The leading team has scored 0.13 points per game for the season that the second place player.
What is PPG Statistics?
The average number of points a player scores in a game of a sport, over the course of a series of games, a season, or a career, is known as points per game, or PPG, and it is an important statistic. By dividing the total points by the number of games, it is calculated. Basketball and ice hockey are two sports that frequently use PPG statistics.First, consider the PPG of the current leader of the season from among the two basketball players.
The total number of points obtained by the current leader is equal to 2112.
The total number of games played by the current leader is equal to 77.
The points per game obtained by the current leader can be calculated as follows,
PPG = Total Points Obtained / Total Number of Games
[tex]\implies PPG=\frac{2112}{77}\\\implies PPG=27.42[/tex]
Now, consider the PPG of the second place player for the season.
The total number of points obtained by the second place player is equal to 2020.
The total number of games played by the second place player is equal to 74.
The points per game obtained by the second place player can be calculated as follows,
PPG = Total Points Obtained / Total Number of Games
[tex]\implies PPG=\frac{2020}{74}\\\implies PPG=27.29[/tex]
Subtracting the points per game of both players, we get
[tex]27.42-27.29=0.13[/tex]
Hence, the leading team has scored 0.13 points per game (PPG) for the season compared to the second place player.
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determine whether each of these pairs of sets are equal
a) (1, 3, 3, 3, 5, 5, 5, 5, 5}, {5, 3, 1} b) {{1}}, {1, {1}} c) Ø, {0}
These pairs of sets of numbers: (a) {1, 3, 3, 3, 5, 5, 5, 5, 5},{5, 3, 1} b) {{1}},{1,{1}} ) ∅,{∅} are equal, not equal and not equal respectively
How to determine the equality and not equality of set of numbers?The given pairs of sets of numbers are
a) (1, 3, 3, 3, 5, 5, 5, 5, 5}, {5, 3, 1} b) {{1}}, {1, {1}} c) Ø, {0}
To determine the reasons for the answers we have
(a) {1, 3, 3, 3, 5, 5, 5, 5, 5},{5, 3, 1}
All the number are distinct elements without any repetition is the same in both sets.
This implies that the sets are equal
b) {{1}},{1,{1}}
From the second set of numbers, the number of elements is not the same in both sets. The number of elements in the two sets are 1 and 2.
This therefore means that the pair of numbers are not equal
c) ∅,{∅}
In the third set of numbers, the number of elements is not the same in both sets.
The number of elements in the pairs are 0 and 1 in each of the sets . This implies that the pair of sets of numbers are not equal
In conclusion these pairs of sets of numbers: (a) {1, 3, 3, 3, 5, 5, 5, 5, 5},{5, 3, 1} b) {{1}},{1,{1}} ) ∅,{∅} are equal, not equal and not equal respectively
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Which equation represents the volume of the box
The equation represents the volume of the box as V = - 4s³ + 250s².
The correct option is option A
What is volume?The volume of any object is the capacity. How much it can hold.
What is the formula of volume?The formula of volume is a product of length, breadth and height.
Volume = L × B × H
Given:
The perimeter of the square base of side s plus height h = 250cm
as per the given question,
The perimeter of the square base of side s plus height h = 250cm
2( s + s ) + h = 250
2 (2s) + h = 250
4s + h = 250
We can express h in the terms of s as,
h= 250 - 4s
Volume = length X breadth X height
Volume = s × s × h
V = s² × h
V = s² × (250 - 4s)
V = 250s² - 4s³
The equation represents the volume of the box as V = - 4s³ + 250s².
The correct option is option A
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g(x) = -2(3x + 4)(x - 1)(x – 3)^2 be a polynomial function.
State the leading term, degree, and if the leading coefficient is positive or negative.
I mostly understand this, but don't know how the square affects things.
The polynomial is of degree 4, and the leading coefficient is -6.
How to find the degree of the polynomial?A polynomial of degree N with a leading coefficient A and the zeros {x₁, x₂, x₃, ..., xₙ} (notice that we have as many zeros as the degree of the polynomial) is written as:
p(x) = A*(x - x₁)*...*(x - xₙ)
Here we have the polynomial:
g(x) -2*(3x + 4)*(x - 1)*(x - 3)²
We can expand this as:
g(x) = -2*(3x + 4)*(x - 1)*(x - 3)*(x - 3)
Think that as we have "two zeros" at x = 3.
So we have 4 factors, then the degree of the polynomial is 4.
To find the leading coefficient we just need to look at the term that comes by multiplying all the terms with "x", we will get:
-2*(3x)*x*x*X
-6*x⁴
The leading coefficient is negative.
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The pattern below has been created by placing toothpicks together a) Find an expression for the total number of toothpicks in any set up b) How many toothpicks should there be in the 45th set up? Show your work.
For 45th set up 140 toothpicks are required.
What is Arithmetic Progression?A progression of numbers in which the difference between any two succeeding numbers is always a fixed amount is known as arithmetic progression (AP). It also goes by the name Arithmetic Sequence.
given:
For First Figure, 8 toothpicks are used
For Second Figure, 11 toothpicks are used
For Third Figure, 14 toothpicks are used
So, we get the series 8, 11, 14, ...
Now, for n= 45
Using Arithmetic Progression
[tex]a_{45} = a+ (45- 1) d[/tex]
= 8 + 44(3)
= 140
Hence, for 45th set up 140 toothpicks are required.
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10. You are ordering shirts for the math club at your school. Short-sleeved shirts cost $ 8 each. Long-sleeved shirts cost $ 20 each. You have a budget of $ 200 for the shirts. The equation 8 x+20 y=200 models the total cost, where x is the number of short-sleeved shirts and y is the number of long-sleeved shirts. Graph the equation. Interpret the intercepts.
x-intercept:_____
y-intercept:_____
The x - intercept is (25, 0) and the y - intercept is (0, 10).
What is intercepts?
The x-intercept and y-intercept are the points at which a line crosses the x- and y-axes, respectively.
Put y = 0 and work out x to find the x-intercept.
Set x = 0 and work out y to find the y-intercept.
Given: You are ordering shirts for the math club at your school.
Short-sleeved shirts cost $ 8 each.
Long-sleeved shirts cost $ 20 each. You have a budget of $ 200 for the shirts.
The equation 8 x+20 y=200 models the total cost,
where x is the number of short-sleeved shirts and y is the number of long-sleeved shirts.
To find the x - intercept plug y = 0 in the above equation.
⇒ 8x + 20(0) = 200
8x = 200
x = 25
So, the point becomes, (25, 0).
To find y - intercept plug x = 0 in the above equation.
⇒ 8(0) + 20y = 200
20y = 200
y = 10
So the point becomes, (0, 10).
Hence, the x - intercept is (25, 0) and the y - intercept is (0, 10).
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create three equations for quadratics in vertex form that have roots at 3 and 5 but have different maximum and/or minimum values.
The three quadratic equation with different maximum and/or minimum values are y = (x-4)² – 1, y = -(x-4)² + 1, and y = -3(x-4)² + 3.
Quadratic equation:
In math, quadratic equation is the algebraic equation of the second degree in x.
The general form of quadratic equation is
ax² + bx + c = 0,
where a and b are the coefficients, x is the variable, and c is the constant term. The first condition for an equation to be a quadratic equation is the coefficient of x² is a non-zero term(a ≠ 0).
Given,
Here we need to find the three equations for quadratics in vertex form that have roots at 3 and 5 but have different maximum and/or minimum values.
As per the definition of quadratic equation, here we have to write the quadratic equation, that have the roots of 3 and 5,
Here the problem was going to call for two equations but then we have realized that it could be as simply as multiplying the a and c values by -1. Therefore, the equation are,
=> y = (x-4)² – 1,
=> y = -(x-4)² + 1,
=> y = -3(x-4)² + 3.
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The Christmas lights on the tree and the lights on the porch blink at a consistent rate. The tree lights blink every 4 seconds which the porch lights blink every 6 seconds after how many second will they blink together
Answer:
The tree lights and the porch lights will blink together every 12 seconds.
Step-by-step explanation:
In order to determine when the two sets of lights will blink together, you must find the least common multiple (LCM) of the time periods for each set of lights. The LCM of 4 and 6 is 12, which means that the tree lights and the porch lights will both blink again after 12 seconds have passed. Therefore, they will blink together every 12 seconds.
In the diagram below of triangle PQR, S is the midpoint of PR and the midpoint of QR. If
ST= -22+9x and PQ+ 9x-8 what is the measure of PQ?
Answer PQ=_____
The measure of PQ in the triangle is 28 units.
How to find mid point of a triangle?The line segment connecting the midpoints of two sides of a triangle is parallel to the third side and is congruent to one half of the third side.
Therefore, using the mid point theorem, Let find the measure of PQ.
ST = -22 + 9x
PQ = 9x - 8
The measure of PQ can be found as follows:
ST = 1 / 2 (PQ)
-22 + 9x = 1 / 2 × (9x - 8)
-22 + 9x = 9x - 8 / 2
cross multiply
2(-22 + 9x) = 9x - 8
-44 + 18x = 9x - 8
-44 + 8 = 9x - 18x
- 36 = - 9x
x = - 36 / - 9
x = 4
Therefore,
PQ = 9(4) - 8 = 36 - 8 = 28 units
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A quadrilateral has 4 sides. One angle of a regular quadrilateral measures (6w+13) Determine the value of w. Round to the nearest whole number.
Ow=13
Ow=23
Ow=59
Ow=90
The value of w for the expression of angle 6w + 13 will be 13. The correct option is A.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that a quadrilateral has 4 sides. One angle of regular quadrilateral measures (6w+13).
The value of 'w' will be calculated as,
6w + 13 = 90
6w = 90 - 13
6w = 77
w = 12.83 or 13
Therefore, the value of w for the expression of angle 6w + 13 will be 13. The correct option is A.
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Old Faithful in Yellowstone National Park has a mean time between eruptions of 85 minutes. If the interval of time between eruptions is normally distributed with a standard deviation of 21.25 minutes. What is the probability that a randomly selected sample of 35 time intervals between eruptions has a mean longer than 95 minutes?
The probability that the randomly selected time interval is longer than 95 minutes while solving for the mean time of the eruptions is 0.3192.
How to solve for the probability of a ramdom sample?mean of x = 85 minutes
σ = 21.25 minutes
x ~ N(σ², μ)
p(x < 95)
1-p(x≤95)
1 - p(z≤0.47)
Using the z table here
1-0.6808 = 0.3192
Probability of x > 95 = 0.3192
b. n = 20
from central limit theorem
1 - p (z < 2.1045)
1-0.99826 = 0.0174
1 - p (z < 2.58)
1-0.9951
= 0.0049
. What we can observe from these results is that as the sample increase is increasing from 1, 20 to 30, the probability keeps decreasing.e. The probability is very small so one has to be doubtful if they are a really the population mean or if it has to be more than that.
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Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options. The radius of the circle is 3 units. The center of the circle lies on the x-axis. The center of the circle lies on the y-axis. The standard form of the equation is (x – 1)² + y² = 3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
By using the concept of circle, it can be concluded that-
Center = (1, 0) lies on x axis
The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
What is a circle?
Circle is a two dimensional round figure in which every point on the circle maintains a fixed distance from a point known as the center of the circle and the fixed distance is called radius of the circle
The equation of circle is
[tex]x^2 + y^2 - 2x - 8 = 0.[/tex]
[tex]x^2 - 2x + 1 - 1-8+y^2 =0\\(x -1)^2 + y^2 = 9\\(x - 1)^2 + y^2 = 3^2[/tex]
Center = (1, 0) lies on x axis
Radius of the given circle is 3 units
Radius of x² + y² = 9 is 3
So, the radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
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help meeeeeeeeeee pleaseee
The pressure of 28 inches of mercury occurs about 6 miles from the eye of hurricane.
What is barometric air pressure?In essence, atmospheric pressure is the force that the weight of the air above a particular point on the Earth's surface exerts at that location.
In other words, the weight of the air molecules as a whole determines the atmospheric pressure, which is produced by the air that surrounds the Earth.
Lower pressure is felt by air molecules at higher altitudes because there are fewer molecules pressing down on them from above, while higher pressure is felt by air molecules at lower altitudes because they are closer together and are under more pressure from molecules piled on top of them.
F(x) is the pressure in inches of mercury
It is given pressure 28 inches of mercury
Put F(x) equal to 28
F(x) = 0.48㏑(x+2) +27
28 = 0.48㏑(x+2) + 27
28-27= 0.48㏑(x+2)
1= 0.48㏑(x+2)
1/0.48= ㏑(x+2)
25/12= ㏑(x+2)
x+2= [tex]e^{\frac{25}{12} }[/tex]
x+2=8.03119
x=8.03119-2
x= 6.03119
x = 6(round off)
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A pre-paid phone company charges $17.75 as a monthly access fee and $0.13 per minute of calling time.
What will the monthly cost be if you make 176 minutes of calls this month?
Answer:
$40.63
Step-by-step explanation:
If the phone company charges $17.75 already, and each minute costs $0.13, then we can do an equation that looks something like this:
17.75 + (0.13 × 176) = total price
We need to figure out how much 0.13 multiplied by 176 is.
0.13 × 176 = 22.88
Now that we figured out that 0.13 multiplied by 176 is equal to 22.88, we need to add the monthly access fee.
22.88 + 17.75 = 40.63
The monthly cost will be $40.63.
Which is a strict inequality?
A. y>4
B. y≤4x+2
C. y≥x
D. y=−8x+3
The option that is a strict inequality is A. y>4
How can you tell if an inequality is strict?It should be noted that inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal.
Inequalities involving < or ">" are considered "strict inequalities," whereas those involving "" or "" are not. If you "switch" the two sides of an inequality, you must then reverse the inequality symbol's direction. For example, because 4 5 is true, it follows that 5 > 4.
In conclusion, the correct option is A.
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Solve the following system of equations.
-2x+y = 9
5x+y = -12
Answer: (x,y) = (-3,3)
Step-by-step explanation:
1. Solve the equation for y
y=9+2x
2. Substitute the given value of y into the equation 5x+y= -12
5x+9+2x= -12
3. Solve x variable
x= -3
4. Substitute the given value of x into the equation y=9+2x
y=9+2x(-3)
5. Solve the equation for y
y=3
Final answer:
x=-3
y=3
an 8 oz soda can costs $0.96, a 12 oz soda can costs $0.72 and a 32 oz cup of soda costs $2.24. which is the lowest cost per ounce?
The lowest cost per ounce is 12 ounces of soda which cost $0.72.
How to find the lowest cost per ounce?An 8-ounce of soda can costs $0.96, a 12-ounce soda can costs $0.72 and 32 ounces of a cup of soda costs $2.24.
The lowest cost per ounce can be calculated as follows:
For 8 ounces of soda can costs $0.96.
cost per ounces = 0.96 / 8
cost per ounce = 0.12 dollars per ounce
For 12 ounces soda can costs $0.72.
cost per ounces = 0.72 / 12
cost per ounce = 0.06 dollars per ounce
For 32 ounces soda can cost $2.24.
cost per ounces = 2.24 / 32
cost per ounce = 0.07 dollars per ounce
Therefore, the lowest is 12 ounces of a soda can.
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Force An 8.0-pound weight is lying on a sit up bench at the gym. If the bench is
inclined at an angle of 15°, there are three forces acting on the weight, as shown
in Figure 12. Find the magnitude of N and the magnitude of F.
Answer: 7
Step-by-step explanation: 7+2
The area of a circle is 113.04 square miles. What is the circle's radius?
Use 3.14 for л.
Submit
miles
Answer: 6 miles exactly
Step-by-step explanation:
Answer:
6
Step-by-step explanation:
A=πr^2
113.04=3.14×r^2
113.04/3.14=r^2
36=r^2
√36=r
r=6
Which one doesn't belong: 2 PARTS TO 5 PARTS, 2 FOR EACH 5, 2 OUT OF EVERY 5, OR 2 FOR EVERY 5? Explain your reasoning.
2 parts to 5 parts does not belong to the given options and 2 for every 5 does not matches.
What is Division?A division is a process of splitting a specific amount into equal parts.
Given,
2 parts to 5 parts
2 for each 5
2 out of every 5
2 for every 5
Division has two parts the numerator and denominator.
The numerator represents the part and denominator represents the whole.
2 parts to 5 parts does not belong to the given options and 2 for every 5 does not matches.
Hence, 2 parts to 5 parts does not belong to the given options and 2 for every 5 does not matches.
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Simplify and state the restrictions on the domain:
The required simplification of given function is [tex]\frac{(x-1)^{2}}{x-2}[/tex] and restriction on domain are x ≠ 1, 2.
Explain domain of the function?The domain of a function is the set of all possible inputs for the function. For example, the domain of f(x)=x² is all real numbers, and the domain of g(x)=1/x is all real numbers except for x=0. We can also define special functions whose domains are more limited.
According to question:We have,
[tex]\frac{(x+3)(x-1)}{x-2}[/tex] ÷ [tex]\frac{x+3}{x-1}[/tex]
[tex]\frac{(x+3)(x-1)}{x-2}[/tex] × [tex]\frac{x-1}{x+3}[/tex]
[tex]\frac{(x-1)^{2}}{x-2}[/tex]
For domain, Function should have solution should not be not defined.
For this, denominator must not equal to zero
Then, x -2 ≠ 0, x - 1 ≠ 0
x ≠ 2, x ≠ 1
Thus, option(3) [tex]\frac{(x-1)^{2}}{x-2}[/tex] x ≠ 1,2 is correct.
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Answer:
(b) (x -1)²/(x -2), x ≠ -3, 1, 2
Step-by-step explanation:
You want to know the domain restrictions and the simplified form of ...
[tex]\dfrac{(x+3)(x-1)}{(x-2)}\div\dfrac{x+3}{x-1}[/tex]
SimplifyWe can "invert and multiply", then cancel the common factor from numerator and denominator.
[tex]\dfrac{(x+3)(x-1)}{x-2}\div\dfrac{x+3}{x-1}=\dfrac{(x+3)(x-1)}{x-2}\times\dfrac{x-1}{x+3}=\dfrac{(x+3)(x-1)^2}{(x+3)(x-2)}\\\\=\dfrac{(x-1)^2}{x-2}\qquad x\ne -3[/tex]
DomainThe values of x that must be excluded from the domain are those values for which any part of this expression is undefined. The expression is undefined when any denominator is zero: at x = 2 (left "factor"), at x = 1 (right "factor"), and at x = -3.
The factor (x +3) doesn't show up in the simplified form, but it is a "hole" in the graph of the original expression—a value of x where the function is not defined.
Here is a summary of what you get at the restricted values:
-3: (0)(-4)/-5 ÷ 0/-4 . . . . division by 01: (4)(0)/-1 ÷ 4/0 . . . . . . . divisor undefined2: (5)(1)/0 ÷ 5/1 . . . . . . . division by 0The simplified form with restrictions is ...
[tex]\boxed{\dfrac{(x-1)^2}{x-2},\ x \ne -3,1,2}[/tex]
Sue and her brother wanted to buy 25 pieces of candy for their family's stockings. They chose to buy Kit Kats and Skittles. After shopping they spent $ 20.70. Skittles
cost 80 cents each and kit kats cost 90 cents each. How many of each candy did they get at the store? Let s-skittles and k=kit kats.
Which systems of equations represents this situation?
Answer:
18 Skittles and 7 Kit Kats
Linear system of equations in two variables
Step-by-step explanation:
We a linear system of two equations which can be solved simultaneously
Total pieces of candy equation
s + k = 25 [1]
Total cost equation
0.8s + 0.9k = 20.70 [2]
Multiply [1] by 0.80
0.80s + 0.80k = 20 [3]
Subtract [3] from [2]
0.80s + 0.90k = 20.70
[tex]-[/tex]
0.80s + 0.80k = 20
[tex]\cdots\cdots\cdots\cdots\cdots\cdots\cdots\cdots\cdots\cdots\cdots[/tex]
0.1k = 0.70
k = 0.70/0.10 = 7
In [1]
[tex]s + 7 = 25\\\\s = 25-7\\\\s = 18\\\\[/tex]
Answer: 18 Skittles and 7 Kit Kats
Ahmad drove 350 miles in 5 hours.
At the same rate, how many miles would he drive in 7 hours?
Answer:
490 miles
Step-by-step explanation:
Since Ahmad is driving 350 miles in 5 hours, he's averaging 70 miles per hour.
350/5 = 70 mph
Driving 7 miles at 70 mph:
7 x 70 = 490 miles
Answer: 490 miles!
Step-by-step explanation:
350 x 7hrs divided by 5hrs would be = 490miles
multiple 350 and 7 ( 350x7) which will equal 2450 then divide by 5 and you will get 490 milesHow did I get 490? or why didn't you do 350 x 5?
Well because the question asks how many miles would he drive in 7 hours? you will need to multiple the droven miles which is 350miles because that is part of the getting answer, and the question of having to know how many miles would he drive in 7 hours, you wouldn't do 350 x 5 because its not asking " Ahmad drove 350 miles in 5 hours, how many miles would he drive in 5 hours? and which would equal 250 which not correct because it doesn't make sense if he's drove 350 miles in 5 hours and then drove 250miles in 7 hours, back to the explanation, after multiplying 350 into 7 you will end up at 2450, no this isn't the answer you need to divide because it would take more than 7 hours to drive 2450 miles, next you divide by the hours driven in 350 miles which in this in this case would be 5 because your diving 2450 by 5 because sense u cannot get the answer by multiplying 350x5 so this is time where your gonna use the 5 because 350 x 7= 2450 is too large in miles for 7 hours your gonna divide the 2450 to lower it down to 490 miles, doesn't that sound more accurate? the miles increase by 1.4 ( 140 miles ) so another way u could have gotten the answer was by doing 350 + 140 = 490 but however you would need to know how much the miles have increase which u can do by 490 - 350 which equals to 140 miles.
PLEASE HELPED I"M TIMED I WILL GIVE BRAINLIST
Answer:
Below
Step-by-step explanation:
Angle 2 or angle HFE
Vertex is F
GF and FE are the sides of angle 1
State if the triangles in each pair are similar. If so, state how you know they are similar and complete the similarity statement
If two figures have three sides similar then they will be similar by side-by-side property which is written as SSS.
What is the similarity?If two objects are having the same shape then they will be termed as similar. So in mathematics, if two figures have the same shapes, lines or angles then they are called similar.
If two figures have three sides similar then they will be similar by side-by-side property which is written as SSS.
Now in the given figure, the side YD is similar and equal to the side OD so option C will be the correct answer.
Hence the information do you need to prove the triangles are congruent by SSS Will be YD ≅ OD.
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Teri invested $1500 in an account with an interest rate of 2.25% compounded continuously. How long will it take for Teri's account to earn $5000?
It will take 54 days for Teri's account to earn an amount of $5000.
What is compound interest?Compound interest, also known as interest on principal and interest, is the practice of adding interest to the principal amount of a loan or deposit.
It occurs when interest is reinvested, or added to the loaned capital rather than paid out, or when the borrower is required to pay it, so that interest is generated the next period on the principal amount plus any accumulated interest. In finance and economics, compound interest is common.
It is given by formula
A = [tex]p*e^{r*t}[/tex]
where:
A is final amount
p is principal amount
r is rate of interest and
t, is time period
Given: A= $5000, p=$1500, r=2.25% = 0.0225
To find: time period to get compounded amount
5000=1500×[tex]e^{0.0225*t}[/tex]
[tex]e^{0.0225t}[/tex] = [tex]\frac{10}{3}[/tex]
0.0225t = ㏑ ([tex]\frac{10}{3}[/tex])
t = 53.5099 ≈ 54 days
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The ratio of hybrid cars to gasoline-powered cars in the parking lot of a
local office building is 3:11. If a car in the lot is selected at random to get
the reserved parking space nearest the building, find the probability the car
selected is a hybrid. Express your answer as a simplified fraction.
The probability of getting a Hybrid car = 3/14
Probability:The probability formula states that the ratio of favorable outcomes to all outcomes determines the likelihood that an event will occur.
The formula for the probability of an event is given by
P(E) = No of favorable outcomes/ total number of outcomes
Here we have
The ratio of hybrid cars to gasoline-powered cars is 3:11
Let 3x and 11x be the number of hybrid cars and gasoline-powered cars
[ Since they are in 3: 11 ratio]
Then total number of cars = 3x + 11x = 14x
From the given data,
Total number of cars = 280
=> 14x = 280
=> x = 20
Number of Hybrid cars, 3x = 3(20) = 60
Here we select a car from a random experiment
Number of outcome = 280
Number of outcomes that we get Hybrid car = 60
Thus the probability of getting a Hybrid car = [tex]\frac{60}{280}[/tex]
= [tex]\frac{6}{28}[/tex] = [tex]\frac{3}{14}[/tex]
Therefore,
The probability of getting a Hybrid car = 3/14
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Complete question:
The ratio of hybrid cars to gasoline-powered cars in the parking lot of a local office building is 3:11. if there are 280 cars in the lot and one is to be selected at random to get the reserved parking space nearest the building, find the probability the car selected is a hybrid. express your answer as a fraction.
During a football game, a team lost 10 yards on its first play and 20 yards on its third play.
Write an integer to represent the loss on each play.
The required integer to represent the loss on each play is -5m-5.
What are integers?Any positive or negative number without fractions or decimal places is known as an integer, often known as a "round number" or "whole number."
Given:
During a football game, a team lost 10 yards on its first play and 20 yards on its third play.
To write an integer to represent the loss on each play:
Use -10 to represent losing 10 yards.
Use -20 to represent losing 20 yards.
Add both of the expression,
(-10) + (-20)
= -10 -20.
Whenever we add two negative values, the sum is negative.
(-10) + (-20) = -10 -20 = - 30
Let m be the required integer.
So, -5m-5 is the loss on each play.
Where m is the number of play.
Therefore, the required integer is -5m-5.
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Janessa loves to travel. She earns $2,500 per month, and saves 3% of each paycheck for travel. After a full year of saving, she plans her annual trip. For her most recent trip, two-thirds of her savings went to plane fare and lodging. After plane fare and lodging, how much of her trip savings does Janessa have left?
The amount the she had in her savings before the trip was $825.
How much of Janessa's travel funds remains?Calculating amount
From the question, we are to calculate how much Janessa has in her savings before the trip
Let the amount she has in her savings before the trip be x
From the given information,
Janessa spent a third of her savings on airfare for a vacation"
That is,
She spent (1/3)x
The amount remaining after this time will be x - (1/3)x = (2/3)x
"She then spent another $300 on hotels"
The amount remaining after this time will be (2/3)x - $300
"If she has $250 left for meals and souvenirs"
That is,
(2/3)x - $300 = $250
Now, solve for x
(2/3)x - $300 = $250
(2/3)x = $250 + $300
(2/3)x = $550
x = $550 × 3/2
x = $825
Hence, the amount the she had in her savings before the trip was $825
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Ariana is going to invest $62,000 and leave it in an account for 20 years. Assuming the interest is compounded continuously, what interest rate, to the nearest tenth of a percent, would be required in order for Ariana to end up with $233,000?
The interest rate required for Ariana to end up with $233,000 is approximately 6.6%.
What interest rate is required for Ariana to end up with $233,000?The compound interest formula can be expressed as;
A = P(1 + r/n)^(n*t)
Where A is accrued amount, P is principal, r is interest rate, t is time elapsed.
Given the data in the question;
Principal P = $62,000Accrued amount A = $233,000Compounded continuously Time t = 20 yearsInterest rate r = ?Using the formula A = P(1 + r/n)^(n*t).
Solve for r when interest is compounded continuously.
r = In( A / p ) / t
Plug the given values into the above equation.
r = In( $233,000 / $62,000 ) / 20
r = In( $233,000 / $62,000 ) / 20
r = 0.0661952
Now, convert r to R as a percentage
R = r × 100%
R = 0.0661952 × 100%
R = 6.6%
Therefore interest rate needed by Ariana to the nearest tenth of a percent is 6.6%.
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An interior designer is designing a room. Her options include 6 paint colors, 4 types of flooring, 6 different curtains, 3 furniture sets, and 3 light fixtures. How many
different room designs can be created from these options?
Answer
The total number of different room designs is 1296.
What is the fundamental principle of counting?According to the fundamental counting principle, if there are n ways to do one thing and m ways to do another, then there are n×m methods to accomplish both things.
Given that, there are 6 paint colors, 4 types of flooring, 6 different curtains, 3 furniture sets, and 3 light fixtures.
As per the basic principle of counting, the total number of different room designs is:
6 × 4 × 6 × 3 × 3
= 1296
Hence, the total number of different room designs is 1296.
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