Step-by-step explanation:
the perimeter of a rectangle is
2×length + 2×width
in our case
length = width + 3
and
2×length + 2×width = 30
using the first equation in the second :
2×(width + 3) + 2×width = 30
width + 3 + width = 15
2×width + 3 = 15
2×width = 12
width = 12/2 = 6 ft
length = width + 3 = 6 + 3 = 9 ft
Your grandfather invested a lump sum 18 years ago at 5% interest. Today, he gave you the proceeds of that investment, which amounted to R6 649,93 in total. How much did your grandfather originally invest?
The lumpsum amount invested in 18 years ago for the given value Future value and interest is = Rs 2763,18.3268
What about lumpsum?
In mathematics, a lump sum refers to a single, fixed amount of money or quantity of something that is paid or received all at once, rather than being paid or received in installments or over a period of time.
The term "lump sum" can be used in various mathematical contexts, such as in finance, where it can refer to a single payment or investment, or in statistics, where it can refer to a single value or data point.
Define future value:
In mathematics, future value (FV) refers to the value of an investment or cash flow at a specified date in the future, assuming a certain rate of return.
The future value of an investment is the amount of money that an investor would expect to have at a specified date in the future if they were to invest a certain amount of money today, and if that investment earns a certain rate of return over time.
⇒ The formula for calculating the future value of an investment is:
[tex]FV = PV x (1 + r)^n[/tex]
According to the given information:
Interest Rate = 5%
Time Period = 18 years
Future Value = Rs 6649,93.
Using the concept of TVM calculation we have that,
Present value = [tex]\frac{Future Value}{(1+r)^{t} }[/tex]
So, the Present Value = [tex]\frac{664993}{(1+0.05)^{18} } = 2763,18.3268[/tex]
Hence, the Lumpsum Amount is Rs 2763,18.3268
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The proof shows that ABCD is a rhombus. Which of the following is the
missing reason?
A. Reflective property
B. Symmetric property
C. Transitive property
D. Addition property
The correct answer is B. Symmetric property.
The symmetric property states that if a = b, then b = a. In the context of geometry, this property can be used to show that if one side of a figure is congruent to another side, then the second side is also congruent to the first. In the case of the given proof, it is possible that the symmetry of the figure is used to show that opposite sides of the rhombus are congruent.
The reflective property (A) is not typically used to prove that a figure is a rhombus, as it relates to the reflection of a figure across a line. The transitive property (C) and the addition property (D) are also unlikely to be used in this context, as they relate to the properties of equality and addition, respectively, rather than geometric properties of figures.
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The sum of twice a number,n, and 14 is 30. Write an equation that models this statement.Then explain how you might use reasoning to find the value of n.
Answer:
2n + 14 = 30
Step-by-step explanation:
Since you know that 2n + 14 = 30, we can determine the values by first subtracting 14 from 30. Our equation would then be 2n = 16. Divide 2 from both sides and n = 8.
This model represents the total on the top and the 2 parts on the bottom.
Who knows this? I need help
#16
Answer:
Step-by-step explanation:
adjacent: [tex]\angle BOC, \angle EOD[/tex] (both are adjacent)
complementary: [tex]\angle BOC[/tex]
supplementary: [tex]\angle EOD[/tex]
vertical angles: [tex]\angle AOE[/tex]
Simplify 1/cos x + 1/cos x -1
Answer:
-2cotxcscx
Step-by-step explanation:
Step 1: Find a common denominator
Step 2: Simplify
At age 25 , someone sets up an IRA (individual retirement account) with an APR of 4 %. At the end of each month he deposits $95 in the account. How much will the IRA contain when he retires at age 65? Compare that amount to the total deposits made over the time period.
Question content area bottom
Part 1
After retirement the IRA will contain $
enter your response here.
(Do not round until the final answer. Then round to the nearest cent as needed.)
The formula for the future value of an annuity is FV = Pmt * (((1 + r)n - 1) / r) to calculate the balance of the IRA at age 65. To compare this amount to the total deposits made over the time period, Total Deposits = Pmt * n = $45,600.
How will you calculate the balance of the IRA?To calculate the balance of the IRA at age 65, we need to use the formula for the future value of an annuity:
FV = Pmt * (([tex](1 + r)^n[/tex] - 1) / r)
Where:
Pmt = $95 (the monthly deposit amount)
r = 4% / 12 = 0.003333 (the monthly interest rate)
n = (65 - 25) * 12 = 480 (the total number of months, assuming retirement at age 65)
Plugging in these values, we get:
FV = 95 * (([tex](1 + 0.003333)^480[/tex] - 1) / 0.003333)
FV = $98,052.52
Therefore, the IRA will contain $98,052.52 at age 65.
Part 2
To compare this amount to the total deposits made over the time period, we can calculate the total deposits as:
Total Deposits = Pmt * n
Plugging in the values, we get:
Total Deposits = 95 * 480
Total Deposits = $45,600
Therefore, the IRA will contain significantly more than the total deposits made over the time period, due to the power of compounding interest.
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The function S=m^(2)+6m+8 models the growth of book sales in m months, where S is an amount in thousands of dollars. In how many months do book sales reach $80,000 ?
Answer:
We are given the function S = m^2 + 6m + 8 which models the growth of book sales in m months, where S is an amount in thousands of dollars. We want to find in how many months book sales reach $80,000.
We can set up an equation as follows:
S = m^2 + 6m + 8 = 80
Subtracting 80 from both sides, we get:
m^2 + 6m - 72 = 0
We can factor this quadratic equation as:
(m + 12)(m - 6) = 0
This gives us two possible solutions:
m + 12 = 0 or m - 6 = 0
Solving for m in each case, we get:
m = -12 or m = 6
Since we are looking for a number of months, we can discard the negative solution.
Therefore, book sales reach $80,000 in 6 months.
So, the answer is: 6 months.
What is the volume of this cone?
The volume of the cone is 2119. 5 cubic centimeters
How to determine the volume of the coneThe formula used for calculating the volume of a cone is expressed as;
V = πr² h/3
Given that the parameters are namely;
V is the volume of the cone.π takes the constant value of 3.14h is the height of the cone.r is the radius of the cone.Now, substitute the values, we have;
Volume , V = 3.14 × 15² × 9/3
Divide the values, we have;
Volume = 3.14 × 225 × 3
Multiply the values, we get;
Volume, V = 2119. 5 cubic centimeters
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Dave bought a new game for $28. The tax rate was %7. How much was the tax and the total price?
The tοtal price οf the game including tax is $29.96.
What are the variοus types οf taxes?Physical assets such as prοperty and transactiοns such as the sale οf stοck οr a hοme are subject tο taxatiοn. Taxes include incοme, cοrpοrate, capital gains, prοperty, inheritance, and sales taxes.
Because the tax rate is 7%, the tax amοunt is 7% οf the purchase price. Tο calculate the tax, multiply the purchase price by the tax rate expressed as a decimal:
0.07 x $28 = $1.96 in taxes
As a result, the purchase tax is $1.96.
Tο calculate the tοtal price, add the purchase price and the tax:
Purchase price + Tax = Tοtal Price
Tοtal cοst: $28 + $1.96 = $29.96
As a result, the tοtal cοst οf the game, including tax, is $29.96.
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Each year, the school has a goal to have a third as many students in remedial mathematics courses as the year before. Currently the school has 1,200 students in remedial math. Approximately how many students will be enrolled in four years?
(a) 44 (b)15 (c) 32,400 (d) 1
Answer:
44 students
Step-by-step explanation:
1200 for the first year
a third of that is 400
400 for the second year
a third of that is 133.4
133.4 for the third year
a third of that is 44
the great zlatan ibrahimović always scores a goal if he manages to take no less than six shots in a game (and sometimes he scores even without shooting). the following is a probability distribution of the number of shots zlatan ibrahimović must make to score a goal:
No. of shots Probability of scoring
0 0.02
1 0.13
2 0.34
3 0.32
4 0.16
5 0.02
6 0.01
(A). Calculate the expected ( mean) number of shots he takes to score a goal ?
(B). Calculate the standard deviation of the distribution.
a) The expected (mean) number of shots that Zlatan Ibrahimović must make to score a goal is 3.11.
b) The standard deviation of the distribution is 2.46.
How are the expected number and standard deviation computed?The expected number or mean (μ) of a distribution is computed as sum resulting from the multiplication of each value of the random variable by its probability and adding the products.
The formula for the mean is given as E(x) = ∑x P(x).
On the other hand, to compute the standard deviation (σ) of a probability distribution, we find each deviation from its expected value, square it, multiply it by its probability, add the products, and take the square root.
No. of shots Probability Expected Squared Squared Deviation
of scoring No. of shots Deviation x Probability
0 0.02 0 9.6721 0.193442
1 0.13 0.13 8.8804 1.154452
2 0.34 0.68 5.9049 2.007666
3 0.32 0.96 4.6225 1.4792
4 0.16 0.64 6.1009 0.976144
5 0.02 0.1 9.0601 0.181202
6 0.01 0.6 6.3001 0.063001
The expected (mean)
number of shots = 3.11 6.055107
Standard Deviation = Square root of 6.055107 = 2.46
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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.
Answer:
To determine which statements are true, we can use the standard form of the equation of a circle:
(x - h)^2 + (y - k)^2 = r^2
where (h, k) is the center of the circle and r is the radius.
Using this form, we can rewrite the given equation as:
(x - 1)^2 + y^2 = 3^2 + 1^2 = 10
Comparing this to the standard form, we can see that the center of the circle is (1, 0), so the statement "The center of the circle lies on the x-axis" is true. However, the statement "The center of the circle lies on the y-axis" is false.
To find the radius, we can rearrange the equation as follows:
x^2 - 2x + y^2 = 8
Completing the square for x, we get:
(x - 1)^2 + y^2 = 9
This shows that the radius of the circle is 3, so the statement "The radius of the circle is 3 units" is true, as well as the statement "The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9."
Therefore, the three true statements are:
1.The radius of the circle is 3 units.
2.The center of the circle lies on the x-axis.
3.The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
Step-by-step explanation:
hope its help <:
The ratio of boys to girls in a class is 4:5 a)What fraction of the class are boys b) what a fraction of the class are boys!
the fraction of the class that are boys is 4/9. And the fraction of the class that are girls is 5/9.
What is ratio?
A ratio is a comparison of two or more quantities that are related in some way. It expresses the relationship between these quantities in terms of the number of times one quantity contains another. Ratios are usually expressed as a fraction, where the numerator represents the first quantity and the denominator represents the second quantity. For example, the ratio of boys to girls in a class of 40 students may be expressed as 2:3 or 2/3, meaning there are 2 boys for every 3 girls. Ratios can also be expressed in other forms, such as percentages or decimals. Ratios are commonly used in mathematics, science, engineering, and everyday life to compare quantities and make predictions or decisions.
A fraction is a number that represents a part of a whole or a ratio of two quantities. It consists of two numbers, a numerator and a denominator, separated by a line. The numerator represents the number of parts being considered, while the denominator represents the total number of parts in the whole or in the comparison. Fractions are used in many areas, such as mathematics, science, engineering, cooking, and everyday life. They can be added, subtracted, multiplied, and divided, and can be converted to decimals or percentages.
a) The total ratio of boys to girls in the class is 4+5 = 9. Therefore, the fraction of the class that are boys is 4/9.
b) The question is unclear as it seems to be asking for the same answer as in part (a). If you meant to ask for the fraction of the class that are girls, you can use the same approach: the fraction of the class that are girls is 5/9.
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Ice cream is packaged in cylindrical gallon tubs. A tub of ice cream has a total surface area of 183.69 square inches.
If the diameter of the tub is 6 inches, what is its height? Use π = 3.14.
A 2.25 inches
B 4.5 inches
C 6.75 inches
D 12.75 inches
Answer:
6.75 inches.
Step-by-step explanation:
[tex]183.69 = 2*3.14*3^2 + 2*3.14*3*h[/tex]
[tex]= 56.52 + 18.84h[/tex]
[tex]183.69 - 56.52 = 18.84h[/tex]
[tex]127.17 = 18.84h[/tex]
[tex]=\frac{127.17}{18.84}[/tex]
[tex]=6.75[/tex]
What is the base of the exponent in the function f(x)=3(8√3) 2x when the function is written using only rational numbers and is in simplest form?
Answer:
We can rewrite the function as:
f(x) = 3(8√3)^(2x) = 3(2^3√3)^(2x)
Using the properties of exponents, we can rewrite this as:
f(x) = 3(2^(3*2x)√3^(2x)) = 3(2^(6x)√(3^(2x)))
Therefore, the base of the exponent is 2.
In western music, an octave is divided into 12 pitches. For the film Close Encounters of the Third Kind, director Steven Spielberg asked composer John Williams to write a five-note theme, which aliens would use to communicate with people on Earth. Disregarding rhythm and octave changes, how many five-note themes are possible if no note is repeated?
Answer:
This should be a permutation
Step-by-step explanation:
P (n, r) = n!/(n-r)!
P (12,5) = 12!/(12-5)!
P (12,5) = 12!/7!
P(12,5) = 95040
In ΔLMN, n = 27 inches, l = 70 inches and ∠M=149°. Find ∠N, to the nearest degree.
Using trigonometric functions, we can find that the value of the angle N is 3°.
What are trigonometric functions?The six fundamental trigonometric operations make up trigonometry. Trigonometric ratios are useful for describing these methods. The sine, cosine, secant, co-secant, tangent, and co-tangent functions are the six fundamental trigonometric functions. On the ratio of a right-angled triangle's sides, trigonometric identities and functions are founded. Trigonometric formulas are used to determine the sine, cosine, tangent, secant, and cotangent values for the perpendicular side, hypotenuse, and base of a right triangle.
Here, using the cosine theorem:
CosM = n² + l² - m²/2nl
⇒ Cos 149° = 27² + 70² - m²/2 × 27 × 70
⇒ -0.981 = 729 + 4900 - m²/3780
⇒ 5629 - m² = -3708
⇒ m² = 9337.
Now Cos N = m² + l² - n²/2ml
= (9337 + 4900 - 729) / (2 × √9337 × 70)
= 0.9985
Cos N = 0.9985
Putting [tex]Cos^{-1}[/tex] on both sides:
[tex]Cos^{-1}[/tex] Cos N = [tex]Cos^{-1}[/tex] 0.9985
⇒ N ≈ 3°
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The complete question is:
In ΔLMN, n = 27 inches, l = 70 inches and ∠M=149°. Find ∠N, to the nearest degree.
A line has a slope of 5/6
and passes through the point (7,6). Write its equation in slope-intercept form.
Answer:
y = 5/6x + 1/6
Step-by-step explanation:
m = 5/6, x = 7, y = 6
y = mx + b
6 = 5/6(7) + b
b = 6 - 35/6
b = 36/6 - 35/6 = 1/6
y = 5/6x + 1/6
Answer:
Below
Step-by-step explanation:
Here is another way:
Start with point ( 7,6) slope ( m= 5/6) form :
(y-6) = 5/6 ( x-7) expand
y-6 = 5/6 x - 35/6 add 6 to both sides
y = 5/6 x + 1/6 Done.
What is the measure of ∠m
Answer:
26° 180 -81 - 73 = 26
Step-by-step explanation:
Answer:
26
Step-by-step explanation:
triangle= 180
81 + 73 = 154
180 - 154= 26
each classroom has 6 rows of 5 desks. how many desks are thre in 45 classrooms?
There are 1,350 desks in 45 classrooms that each have 6 rows of 5 desks.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.com
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
Each classroom has 6 rows of 5 desks.
So the total number of desks in one classroom.
= 6 rows x 5 desks per row
= 30 desks
To find the total number of desks in 45 classrooms, we can multiply the number of desks in one classroom by the number of classrooms.
= 30 desks per classroom x 45 classrooms
= 1,350 desks
Therefore,
There are 1,350 desks in 45 classrooms that each have 6 rows of 5 desks.
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If you place a 26-foot ladder against the top of a building and the bottom of the ladder is 20 feet from the bottom of the building, how tall is the building? Round to the nearest tenth of a foot. help please now.
Answer: The building is approximately 16.6 feet tall.
Step-by-step explanation:
Use Pythagorean theorem (a²+b²=c²) to solve this.
We know that the ladder is 26 feet long so that would be our hypotenuse (c²). and the distance between the ladder and the building is 20 feet. So, this is the base. The remaining side is x.
Your equation would be: 20²+x²=26²
subtract 20² from 26² --> 276=x²
then take the square root --> 16.6=x
State the principle of mathematical induction
The principle of mathematical induction is a method of proof used in mathematics to prove that a statement is true for all natural numbers.
It is based on the idea that if the statement is true for one number, then it can be used to prove that it is true for the next number. Mathematical induction can be expressed mathematically as follows:
Let P(n) be a statement involving an integer n
Base Case: P(m) is true for some m
Induction Hypothesis: Assume P(k) is true for some k>m.
Induction Step: Show that P(k+1) is true.
Therefore, P(n) is true for all n>m
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Sally opens a savings account with $9,000 that earns 7% interest per year, not compounded How much interest, to the nearest penny, will Sally earn in 7 years?
Answer: Sally will earn $4,830.00 in interest over 7 years.
Step-by-step explanation:
If the interest is not compounded, then Sally will earn simple interest, which can be calculated using the formula:
I = P * r * t
where:
I = the interest earned
P = the principal amount (initial investment)
r = the annual interest rate (as a decimal)
t = the time period, in years
In this case, we have:
P = $9,000 (the initial deposit)
r = 7% = 0.07 (the annual interest rate)
t = 7 (the number of years)
So, plugging in the values:
I = $9,000 * 0.07 * 7
I = $4,830.00
Therefore, Sally will earn $4,830.00 in interest over 7 years.
calculate the total distance that the water tanker has covered in March 2022
The total distance that the water tanker has covered in March of 2022 is given as follows:
1860 kilometers.
What is the relation between velocity, distance and time?Velocity is given by the change in the distance divided by the change in the time, hence the following equation is built to model the relationship between these three variables:
v = d/t.
The parameters for this problem are given as follows:
Velocity of 60 kilometers a day.Time of 31 days, as the month of March has 31 days.Hence the total distance is then obtained as follows:
d = v x t
d = 60 x 31
d = 1860 kilometers.
Missing InformationThe complete question is:
"Assuming that the water tanker travels an average of 60 kilometers a day, calculate the total distance that the water tanker has covered in March 2022".
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PLEASE HELP WILL GIVE BRAINLIEST!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
The notation Σ-2 (3η + 5) is incorrect for representing the arithmetic series 8 + 11+ ... + 29.
The correct notation for the arithmetic series 8 + 11 + ... + 29 should be:
Σ_{i=1}^{11} (6i + 2)
The series has 11 terms, and each term can be found by adding 3 to the previous term, starting with the first term 8. Therefore, the general form of the series is 6i + 2, where i represents the index of the term in the series.
In contrast, the notation Σ-2 (3η + 5) appears to have multiple errors. The use of a negative index (-2) is not valid, as the index should start from 1 or 0. Also, the use of the Greek letter eta (η) instead of i as the index variable is unconventional and likely to cause confusion. Finally, the expression inside the parentheses does not appear to correspond to the terms of the arithmetic series.
The correct notation for the arithmetic series 8 + 11 + ... + 29 should be:
Σ_{i=1}^{11} (6i + 2)
To explain the error in the given notation Σ-2 (3η + 5), we can break it down as follows:
The use of a negative index (-2) is incorrect. The index of summation should always be a non-negative integer.
The use of the Greek letter eta (η) instead of i as the index variable is unconventional and may cause confusion or errors.
The expression inside the parentheses, 3η + 5, does not represent the terms of the arithmetic series. In particular, it does not involve the index variable i or the common difference 3.
Therefore, the correct notation for the given arithmetic series is Σ_{i=1}^{11} (6i + 2).
determine what type of transformation is represented
The type of transformation represented in the figure is the translation transformation i.e. (c) none of these
Identifying the type of transformation representedGiven the triangles ABC and A'B'C'
The transformation between the triangles is translation
The translation transformation is a type of transformation that moves an object without changing its size, shape, or orientation.
This transformation involves sliding an object in a particular direction by a certain distance, either horizontally or vertically.
In this case, the direction is horizontally and vertically
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A student wants to investigate the chemical changes that a piece of wood undergoes when it is burned. He believes wood that burns for 15 minutes will weigh less than unburned wood. Design a laboratory experiment that would allow the student to test his predictions, using appropriate equipment and technology. Be sure to consider safety requirements in your answer.
Answer:
Experimental Procedure:
Materials:
Piece of wood
Electronic balance
Bunsen burner
Heat-resistant mat
Stopwatch or timer
Safety goggles
Lab coat
Safety Precautions:
Wear safety goggles and a lab coat to protect your eyes and clothing from any sparks or flames.
Place the heat-resistant mat under the Bunsen burner to prevent any accidental fires.
Use the Bunsen burner only under adult supervision.
Be cautious when handling hot objects, and allow them to cool before touching.
Procedure:
Measure the initial mass of the piece of wood using an electronic balance, and record it in a table.
Light the Bunsen burner, and place the piece of wood over the flame using tongs. Ensure that the wood is fully engulfed in the flame.
Use a stopwatch or timer to time how long the wood burns for (in this case, 15 minutes).
After 15 minutes, turn off the Bunsen burner and remove the piece of wood from the flame using tongs.
Allow the wood to cool, and then measure its final mass using the electronic balance, and record it in the table.
Calculate the difference between the initial and final mass of the wood, and record it in the table.
Repeat steps 1-6 three times to obtain three sets of data.
Calculate the average mass of the burned wood and compare it to the initial mass of the unburned wood to determine if the student's prediction was correct.
Conclusion:
If the average mass of the burned wood is less than the initial mass of the unburned wood, the student's prediction was correct, and he can conclude that the wood underwent a chemical change when it was burned. If the average mass is greater than or equal to the initial mass, the prediction was incorrect, and the student may need to revise his hypothesis or experimental design.
Review the graph of a piecewise function.
The range of the function is the set of all real numbers greater than or equal to -2, because the lowest possible value of the function is -2, which occurs at x = 2.
What is a piecewise function ?
A piecewise function is a function that is defined by different equations on different parts of its domain. The graph of a piecewise function consists of several distinct parts, each corresponding to a different equation.
The graph shown is an example of a piecewise function. The function is defined using different equations on different intervals of the domain.
On the interval from negative infinity to negative 2, the function is defined by the equation y = 2. This means that the value of the function is always 2 on this interval, regardless of the value of x.
On the interval from negative 2 to 2, the function is defined by the equation y = -x. This means that the value of the function is equal to the negative of x on this interval.
On the interval from 2 to positive infinity, the function is defined by the equation y = 2. This means that the value of the function is always 2 on this interval, regardless of the value of x.
At the point x = -2, the function experiences a discontinuity, because the two equations that define it have different values at this point. The function is not differentiable at this point, because it does not have a well-defined tangent line.
The domain of the function is the set of all real numbers, because there are no restrictions on the values of x that are allowed.
Therefore, The range of the function is the set of all real numbers greater than or equal to -2, because the lowest possible value of the function is -2, which occurs at x = 2.
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The surface area of a cylinder is given by the formula SA = 2r2 + 2rh. A cylinder has a radius of 12 cm and a surface area of 1,632 cm^2 . Find the height of the cylinder.
A. 52 cm
B. 56 cm
C. 59 cm
D. 34 cm
Interpret the data in the circle graph. If 560 books were sold at the book fair, find the number of the books that were mystery books.
If 560 books were sold at the book fair,
(Type a whole number.)
of the books were mystery books.
Circle graph
Fantasy 8%
Science
Fiction
12%
Comic 15%
Other 5%
Mystery 20%
-Fictic
Answer:
112
Step-by-step explanation:
According to the circle graph, the mystery books make up 20% of all books sold. So, we can calculate the number of mystery books sold as follows:
Number of mystery books = 20% of 560
= (20/100) x 560
= 112
Therefore, the number of mystery books sold at the book fair was 112.