The volume of a spear can be calculated using the formula V = (4/3) x π x (r^3), where V is the volume, π is the mathematical constant pi (approximately equal to 3.14159), and r is the radius of the sphere.
Since the diameter of the spear is given as 15 cm, the radius would be half of that, which is 7.5 cm (or 0.075 meters).
Plugging in the values, we get:
V = (4/3) x π x (0.075)^3
V = 0.00017678 cubic meters
Rounding this answer to the nearest whole number, we get:
V ≈ 0 cubic meters
Therefore, to the nearest whole number, the volume of a spear with a diameter of 15 cm is 0 cubic meters. However, please note that this answer assumes that the spear is a perfect sphere, which may not be the case in reality.
Over the last three evenings, Teresa received 90 phone calls at the call center. The first evening, she received 6 fewer calls than the second evening. On the third evening, she received 2 times as many calls as the second evening. How many phone calls did she receive each evening?
Answer:
In order: 18, 24, 48
Step-by-step explanation:
Let the number on the three evenings be a, b, and c, in order.
a + b + c = 90
a = b - 6
c = 2b
b - 6 + b + 2b = 90
4b - 6 = 90
4b = 96
b = 24
a = b - 6 = 24 - 6 = 18
c = 2b = 2(24) = 48
In order: 18, 24, 48
if P is the set {1,3,7,9}, Q is the set {2,6,11} and R is the set {4,6,9,11} what is what is set for P u (QnR)
The union of P and (Q n R), denoted as P u (Q n R), will contain all the elements from both sets without repetition. Thus, the final set is:
P u (Q n R) = {1, 3, 6, 7, 9, 11}
To find the set P u (Q n R), we need to first calculate the intersection of sets Q and R, and then take the union of set P with the resulting intersection.
The intersection of sets Q and R, denoted as Q n R, contains the elements that are common to both Q and R. From the given sets:
Q = {2, 6, 11}
R = {4, 6, 9, 11}
The intersection Q n R is {6, 11}, as these are the elements present in both sets Q and R.
Now, we can take the union of set P with the intersection Q n R:
P = {1, 3, 7, 9}
Q n R = {6, 11}
The union of P and (Q n R), denoted as P u (Q n R), will contain all the elements from both sets without repetition. Thus, the final set is:
P u (Q n R) = {1, 3, 6, 7, 9, 11}
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A certain forest covers an area of 5000 km^2. Suppose that each year this area decreases by 7.5%. What will the area be after 8 years? Round your answer to the nearest square kilometer.
Rounded to the nearest square kilometer, the area of the forest after 8 years will be approximately 2773 km².
To find the area of the forest after 8 years, we need to calculate the successive decreases in area over each year.
Let's denote the initial area of the forest as A₀ = 5000 km².
Each year, the area decreases by 7.5%, which means it remains at 92.5% of the previous year's area.
After 1 year, the area will be:
A₁ = A₀ - 0.075 * A₀ = 0.925 * A₀
After 2 years, the area will be:
A₂ = 0.925 * A₁ = 0.925 * (0.925 * A₀) = (0.925)² * A₀
Similarly, we can continue this process for 8 years:
A₈ = (0.925)⁸ * A₀
Now, let's calculate the final area after 8 years:
A₈ = (0.925)⁸ * A₀
≈ 0.55465 * A₀ (rounded to 5 decimal places)
To find the area in square kilometers, we multiply this value by the initial area A₀:
A₈ ≈ 0.55465 * 5000 km²
≈ 2773.25 km²
Rounded to the nearest square kilometer, the area of the forest after 8 years will be approximately 2773 km².
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Which expression is equivalent to log84a
log84+loga-log:(b-4)-4logsc
log84+logs a+ (logs (b-4)-4log.c)
log84a+log8b-4-4log8c-4
og 4a-logs (b-4)-log84c
(b-4)?
The log expression that is equivalent to [tex]\log_8 4a[ \frac{b - 4}{c^4} ][/tex] is log₈4 + log₈a + (log₈(b - 4)) - 4log₈C.
What is the equivalent log expression?The equivalent log expression is determined by applying the rules of logarithm as follows;
The given logarithm expression;
[tex]\log_8 4a[ \frac{b - 4}{c^4} ][/tex]
This expression is expanded as follows; we will use the equal base of 8;
[tex]\log_8 4a[ \frac{b - 4}{c^4} ][/tex] = log₈4 + log₈a + (log₈(b - 4)) - 4log₈C
Note: when we write the division of a log in a linear, we use the operator (-), that is negative sign. Also, the power becomes the coefficient (c⁴ = 4C).
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The complete question is below:
Which expression is equivalent to [tex]\log_8 4a[ \frac{b - 4}{c^4} ][/tex]?
Find the value of x if (-3)^3x+1 × (-3)^4 = (-3)^8
Choose all the sets containing the number
Pi is an irrational number and belongs to the set of real numbers. It is not part of the sets of natural numbers, whole numbers, integers, or rational numbers due to its non-integer and non-fractional nature. Pi is a unique and fundamental mathematical constant with significant applications in various fields of mathematics and science.
Pi, denoted by the Greek letter π, is a mathematical constant that has been widely used throughout history. It is a transcendental number, which means it is not the root of any non-zero polynomial equation with rational coefficients. Pi is approximately equal to 3.14159, but its decimal representation continues infinitely without repetition.
Let's examine each set and determine if pi belongs to them:
1. Natural numbers: Natural numbers are positive integers starting from 1. Since pi is not an integer, it does not belong to the set of natural numbers. Pi represents a ratio of a circle's circumference to its diameter, and it cannot be expressed as a whole number.
2. Whole numbers: Whole numbers include non-negative integers, including zero. Similar to the natural numbers, pi is not a whole number as it is not an integer. Therefore, pi is not part of the set of whole numbers.
3. Integers: Integers consist of positive and negative whole numbers, including zero. Since pi is not an integer, it is not an element of the set of integers. Pi's decimal expansion goes beyond any finite integer value.
4. Rational numbers: Rational numbers are numbers that can be expressed as a fraction of two integers. However, pi is not a rational number. Its decimal representation is non-terminating and non-repeating, which means it cannot be expressed as a fraction of two integers.
5. Irrational numbers: Irrational numbers are numbers that cannot be expressed as a fraction. Pi falls into this category, as it has an infinite and non-repeating decimal expansion. Pi is a famous example of an irrational number, and it cannot be expressed as a simple fraction.
6. Real numbers: Real numbers encompass both rational and irrational numbers. Pi is an irrational number, and therefore, it is included in the set of real numbers. Real numbers represent all possible points on the number line, including both rational and irrational numbers.
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The question probable may be:
Choose all the sets containing the number Pi:
natural numbers
whole numbers
integers
rational numbers
irrational numbers
real numbers
inequality Help me please
Answer:
y > 1/3 x - 3
Step-by-step explanation:
First, we need to find the equation of the dashed line.
The y-intercept, b, is -3.
The slope, m = rise/run = 1/3.
The equation of the line is
y = 1/3 x - 3
The line is dashed, not solid, so we will use < or >, but not ≥ or ≤.
The shading is above the line, so we use >.
Answer: y > 1/3 x - 3
Which sequence of transformations proves that shape I is similar to shape II?
The sequence of transformations that proves that the shapes are similar is given as follows:
B. a reflection across the x-axis, and then a dilation by a scale factor of 1.5
How to obtain the transformations?First, we have that the orientation of the figure, hence it was reflected.
The figure was reflected from the second quadrant to the third quadrant, hence the figure was reflected over the x-axis.
The base segment changes from a length of 2 units to a 3 units, hence the scale factor of the dilation is given as follows:
3/2 = 1.5.
Hence option B is the correct option for this problem.
Missing InformationThe missing parts of the problem are given by the image presented at the end of the answer.
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Solve for x
10
07
05
08
6x+8
K
U
N
122°
L
M
194°
The sin(14°) = opp/1opp = sin(14°)The exact value of x in M194° is therefore x = sin(14°) or approximately 0.2419 (rounded to four decimal places).
To solve for x in M194°, we first need to understand the concept of reference angles.A reference angle is the acute angle formed between the terminal side of an angle and the x-axis in standard position.
To find the reference angle of M194°, we subtract 180° from 194°:
Reference angle = 194° - 180° = 14°We can use this reference angle to determine the quadrant in which M194° lies and find the exact value of x using trigonometric ratios.
The angle M194° is in the third quadrant since it is greater than 180° but less than 270°.
In the third quadrant, sine and cosecant are positive. Therefore, we can use the sine ratio to solve for x.sin(14°) = opp/hypwhere opp is the opposite side and hyp is the hypotenuse. Since the hypotenuse is not given, we can assume it to be 1.
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Given f(x) figure out the following
Answer:
See below
Step-by-step explanation:
[tex]f(g(2))=f(6\cdot2-8)=f(12-8)=f(4)=2(4)^2+1=2(16)+1=32+1=33[/tex]
[tex]f(g(x))=f(6x-8)=2(6x-8)^2+1[/tex]
[tex]g(f(x))=g(2x^2+1)=6(2x^2+1)-8=12x^2+6-8=12x^2-2[/tex]
[tex](g\circ g)(x)=g(g(x))=g(6x-8)=6(6x-8)-8=36x-48-8=36x-56[/tex]
[tex](f\circ f)(-2)=f(f(-2))=f(2(-2)^2+1)=f(9)=2(9)^2+1=2(81)+1=163[/tex]
Content: / Missing Titanic Submersible Search Forces on Area Where Underwater Nosies Were Heard
1. Your first paragraph is a summary of what you read in your article.
Tell me the who, what, where, and when. Please use your own
words and include as few direct quotes as possible.
2. Your second paragraph is an analysis of what you read in your
article. Please tell me two things in this paragraph. The first is
why is the event or topic of your article important to US
government and politics, as well as to us as voters and taxpayers?
The second is what are the implications of this event or topic for
US government or politics? Now that this event or topic has been
reported on, what changes (or lack thereof) might we expect to
see happen in US government and politics?
3. Each paragraph should be of equal length, so your paper is ½
summary; analysis.
4. Please do not include your opinion in this assignment. This is a
summary and analysis assignment.
Expert needed for this one
A regular sumof 2500 is invested at the beginning of every year at 3.5% interest companies pounded annually . Find thetltal amount invested at the end of 10 years
[tex]~~~~~~~~~~~~\stackrel{\textit{payments at the beginning of the period}}{\textit{Future Value of an annuity due}} \\\\ A=pmt\left[ \cfrac{\left( 1+\frac{r}{n} \right)^{nt}-1}{\frac{r}{n}} \right]\left(1+\frac{r}{n}\right) \\\\ \qquad \begin{cases} A=\textit{accumulated amount} \\ pmt=\textit{periodic payments}\dotfill & 2500\\ r=rate\to 3.5\%\to \frac{3.5}{100}\dotfill &0.035\\ n= \begin{array}{llll} \textit{times it compounds per year} \end{array}\dotfill &1\\ t=years\dotfill &10 \end{cases}[/tex]
[tex]A=2500\left[ \cfrac{\left( 1+\frac{0.035}{1} \right)^{1 \cdot 10}-1}{\frac{0.035}{1}} \right]\left(1+\frac{0.035}{1}\right)\\\\\\ A=2500\left[ \cfrac{0.4106}{0.035} \right](1.035)\implies A \approx 30354.98[/tex]
22. The diameter of circle F is 8; AB = 10; and AB, BC, and AC are tangent to circle F.
What is the perimeter of triangle ABC?
The perimeter of the triangle ABC is 60units
What is perimeter of a triangle?A triangle is a polygon with three sides having three vertices.
Perimeter is a math concept that measures the total length around the outside of a shape.
Since the radius of the circle is 4,
The hypotenuse = 6+x
base = 4+x
Using Pythagorean theorem
(6+x)² = 10² + (4+x)²
36+12x +x² = 100+ 16 + 8x + x²
collecting like terms
116-36 = 12x -8x
80x = 4x
x = 80/4
x = 20
Therefore ;
hypotenuse = 20+6 = 26
base = 20+4 = 24
Perimeter of the triangle = 26+24+10
= 60 units
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Triangle abc is dilated by a scale factor of 1/2 about the origin and then reflected over the x-axis. What is the location of B” after the sequence of transformations
The answer is option 4.Triangle ABC is dilated by a scale factor of 1/2 about the origin and then reflected over the x-axis. The location of B” after the sequence of transformations is (5,-3).
A scale factor is a measure of how much an object is stretched or shrunk about a fixed point in the plane. We can dilate a triangle by multiplying its coordinates by a scale factor k, where k is a positive real number.A reflection is a transformation that flips a figure over a line of reflection.
The line of reflection is a perpendicular bisector of the segment connecting a point and its image.The order of these transformations makes a difference in the result. When a triangle is dilated first, and then reflected, we can either reflect the original triangle over the x-axis first and then dilate it by a scale factor of 1/2 about the origin or dilate the original triangle first and then reflect it over the x-axis.
When we first reflect the original triangle over the x-axis, we obtain the image of triangle A'B'C', as shown below:AB has an endpoint at (0, 0) and another at (-10, 6), so we reflect over the x-axis as shown above to get A'B', whose endpoints are (0,0) and (10,-6).We then dilate triangle A'B'C' by a scale factor of 1/2 about the origin as shown below:
The image of B after the two transformations is B''.
To find the coordinates of B'', we take the point (5,-3) as the new origin and translate the image points back to their original position by adding 5 to the x-coordinates and subtracting 3 from the y-coordinates.
The image of B after the two transformations is B'' = (5, -3). Thus, the answer is option 4.
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The complete question is:
content loaded
Triangle abc is dilated by a scale factor of 1/2 about the origin and then reflected over the x-axis. What is the location of B” after the sequence of transformations?
1. (-10, 6)
2.(-5,3)
3.(5,3)
4.(5,-3)
i don’t know how to do this can someone explain this
Answer:
Step-by-step explanation:
Donna finished 67% of her homework. What fraction of her homework is
completed?
67/10
0.67/100
67/100
67/1000
Answer:
67/100
Step-by-step explanation:
Percent means out of 100.
67% = 67/100
Answer:
67/100
Step-by-step explanation:
When we say Donna has completed 67% of her homework, we are referring to a percentage, which is a way of expressing a part out of 100. In this case, the percentage is 67%.To convert a percentage to a fraction, we can simply write the percentage as a fraction with 100 as the denominator. In this case, since the percentage is 67%, the fraction would be 67/100.[tex]67\%=\dfrac{67}{100}[/tex]This system of equations is:
• consistent dependent
• consistent independent
O inconsistent
This means the system has:
O a unique solution
Line 1:y=3x+1 Line 2:y=2x-3 Line 3:3y+×=6 Line 4:y=1/3x-1
Alright, let's solve this system of equations whimsically, shall we?
First, imagine these lines as threads of destiny. Each equation is like a thread weaving through the vast fabric of the cosmos, plotted on the 2D plane of our imagination.
So let's embark on this mathematical journey together!
Our first traveler is Line 1, or as we'll call him, "Sir L1." He struts along with the equation y = 3x + 1. His path is clear: for every step he takes in the x direction, he ascends 3 steps in the y. He's quite the climber!
Next, we meet Lady L2 with the equation y = 2x - 3. A bit more relaxed than Sir L1, she ascends 2 steps in the y direction for every step in the x. They clearly don't cross paths—they're too different in their inclinations. This means that Sir L1 and Lady L2 are consistent and independent.
Our third traveler is the mysterious Master L3. His equation is slightly different, written as 3y + x = 6. Let's write this in y = mx + c form to match our other travelers. With a little rearranging, we get y = -1/3x + 2. He's a bit of a downer, descending 1 step in y for every 3 steps in x. Observing him from afar, it's clear he never intersects with Lady L2 or Sir L1. They're all leading their independent lives.
Lastly, we have the young Miss L4, with her equation y = 1/3x - 1. She's a gentle traveler, ascending only a third of a step in y for every step in x. However, like the others, she doesn't cross paths with any of our other travelers.
So, in this whimsical world of equations, it appears that none of our travelers cross paths. Each one treads their own unique path. This means our system of equations is indeed consistent, but each line is independent, meaning they don't intersect, and each has a unique solution. There are no shared points of intersection. It seems our travelers are lone wolves in this cosmos of coordinates!
what is 6 over square root of 8x
Answer: 0.4714
Step-by-step explanation: square root of 8 is 2.8284 divided by 6 = 0.4714.
[tex] \frac{6}{ \sqrt{8x} } \\ \frac{ {6}^{2} }{ {( \sqrt{8x)} }^{2} } \\ \\ \frac{36}{8x} \\ \ \\ \frac{36 \div 4}{8x \div 4} \\ \\ \frac{9}{2x} [/tex]
this is one of the ways to simplify it
you can divide 9 by 2 the answer will be 4.5x
Given f(x)=x^2, after performing the following transformations: shift upward 66 units and shift 19 units to the right, the new function g(x)=
The new function g(x) after shifting upward 66 units and shifting 19 units to the right is g(x) = (x - 19)^2 + 66.
After performing the described transformations on the function f(x) = x^2, the new function g(x) can be determined.
Shift upward 66 units:
To shift the graph of f(x) upward by 66 units, we add 66 to the original function:
f(x) + 66 = x^2 + 66
Shift 19 units to the right:
To shift the graph of f(x) 19 units to the right, we replace x with (x - 19):
f(x - 19) = (x - 19)^2
Combining both transformations, the new function g(x) is:
g(x) = (x - 19)^2 + 66
As a result, the new function g(x) is now g(x) = (x - 19)2 + 66 after being shifted up 66 units and 19 units to the right.
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Together, two teachers have a total of 40 students. Ms. fielder has 6 more students than Mr. Pearce. How many students does Ms. Felder have
Answer:
26
Step-by-step explanation:
Since 2 teachers have 40 students together, we have to divide 40 by 2:
40÷2=20
Now the new information is "Ms. fielder has 6 more students than Mr. Pearce." So we minus 6 from one side and add it to 5 the other:
20-6=14
20+6=26
So Ms. Felder has 26 students in all.
I hope this helps...
Please mark me brainliest.
Have a nice day!
Hereeeeeeeeeeeeeee look at the photo for the question
Answer:c
Step-by-step explanation:
How do I find the value of X?
Answer: 8
Step-by-step explanation:
From the circle.
CF . BF = EF . DF
9.6 = 3. (10+x)
54= 30+3x
3x = 24
x = 8
3 A patient is to take 2 3/5 tablespoons of medicine per day in 4 equally divided doses. How much medicine is to be taken in each dose? There are tablespoons of medicine in each dose. (Simplify your answer. Type a whole number, fraction, or mixed number.)
The amount of medicine to be taken in each dose is 13/20 tablespoons.
To find the amount of medicine to be taken in each dose, we need to divide the total amount of medicine (2 3/5 tablespoons) by the number of doses (4).
First, let's convert the mixed number 2 3/5 into an improper fraction:
2 3/5 = (2 * 5 + 3)/5 = 13/5
Now, we can divide 13/5 by 4 to find the amount of medicine per dose:
(13/5) / 4 = 13/5 * 1/4 = 13/20
Therefore, 13/20 teaspoons of the medication should be consumed for each dose.
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The lengths of pregnancies are normally distributed with a mean of 266 days and a standard deviation of 15 days. a. Find the probability of a pregnancy lasting 309 days or longer. b. If the length of pregnancy is in the lowest 2%, then the baby is premature. Find the length that separates premature babies from those who are not premature.
a. The probability of a pregnancy lasting 309 days or longer is approximately 0.0021, or 0.21%.
b. The length that separates premature babies from those who are not premature is approximately 235.25 days.
a. To find the probability of a pregnancy lasting 309 days or longer, we need to calculate the area under the normal distribution curve to the right of 309 days.
Using the z-score formula: z = (x - μ) / σ, where x is the value of interest, μ is the mean, and σ is the standard deviation, we can calculate the z-score for 309 days:
z = (309 - 266) / 15 = 43 / 15 ≈ 2.87
Now, we can use a standard normal distribution table or a calculator to find the probability associated with the z-score of 2.87. From the standard normal distribution table, we find that the area to the right of 2.87 is approximately 0.0021.
Therefore, the probability of a pregnancy lasting 309 days or longer is approximately 0.0021, or 0.21%.
b. To find the length that separates premature babies from those who are not premature, we need to determine the z-score corresponding to the lowest 2% of the normal distribution.
From the standard normal distribution table, we find the z-score associated with the lowest 2% to be approximately -2.05.
Now, we can use the z-score formula and solve for x to find the corresponding length:
-2.05 = (x - 266) / 15
Solving for x:
x - 266 = -2.05 * 15
x - 266 = -30.75
x = -30.75 + 266
x ≈ 235.25
Therefore, the length that separates premature babies from those who are not premature is approximately 235.25 days.
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Question Translate and solve using proportions: What percent of 96 is 18? Provide your answer below:
Answer:
18.75%
Step-by-step explanation:
x/100 = 18/96
96x = 100 × 18
x = 18.75
Which of the following are solutions to the equation below?
Check all that apply.
The solutions to the equation that are given can be seen in options A and E
What is a quadratic equation?
A quadratic equation is a polynomial equation of the second degree, which means it contains at least one term with an exponent of 2. The general form of a quadratic equation is:
ax^2 + bx + c = 0
In this equation, "x" is the variable, and "a," "b," and "c" are coefficients, where "a" cannot be zero. The coefficients "a," "b," and "c" can be any real numbers, including positive, negative, or zero.
x^2 + 10x +25 =8
x^2 + 10x + 25 - 8 = 0
x^2 + 10x + 17 = 0
x = -5 ± 2√2
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What is the difference if x≠0? [tex]13x^{2} \sqrt7x^{8}-3\sqrt7x^{12}[/tex]
The required expression is
[tex]( 10x^{6}) \sqrt7[/tex]
Simplification of radical expressions:Radical expressions are algebraic expressions involving radicals. The radical expressions consist of the root of an algebraic expression (number, variables, or combination of both).
The root can be a square root, cube root, or in general, nth root.
Simplifying radical expressions implies reducing the algebraic expressions to the simplest form and, if possible, completely eliminating the radicals from the expressions.
Given the radical expression
[tex]13x^{2} \sqrt7x^{8}-3\sqrt7x^{12}[/tex]
Take the square root of x⁸ and x¹²
[tex]13x^{2} \sqrt7x^{4}-3\sqrt7x^{6}[/tex]
Factor out √7 which is common to both terms
[tex]\sqrt7(13x^{6} -3x^{6})[/tex]
Simplify the terms in the bracket
[tex] \sqrt7( 10x^{6} )[/tex]
Rewrite the expression
[tex]( 10x^{6}) \sqrt7[/tex]
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On a coordinate plane, (negative 4, 6) is plotted.
Which ordered pair represents the reflection of the point (–4, 6) across both axes?
(4, 6)
(4, –6)
(–4, 6)
(–4, –6)
The reflection of the point (–4, 6) across both axes is (b) (4, -6)
How to determine the reflection of the point (–4, 6) across both axes?From the question, we have the following parameters that can be used in our computation:
Point = (-4, 6)
The rule of reflections across both axes is
(x, y) = (-x, -y)
Using the above as a guide, we have the following:
Image = (4, -6)
Hence, the reflection of the point (–4, 6) across both axes is (b) (4, -6)
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a jar contains 54 quarters and pennies. the total value of the coins is $3.90. which system of equations can be used to find p the number of pennies and q the number of quarters?
The equation for the total value is 0.01p + 0.25q = 3.90
The equation for the total number of coins is p + q = 54
How can a system of equations be used to find it?Let p represent the number of pennies and q represent the number of quarters in the jar.
The total value of the coins can be expressed as the sum of the values of the pennies and quarters.
Since each penny is worth $0.01 and each quarter is worth $0.25, the equation for the total value can be written as:
0.01p + 0.25q = 3.90
Additionally, we know that there are a total of 54 coins in the jar, so the equation for the total number of coins can be written as:
p + q = 54
These two equations form a system that can be solved simultaneously to find the values of p and q.
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A bank offers two different types of savings account which pay interest as shown below. Vinnie wants to invest £2800 in one of these accounts for 11 years. a) Which account will pay Vinnie more interest after 11 years? b) How much more interest will that account pay? Give your answer in pounds (£) to the nearest 1p. Account 1 Simple interest at a rate of 8% per year Account 2 Compound interest at a rate of 6% per year
The monthly earnings are less than the amount needed to pay the monthly car insurance bill of $200, the answer is no, the car insurance bill cannot be afforded.
Calculation of bi-weekly paycheck based on 20 hour weeks at a rate of $9.00 per hour is done below:
Earnings before deductions = $9.00 x 20 = $180.00
Now, we will calculate the total amount of deductions made from the earnings.
Total deductions = Federal Income Tax (11.9%) + State Income Tax (3.6%) + F.I.C.A (7.65%) + professional dues
= 11.9% + 3.6% + 7.65% + professional dues
= 23.15% + professional dues
Since the amount of professional dues is not given, we will assume it to be 2%.
Total deductions = 23.15% + 2% = 25.15% of earnings.
Now, we will calculate the amount of deductions made from the earnings.
Amount of deductions = 25.15% x $180.00
= $45.27
Thus, total earnings after deductions = $180.00 - $45.27
= $134.73
Now, we will determine whether or not the monthly car insurance bill of $200 can be paid from the bi-weekly paycheck.
Bi-weekly earnings = $134.73 x 2
= $269.46
Monthly earnings = $269.46 x 2
= $538.92
Since the monthly earnings are less than the amount needed to pay the monthly car insurance bill of $200, the answer is NO.
Therefore, the car insurance bill cannot be afforded.
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a) Account 2 with compound interest at a rate of 6% per year will pay Vinnie more interest after 11 years.
b) Account 2 will pay £221.60 less interest compared to Account 1 after 11 years.
How to calculate the higher interest?a) For Account 1 with a simple interest at a rate of 8% per year:
Interest = Principal * Rate * Time
We are given:
Principal = £2800
Rate = 8% = 0.08
Time = 11 years
Thus:
Interest = £2800 * 0.08 * 11
Interest = £2464
For Account 2 with compound interest at a rate of 6% per year:
Interest = Principal * [(1 + Rate)^{Time}] - Principal
Interest = £2800 * (1 + 0.06)¹¹ - £2800
Interests = £3042.40 - £2800
Interest = £242.40
b) The difference in interest earned by the two accounts is:
Difference = Interest in Account 2 - Interest in Account 1
Difference = £242.40 - £2464
Difference = -£221.60
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