're playing a game of pool and it's your turn, but you have no direct shots. To make any shot, you will need to bank the cue ball (the white ball) off the side of the table before it hits your ball.
That means that you hit the cue ball so that it bounces off the side and then hits your colored ball, moving it in the direction of a pocket (hole). The angle that the ball hits the bumper is equal to the angle that it bounces off the bumper.
The cue ball is 18 inches from the top bumper (side of pool table) and 50 inches from the right bumper. The dimensions of the pool table are 96 inches in the horizontal direction by 46 inches in the vertical direction
By Solving this proportion will give you the value of the angle you need to aim your shot.
What is angle of elevation ?
angle elevation can be defined as the angle formed between line of sight and horizontal line.
Draw a diagram of the pool table, labeling the dimensions of the table and the position of the cue ball.
Since the cue ball is 18 inches from the top bumper and 50 inches from the right bumper, you can draw a right triangle with these side lengths.
The dimensions of the pool table can also be used to draw a right triangle, with the horizontal dimension (96 inches) as the base and the vertical dimension (46 inches) as the height.
These two triangles are similar because they are both right triangles and they share a right angle. Therefore, the ratios of their sides are equal.
You can use the ratios of the sides of these triangles to determine the angle at which you should aim your shot. To do this, you can set up a proportion using the corresponding sides of the two triangles. For example, you could use the ratio of the base to the height of the small triangle (18 inches to 50 inches) and set it equal to the ratio of the base to the height of the large triangle (96 inches to 46 inches).
Hence, by Solving this proportion will give you the value of the angle you need to aim your shot.
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A company manufactures industrial laminates (thin nylon-based sheets) of thickness 0.016 in., with a tolerance of 0.004 in.
0.016 in.
(a) Find an inequality involving absolute values that describes the range of possible thickness for the laminate. (Use h for
the thickness.)
(b) Solve the inequality that you found in part (a). (Enter your answer using interval notation.)
An inequality involving absolute values that describes the range of possible thickness for the laminate.
|h - 0.016| <= 0.004The range of possible thickness for the laminate is given by the interval (0.012, 0.02).What is inequality?(a) The range of possible thickness for the laminate is given by the tolerance of 0.004 in., so we can write an inequality involving absolute values as:
|h - 0.016| <= 0.004
(b) To solve the inequality, we need to consider two cases:
Case 1: h - 0.016 <= 0.004
h <= 0.02
Case 2: h - 0.016 >= -0.004
h >= 0.012
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Can anyone help please for e and f
Therefore ,this maxima of the preceding problem is 2 ≥ 0 , which leads to x²+90=> f(x) ≥ 9 , indicating that there is no maxima.
Describe maxima.The maxima & minima of the a function are its maximum and minimum points within or across a given range, and these points are collectively referred to as extrema in mathematical analysis. The highest value of the variable. The maximum amount, level, etc. The variable can only take a maximum of 2. Maximum refers to a peak (plural maxima). The lowest position is referred to as minimal (multiple minimum). Extremum is a phrase for the largest or least of anything (multi-extremum). Peaks (or minima) are used if there are better (or worse) sites available elsewhere but they are not nearby.
Here,
Given :
=> f(x) = x²+9 20
=> x²+9>0 and
=> f(x) 9,
maxima are not possible.
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What is the slope of the line passing through the points − 3 4 and 2 − 1?
Therefore, the slope of the line passing through the points (-3,4) and (2,-1) is -1
What is a Straight Line?
A line is an object in geometry that is indefinitely long and has neither breadth nor depth nor curvature. Since lines can exist in two, three, or higher-dimensional environments, they are one-dimensional things. The term "line" may also be used to describe a line segment in daily life that contains two locations that serve as its endpoints.
Define Slope.A line's steepness may be determined by looking at its slope. The slope is computed mathematically as "rise over run" (change in y divided by change in x). Also, The slope of a line is known as "m", is the ratio of the change in the y-coordinate to the change in the x-coordinate of two points on the line.
To find the slope of a line passing through the points (-3,4) and (2,-1), we can use the formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are the coordinates of the two points.
So, using the given points:
m = (-1 - 4) / (2 - (-3))
m = -5 / 5
m = -1
Therefore, the slope of the line passing through the points (-3,4) and (2,-1) is -1
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PLEASE HELP ME ASAP!!!!!!!
In a party, the guest's attendance depends on their vehicle status. If they have four wheelers then the attendance of guests is 2500 and if they have two wheelers then the attendance of guests is 1500. If on the next party, 70% of families will have four wheelers and 30% of families will have two wheelers. What is the expected attendance of guests?
When 70% of families will have four-wheelers and 30% of families will have two-wheelers, the projected guest attendance is 3000+1200 = 4200.
what is percentage ?In mathematics, a percentage is a number or ratio that is expressed as a fraction of 100. Occasionally, the acronyms "pct.," "pct," and "pc" are also used. But it is commonly indicated by the percent sign, "%." The % amount has no dimensions. Percentages are essentially fractions when the denominator is 100. Use the percent sign (%) to indicate that a number is a percentage by placing it next to it. For instance, you score a 75% if you properly answer 75 out of 100 questions on a test (75/100). Divide the money by the total and multiply the result by 100 to calculate percentages. The formula for calculating the percentage is (value/total) x 100%.
given
2500 guests are present when four-wheelers are available.
two wheelers, the number of guests is 1500,
making the total 2500 + 1500 = 4000.
70 percent of families will own four-wheelers, or 3000/4000/100.
30% of families will own two-wheelers, which equals 4000/100 * 30%, or 1200.
When 70% of families will have four-wheelers and 30% of families will have two-wheelers, the projected guest attendance is 3000+1200 = 4200.
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solve the following equations for values of theta between 0 degrees and 360 degrees. 1. 2tan^2 theta - 7 sec theta + 8 = 0
The angles associated to the trigonometric equation 2 · tan² θ - 7 · sec θ + 8 = 0 are θ₁₁ ≈ 131.810°, θ₁₂ ≈ 228.190°, θ₂₁ ≈ 120° and θ₂₂ ≈ 240°.
How to solve a trigonometric equation
In this question we find a trigonometric equation, that is, an equation involving trigonometric functions, that must be solved for the interval between angles of 0° and 360°. This can be done by algebra properties and trigonometric formulas.
First, write the complete expression:
2 · tan² θ - 7 · sec θ + 8 = 0
Second, use trigonometric formulas and algebra properties to reduce the number of trigonometric functions within the equation:
2 · sin² θ / cos² θ - 7 / cos θ + 8 = 0
2 · sin² θ - 7 · cos θ + 8 · cos² θ = 0
2 - 2 · cos² θ - 7 · cos θ + 8 · cos² θ = 0
6 · cos² θ - 7 · cos θ + 2 = 0
Third, use algebraic subtitution and quadratic formula to determine the roots of the quadratic-like equation:
6 · u² - 7 · u + 2 = 0
u = - 7 / (2 · 6) ± [1 / (2 · 6)] · √[(- 7)² - 4 · 6 · 2]
u = - 7 / 12 ± (1 / 12) · 1
u = - 7 / 12 ± 1 / 12
There are two possibilities:
u₁ = - 2 / 3, u₂ = - 1 / 2
Fourth, find the angles associated to roots by inverse trigonometric functions:
u₁ = - 2 / 3
θ₁₁ ≈ 131.810°, θ₁₂ ≈ 228.190°
u₂ = - 1 / 2
θ₂₁ ≈ 120°, θ₂₂ ≈ 240°
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Is 45/20 equal to 225%
Answer:
Yes, it would be 225%.
Step-by-step explanation:
If 20/20= 100% you can evenly take out 200% because there is 45/20.
That leaves you with the 5/20.
5/20= 25%.
If we add those two percentages 200% + 25%= 225%.
I hope that made sense lol, have a great day!
The point (0, 5) lies on a circle with the center at (0, 0). What is the area of the circle?
Find the distance between point k and point L
The distance between two points in a plane is the length of the line segment connecting them. The formula d=((x2 - x1)2 + (y2 - y1)2) is frequently used to determine the separation between two points.
What do you call the distance between points?The length of the line segment bridging two locations in a plane is known as the distance between them. d=((x2 - x1)2 + (y2 - y1)2) is a common formula to calculate the distance between two points. This equation can be used to determine the separation between any two locations on an x-y plane or coordinate plane.
The length of the line segment is the distance between two points. Congruent segments are those that share the same length. By using a ruler to draw a line, we may determine how far apart two points are.
x,y = (-8,0) (-8,0)
or
x/y = -8/0
If there was an association between L and K, we would use x,y = 8,0.
Since the query reads "between point K and point L," the x,y relationship becomes "-8,0."
Therefore, the answer is -8,0.
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Mia is taller than Gage. If m represents Mia’s height and g represents Gages hight write an inequity that shows the relationship between their heights. Answer plsssssssss
The inequality that shows the relationship between thier heights is; g < r or r > g
What is inequality?Inequality is defined as the relation which makes a non-equal comparison between two given functions.
Now we have the following parameters that can be used in our computation:
Reese is taller than Gage.
Also, we have
Reeses's height = r
Gage's height = g
Since Reese is taller than Gage, then it means that
The value of r is greater than the value of g
So, we have the following inequality expression;
r > g
Also, we have;
g < r
Hence, the inequality is g < r
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Alice, Bob, Charles and Darwin are sharing an orange. Bob got twice as many slices as Charles,
Charles got 5 times less slices than Darwin, and Darwin got 8 slices more than Charles. Find the
number of slices in the orange given that Alice got only the peel.
(A) 10 (B) 12 (C) 14 (D) 15 (E) 16
Answer:
E
Step-by-step explanation:
Let
A = # of slices Alice got
B = # of slices Bob got
C = # of slices Charles got
D = # of slices Darwin got
First, write equations based on given information:
A = 0
B = 2C
5C = D
D = C + 8
5C = D -> D = 5C
Now that we have two equations for D, we can set them equal to each other:
5C = C + 8
4C = 8
C = 2
Now just plug in the rest:
A = 0
B = 2(2) = 4
C = 2
D = 2 + 8 = 10
Add all solutions together to get (E) 16 slices
What does r equal?
Answer: r = ________
Answer:
[tex]r=\sqrt{\frac{3V}{\pi h} }[/tex]
Step-by-step explanation:
[tex]V=\frac{1}{3} \pi r^2h[/tex]
Lets solve for [tex]r[/tex].
Multiply both sides of the equation by 3.
[tex]3V=\pi r^2h[/tex]
Divide both sides of the equation by [tex]\pi h[/tex].
[tex]\frac{3V}{\pi h} =r^2[/tex]
Take the square root of both sides.
[tex]\sqrt{\frac{3V}{\pi h} } =r[/tex]
Pls help me with solving systems of linear equations by elimination
Answer:
Step-by-step explanation:
A. 2x = -6
x = -3
3 + y = 5
y = 2
(-3, 2)
-9 - 2 = -11
-11 = -11
3 + 2 = 5
5 = 5
B. 4x + 2y = 1
6x + 4y = 1
-8x - 4y = -2
6x + 4y = 1
-2x = -1
x = 1/2
4(1/2) + 2y = 1
2 + 2y = 1
2y = -1
y = -1/2
-2(-1/2) + 3 = 4(1/2) + 2
1 + 3 = 2 + 2
4 = 4
6(1/2) + 4(-1/2) = 1
3 - 2 = 1
1 = 1
C.
-x + 32y = -25
4x + 8y = 100
-4x + 128y = -100
136y = 0
y = 0
-x = -25
x = 25
(25, 0)
32(0) - 25= -25
-25= -25
5(25) = 100 + 25 - 8(0)
125 = 125
D.
3x + 2y = 6
4x + 5y = -20
-12x - 8y = -24
12x + 15y = -60
7y = -84
y = -12
2(-12) + 3x = 6
-24 + 3x = 6
3x = 30
x = 10
(10, -12)
2(-12) + 3(10) = 6
-24 + 30 = 6
6 = 6
4(10) + 5(-12) + 20 = 0
40 - 60 + 20 = 0
-20 + 20 = 0
0 = 0
Refer to the equation a-6 equals b if a equals 45 what is the value of b?
Answer:
Step-by-step explanation: a=4, b=2.
Answer:
b = 39
Step-by-step explanation:
[tex]a-6=b[/tex]
if a = 45:
[tex]45-6=b\\39=b[/tex]
Hope this helps
(i) change 234mm into m
(ii) change 876m^2 into square cm
Answer: (i) 0.234m
(ii) 8760000cm^2
Step-by-step explanation:
234÷1000=0.2234m
876x10^4=8760000cm^
y=mx+b give the equation of the line in slope intercept form that runs through (-3,6) and (5,-2)
Answer:
y = -x +3
Step-by-step explanation:
You want the equation of the line through the points (-3, 6) and (5, -2) in slope-intercept form.
SlopeThe slope can be found using the formula ...
m = (y2 -y1)/(x2 -x1)
m = (-2 -6)/(5 -(-3)) = -8/8 = -1
InterceptThe y-intercept can be be found using the formula ...
b = y -mx
b = 6 -(-1)(-3) = 3
EquationThe equation in slope-intercept form is ...
y = mx +b
Using the found values, the equation is...
y = -x +3
<95141404393>
Y’all please help my mind isn’t working please
Answer:
Step-by-step explanation:
To find values of y we substitute values of x in the given expression so when x = 0
y = (0)^2 - 6(0) + 3
= 3.
x = 1, y = 1^2 - 6(1) + 3 = -2
x = 3, y = 3^2 - 6(2) + 3 = 0.
Use these values to draw the graph
(a) Read this from the graph
Coordinates of the minimum should be 3, -6)
(b) Equation of the line of symmetry is the vertical line through the minimum point ( x = 3).
(c) Read these from the graph.
(the points where the graph cut the x-axis).
(d) and e - read the values from your graph.
Match the solution to its expression.
Answer:
1/3 + 1/3 = (1+1)/3 = 2/3
1) 2/3
5/7 - 2/7 = (5-2)/7 = 3/7
2) 3/7
so all you have to do is add or sub the fractions together.
1/3 + 1/3 = 2/3
5/7 - 2/7 = 3/7
for the first box is 2/3
Second box is 3/7
GOODLUCK
A bus company uses a grid to locate bus stops. The bus station is at (3, 4). The point (7, 6) represents
the first bus stop. The location of the second bus stop is determined using the same relationships as
those between the coordinates of the bus station and the first bus stop.
City Bus Stops
North
Choose...
12
10-
City Blocks
6
8
4
2
N.
Bus Station
: increases by 2.
2
(7.6)
increases by 4, and the
(11,8)
4 6 8 10 12
City Blocks
Use the drop-down menus to describe the relationships between the coordinates of the first and second
bus stop.
The Choose...
East
Answer: The relationship between the x-coordinates of the first and second bus stop is that the x-coordinate of the second bus stop is 4 units greater than the x-coordinate of the first bus stop.
The relationship between the y-coordinates of the first and second bus stop is that the y-coordinate of the second bus stop is 2 units greater than the y-coordinate of the first bus stop.
Step-by-step explanation:
5. The prices of packages of golf balls are
recorded in the table.
Packages of Golf Balls
1
2
3
4
Cost
$15
$30
$45
$60
A. Write a rule to find the cost of
n packages of golf balls.
B. How much do 7 packages of golf
balls cost?
The rule to find the cost and the cost of 7 packages can be given as 15n and $105 respectively.
What is Proportionality?When two quantities have some dependence in their values they can be said proportional to each other.
It can be of two types such as direct and indirect.
The direct proportionality means the values of both the quantities are increasing or decreasing at the same time while the indirect proportionality implies value of one quantity is increasing while the other is decreasing.
The table for the given case can be written as follows,
Packages of Golf Balls Cost
1 $15
2 $30
3 $45
4 $60
The relation for proportionality can be obtained as,
15/1 = 30/2 = 45/3 = 60/4 = 15
(A) Suppose n be the number of packages.
Then, the cost is given as 15n.
(B) The cost of 7 packages is as below,
⇒ 15 × 7 = $105
Hence, the answers to both part can be given as 15n and $105 respectively.
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Fatuma recently hired a roofer to do some necessary work. On the final bill, Fatuma was charged a total of $1449. $315 was listed for parts and the rest for labor. If the hourly rate for labor was $63, how many hours of labor was needed to complete the job?
(A) First write an equation you can use to answer this question. Use x as your variable and express any percents in decimal form in the equation.
The equation is
(B) Solve your equation in part (A) to find the number of labor hours needed to do the job.
Answer: The number of labor hours was
(A) The equation is:
$63[tex]x[/tex] = $1449 - $315
(B) The labor hours needed to complete the job was 18 hours.
STEPS TO FIND TIME OF THE COMPLETE JOBS(A) To find the number of labor hours needed to complete the job, we can set up an equation using the information given in the problem.
We know that the total bill was $1449, and $315 of that was for parts. So the remaining amount, $1449 - $315 = $1134, was for labor.We also know that the hourly rate for labor was $63. To find the number of hours needed for labor, we can divide the amount for labor by the hourly rate:$63[tex]x[/tex] = $1449 - $315
[tex]x[/tex] = ($1134 / $63)
Solving this equation gives us the number of hours needed for labor, which is 18 hours. We can check this by multiplying 18 hours by the hourly rate, which should give us the same amount for labor:[tex]x[/tex] = ($1134 / $63)
= 18 hours
Double check for:18 hours × $63 = $1134
This confirms that 18 hours is the correct number of labor hours needed to complete the job.
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Are the following statements true or false? Justify your answers. Complete parts (a) through (c) below. (This is a reading assessment question. Be certain of your answer because you only get one attempt on this question.) (a) In statistics, results are always reported with 100 % certainty. Choose the correct answer below A. False. In statistics, results are always reported with 100 % certainty only when discrete variables are measured. Results cannot be reported with 100 % certainty when continuous variables are measured. B. True. Statistics is the science of collecting, organizing, summarizing, and analyzing information to draw conclusions or answer questions. Since it is a science, results are always reported with 100 % certainty. C. True. Statistics would not be useful if they were not presented with 100 % certainty . Statistics is a form of mathematics, which means that as long as correct procedures are used, all results must be correct. D. False. In statistics, results are not reported with 100% certainty. Because statistical studies draw on samples, and because there is variation within groups, results cannot be reported with 100 % certainty.
The correct option that tests the given claim on statistics is; D. False. In statistics, results are not reported with 100% certainty. Because statistical studies draw on samples, and because there is variation within groups, results cannot be reported with 100 % certainty.
How to interpret the conclusion of a statistics research?Statistical research is defined as the rigorous development of improved or new statistical methods grounded in probability and statistical theory.
Statistical data analysis is basically a procedure that is used to perform various statistical operations.
Now, from the question, the claim is that In statistics, results are always reported with 100 % certainty.
Now, this claim needs to be examined because there is no perfect human being and as such since statistics is drawn from a lot of samples and groups, there is guaranteed to be some form of variability in responses or results as the case may be.
Therefore, we can say that is option D.
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I just need help with number 9 in this picture if anyone could pls help!
A class is learning about proportions and ratios, so the teacher decides to use the data about students in the local high school. There are 500-600 students and 29 - 32% of the student body participates in athletics. Which of the following is the most reasonable estimate of the number of students who are considered athletes
Using the provided data, We should consider the mid-value for the number of students and take the average of percentage to find the estimate number, The answer is 168.
What is statistics?Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. It is used to make decisions, predictions and gain knowledge from data. It involves using statistical methods to collect, summarize, and draw conclusions from data. It is used in various fields such as business, economics, social science, engineering, and medicine. It helps to make sense of complex data and make informed decisions.
What do you mean by estimate?In statistics, an estimate is a value that is calculated from a sample of data in order to approximate a population parameter. The most common examples of estimates are sample mean, sample proportion, sample standard deviation, and sample variance. These estimates are used to infer information about the population from which the sample was drawn. For example, an estimate of the population mean is calculated by taking the average of a sample of data and using that value to infer the value of the population mean.
mid-value of 500-600 = 550
average % = 30.5%
Athletes number = 30.5% of 550
=168
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I need some help on the "round to the next period" part. What exactly is the answer then? Thank you!
The time period it will take a principal of $25000 to grow int $28500 at a rate of 4% is approximately 3 years
What is Compound InterestCompound interest is the interest that is calculated on the initial principal and also on the accumulated interest of previous periods. It is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on interest.
In the given question, our data is;
P = 25,000r = 4% = 0.04A = 28,500n = ?x = semi-annually = 2The formula is given as
A = P(1 + r/n)^nx
The given expression is
m(n) = 25000(1 + 0.04/ 2)^2n
m(n) = 28500
28500 = 25000(1 + 0.04 / 2)^2n
Solving for n,
n = 3.3
n ≈ 3
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A group of friends wants to go to the amusement park. They have no more than $90 to spend on parking and admission. Parking is $16.50, and tickets cost $10.50 per person, including tax. Use the drop-down menu below to write an inequality representing pp, the number of people who can go to the amusement park.
The inequality representing p, the number of people who can go to the amusement park, is given as follows:
10.5p + 16.5 ≤ 90.
How to build the inequality?The inequality for this problem is build considering the linear cost function, defined in slope-intercept format as follows:
C(p) = mp + b.
In which the parameters are given as follows:
m is the slope, representing the cost of the ticket per person.b is the intercept, representing the cost of parking.Parking is $16.50, and tickets cost $10.50 per person, hence the numeric values of the slope and the intercept are given as follows:
m = 10.50, b = 16.50.
Thus the cost function is given as follows:
C(p) = 10.5p + 16.5.
They have no more than $90 to spend on parking and admission, hence the inequality is defined as follows:
C(p) ≤ 90.
10.5p + 16.5 ≤ 90.
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