Using the mean value theorem, the least possible value of f(3) is - 2
What is the mean value theorem?The mean value theorem states that for a function f(x) on the interval (a, b), there exists a value c such that
f'(c) = f(b) - f(a)/(b - a)
How to find the least possible value for f(3)?Since ƒ(−1) = 10 and ƒ'(x) ≥−3 for all values of x, we require the least possible value of f(3).
Using the mean value theorem where
b = 3, a = -1 and f'(c) ≥ 3.We choose f'(c) = 3 since f'(x) = 3 is the minimum value of f'(x).
So, substituting the values of the variables into the equation, we have that
f'(c) = f(b) - f(a)/(b - a)
f'(x) = f(3) - f(-1)/(3 - (-1))
f'(x) = f(3) - f(-1)/(3 + 1)
f'(x) = f(3) - f(-1)/4
So, making f(3) subject of the formula, we have that
f(3) = f(-1) + 4f'(x)
Since
f'(x) = 3 and f(-1) = 10,Substituting the values of the variables into the equation, we have that
f(3) = f(-1) + 4f'(x)
f(3) = 10 + 4(-3)
f(3) = 10 - 12
f(3) = - 2
So, the least possible value is - 2
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How can you tell if a graph is linear or logarithmic?
A linear graph will have a straight line, whereas a logarithmic graph will have a curved line.
1. Look at the graph and identify the shape of the line.
2. If the line is straight, then the graph is linear.
3. If the line is curved, then the graph is logarithmic.
When looking at a graph, you can tell if it is linear or logarithmic by examining the shape of the line. A linear graph will have a straight line, whereas a logarithmic graph will have a curved line. This is due to the fact that a linear graph is plotted by plotting the points of a linear equation, whereas a logarithmic graph is plotted by plotting the points of a logarithmic equation. The linear equation is of the form y = mx + b, where m is the slope of the line and b is the y-intercept. The logarithmic equation is of the form y = logb(x), where b is the base of the logarithm. Thus, the shape of the line will depend on the form of the equation used to plot the graph. If the line is straight, then it is a linear graph, and if it is curved, then it is a logarithmic graph.
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two cards are chosen at random from a deck of 52. what is the probability that both cards are numbers (2 through 10) totaling to 12
The probability is 0.3845.The probability of anything occurring is known as probability.
How are probabilities calculated?The probability of anything occurring is known as probability. To determine probability, divide the total number of possible outcomes by the number of possible ways an event could occur.The likelihood or chance that a specific event will occur is represented by a probability. Both proportions between 0 and 1 and percentages between 0% and 100% can be used to describe probabilities.To determine probability, divide the total number of possible outcomes by the number of possible ways an event could occur.Explanation:
2/52 * 10/52 = 20/52 = 0.3845.
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A coat hanger has four knobs, and each knob can be painted any color. If six different colors of paint are available, how many ways can the knobs be painted
If six different colors of paint are available, 360 ways can the knobs be painted.
how many ways can the knobs be painted?A coat hanger has four knobs, and each knob can be painted any color. If six different colors of paint are available,
When examining permutations and combinations, we use factorials. Permutations tell us how many different ways we can arrange things if their order matters. Combinations tells us how many ways we can choose k item from n items if their order does not matter.
coat hanger has four knobs
6! / 4! ( 4!)
6 * 5 * 4* 3 / 4 * 3 * 2* 1 (4 * 3 * 2 * 1)
= 30 * 1 2
=360
360 ways can the knobs be painted.
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. Which of the following is the graph of the equation y = 2x + 3?
Answer:
The graph of the equation y = 2x + 3 is a straight line that passes through the point (0,3) and has a slope of 2.
It can be represented as a set of points in a coordinate plane. The slope of the line is 2, so for every unit increase in x (horizontal coordinate), y (vertical coordinate) increases by 2 units. The y-intercept of the line is 3, so when x is 0, y equals 3.
A line passing through (0,3) with a slope 2 can be represented as (x, 2x + 3)
It is important to note that an equation in the form of y = mx + c, with m being the slope and c being the y-intercept, always represents a straight line in a coordinate plane.
Step-by-step explanation:
Choose three true statements about the angles of the figure
1: Z1 and the 55* angle are adjacent
2: mZ1=55* because Z1 and the 55* angle are vertical angles
3: mZ2=125* because Z2 and the 55* angle are supplementary
4: mZ2 cannot be determined from the information
5: mZ1=180*-55*
6: mZ2=180*-55*-45*
Answer:
2,5,6
Step-by-step explanation:
-Z1 and 55*are vertical angles
-Z1 and 55*are angles on a straight line=180*
this means 180*=55*+Z1
make Z1 subject of the formula- Z1=180*-55*
- mZ2,55*,45* are all angles in the given triangle
since the sum of angles in a triangLe =180*
therefore-180*=Z2+55*+45*
make Z2 the subject of the formulary
Z2=180*-55*-45*
What equation represents a linier function that is proportional
Answer:
d
Step-by-step explanation:
A line with a slope of 0 passes through the points (-2,0) and (-8,c). What is the value of c?
The value of c will be 0.
What is a slope?The slope of a line is defined as the change in y coordinate with respect to the change in x coordinate of that line. The net change in y coordinate is Δy, while the net change in the x coordinate is Δx.
The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
m = y2 - y1 / x2 - x1
where m = 0
y2 = c
y1 = 0
x1 = -2
x2 = -8
0 = c - 0 / -8 - -(2)
0 = c - 0 / -8 + 2
0 = c - 0 / -6
c - 0 = -6(0)
c - 0 = 0
c = 0
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What is the value of log2 base 2?
the value of log2 base 2 is 1 because if base and logrithm value is same then it is always one
How do you find the value of log base 2?
Properties of Log Base 2
Multiply two numbers with base 2, then add the exponents. Divide two numbers with the base 2, subtract the exponents. Power Rule: Raise an exponential expression to power and multiply the exponents.
Use the change-of-base formula:
since we know that natural log and log with base 10 are different
So, if we want to write log3(6) as a logarithm of base 2, in these example a = 3, x = 6, b = 2:
Hence , the value of log2 base 2 is 1 because if base and logrithm value is same then it is always one
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A high school statistics class wants to conduct a survey to determine what percentage of students in the school would be willing to pay a fee for participating in after-school activities. Twenty students are randomly selected from each of the freshman. sophomore. junior, and senior classes to complete the survey. This plan is an example of which type of sampling ? a. Cluster
b. Convenience c. Simple random d. Stratified random e. Systematic
A high school statistics class wants to conduct a survey to determine what percentage of students in the school would be willing to pay a fee for participating in after-school activities. Twenty students are randomly selected from each of the freshman. sophomore. junior, and senior classes to complete the survey. This plan is an example of Stratified random type of sampling .
What does "stratified random sampling" mean?
A population is divided into smaller subgroups known as strata as part of a sampling technique called stratified random sampling.
During stratified random sampling, also known as stratification, groups of people are divided into groups based on shared traits or characteristics, such as level of education or income.
What is a good illustration of a stratified sampling technique?
A stratified sample is one that guarantees that the various strata (subgroups) of a given population are fairly represented in the sample population as a whole.
One could, for instance, divide a sample of persons into age-related subgroups, such as 18–29, 30-39, 40–49, 50–59, and 60 and above.
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Evaluate the gradient of f(x, y, z) = log(x2 + y2 + z2) at (1, 0, 1)
The gradient of f(x, y, z) = log(x2 + y2 + z2) at (1, 0, 1) is (2/1, 0, 2/1)
This gradient is a vector that points in the direction of the greatest rate of increase of the function f(x, y, z) = log(x2 + y2 + z2). To evaluate this gradient, the partial derivatives of the function with respect to x, y, and z must be calculated.
The partial derivative of the function with respect to x is (2x / (x2 + y2 + z2)). When x is 1, this simplifies to 2/1. Similarly, the partial derivative with respect to y is 0, and the partial derivative with respect to z is (2z / (x2 + y2 + z2)), which simplifies to 2/1 when z is 1. Therefore, the gradient of f(x, y, z) = log(x2 + y2 + z2) at (1, 0, 1) is (2/1, 0, 2/1).
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Given ƒ(x) = − x² – 14, find ƒ (6)
Answer:
f(6) = - 50
Step-by-step explanation:
substitute x = 6 into f(x) , that is
f(6) = - 6² - 14 = - 36 - 14 = - 50
Answer:
-50
Step-by-step explanation:
f ( x ) = - x² - 14
Accordingly, to find the value of f ( 6 ) you have to replace x with ( 6 ).
f ( 6 ) = - (6)² - 14
f ( 6 ) = - 36 - 14
f ( 6 ) = -50
B. ) For Service B, is the additional charge per mile greater or less than 30 cents per
mile of the trip? Explain your reasoning.
The additional charge per mile for Service B is less than 30 cents per mile of the trip. This is because the rate for Service B is 20 cents per mile plus a flat fee of $10, which works out to less than 30 cents per mile for longer trips.
For a trip of 10 miles, Service B would cost
(10 x 0.20) + 10
= $12.
For a trip of 20 miles, Service B would cost
(20 x 0.20) + 10
= $22.
Therefore, the additional charge per mile for Service B is
(12/10)
= 1.2 for the 10 mile trip and
(22/20)
= 1.1 for the 20 mile trip.
Both of these are less than 30 cents per mile.
The additional charge per mile for Service B is less than 30 cents per mile of the trip because the rate for Service B is 20 cents per mile plus a flat fee of $10, which works out to less than 30 cents per mile for longer trips. To demonstrate this, for a 10 mile trip, the total cost would be $12, and for a 20 mile trip, the total cost would be $22. This works out to an additional charge per mile of 1.2 and 1.1 cents respectively, which are both less than 30 cents per mile.
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A recipe ue 1/3 cup of flour and 1/8 cup of ugar. How much flour and ugar doe the recipe ue altogether
Altogether, the recipe uses 1/2 cup of flour and 1/8 cup of sugar.
What is altogether?Altogether in math refers to the sum of two or more numbers or values. It is a way of combining two or more items to obtain a total. In math, the term "altogether" is used to denote the sum of all the individual items, as opposed to all of them considered as one. For example, the sum of the numbers 2, 4, and 6 is 12, which is the "altogether" in math.
To calculate this, we must convert the fractions into decimals and then add them together.
The 1/3 cup of flour can be converted to 0.33 cup, and the 1/8 cup of sugar can be converted to 0.125 cup.
When added together, they equal 0.455 cup, or 1/2 cup. Therefore, the recipe uses a total of 1/2 cup of flour and 1/8 cup of sugar.
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The perimeter of a rectangle is 84cm and it's length is 6cm longer than it's breadth. Find the length and breadth of the rectangle
Answer:
Step-by-step explanation:
The perimeter of a rectangle is the sum of all its sides. Since the perimeter is given as 84 cm, we can set up the following equation to represent the problem:
2l + 2b = 84
Where l is the length of the rectangle and b is the breadth.
We are also told that the length is 6 cm longer than the breadth. We can represent this relationship with the equation:
l = b + 6
Substituting the second equation into the first equation, we get:
2(b + 6) + 2b = 84
Expanding the left side of the equation gives:
2b + 12 + 2b = 84
Combining as terms gives:
4b + 12 = 84
Subtracting 12 from both sides gives:
4b = 72
Dividing both sides by 4 gives:
b = 18
Substituting this value back into the equation l = b + 6 gives us:
l = 18 + 6
l = 24
Therefore, the length of the rectangle is 24 cm and the breadth is 18 cm.
What is the difference between an undecidable problem and an intractable problem?
Therefore , the solution of the given problem of tractable problem comes out to be Undecidable troubles are those for which there will never be a computer solution.
What does a tractable problem actually mean?a technique that completes a manageable task in a polynomial period of time. Utilizing the polynomial upper bound is advantageous. A problem is said to be intractable if it cannot be solved in a polynomial amount of time. The bound has a minimum that is exponential.
Here,
Intractable problems would be those in which there is significant proof that, while they can be solved by a desktop, they cannot be solved quickly enough to be actually useful in practice.
Undecidable troubles are those for which there will never be a computer solution, whereas undecidable difficulties are those for which there will never be a computer solution.
Therefore , the solution of the given problem of tractable problem comes out to be Undecidable troubles are those for which there will never be a computer solution.
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A colony of 100,000 bacteria doubles every 31 minutes. To the nearest whole number, what will the population be 124 minutes from now?
Answer:
Below
Step-by-step explanation:
How many times will the colony double ? 124 / 31 = 4 times
2^4 * 100 000 = 1 600 000
What is the best sequence of names to
identify the elements of this set of
numbers?
(0.67,3-√4,√8,0.14)
1) real, rational, irrational, irrational,
irrational
2) rational, real, integer, irrational,
irrational
3) rational, rational, real, real,
irrational
4) rational, rational, integer, irrational,
rational
On solving the provided question, we can say that - sequence (0.67,3-√4,√8,0.14) are the rational, real, integer, irrational, irrational.
what is a sequence?A sequence is a collection of numerals (referred to as "terms"), for example, 2, 5, 8. A specific pattern that some sequences follow may be leveraged to make them infinitely long. To continue the series, add 3 and use the example of 2,5,8. Formulas that show where to look for words inside a sequence can be found there. Informally, a sequence in mathematics is a collection of items that are in some order (or events). It has components, much like a set (also called elements or terms). The length of the sequence refers to the total, potentially unlimited number of ordered items. arranging two or more objects in a logical sequence. Chronological.
here,
the given sequence is (0.67,3-√4,√8,0.14)
as we can see that in the sequence we have a rational number, integer, real number and a irrational so,
the answer is rational, real, integer, irrational, irrational.
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For each set of values for a and b evaluate the given expressions and record your answers in the table. ( I only need this one).
A = -1/2 B =6
A divided by -b
PLEASE HELP
Answer:
Set1 = 1/12
Set2 = 1/12
Set3 = -12
Step-by-step explanation:
Substitute, use Keep-Change-Flip to handle division when there's fractions involved. See image.
Also to multiply fractions, multiply
top×top and bottom×bottom straight across. Also negative times a negative is a positive and negative is like opposite so -(-6) is 6 and -(-1/2) is 1/2.
see image.
The experimental calculation of the specific heat of aluminum was found to be. 156 cal/g °C, but the actual value was given as. 185 cal/g °C. What is the percent error?
The percentage error is 16%
We know that the formula for the percentage error.
E = (absolute error / actual value) × 100
The formula for the absolute error is:
A = |actual value - experimental value|
A = |V1 - V2|
where V1 is the actual value
V2 is the experimental value
E is the percentage error
A is the absolute error
In this question, the experimental calculation of the specific heat of aluminum = 156 cal/g °C
And the actual specific heat of aluminum = 185 cal/g °C
Using above formula of absolute error,
A = |185 - 156|
A = 29 cal/g °C
And the percent error would be,
E = (absolute error / actual value) × 100
E = (29 / 185) × 100
E = 0.16 × 100
E = 16%
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What is y 0 on a graph?
y=0 is the linear equation to denote the x - axis, as all the points on the x- axis, have their y co-ordinate =0.
What is linear equation ?
A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept. Occasionally, the above is called a "linear equation of two variables," where y and x are the variables.
Because the equation y=0 has a slope of 0, the resulting graph must be a straight horizontal line. This is true for all equations with a slope of 0.
Hence , y=0 is the linear equation to denote the x - axis, as all the points on the x- axis, have their y co-ordinate =0.
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Adam is trying to spot a meteor. The probability he will see one in the next 10 minutes is 0.56.
What are the odds in favor of Adam seeing a meteor in the next 10 minutes?
Answer: The odds in favor of an event happening are the ratio of the probability of the event happening to the probability of the event not happening. To find the odds in favor of an event, you can use the formula:
Odds in favor = probability of event occurring / (1 - probability of event occurring)
In this case, the event is that Adam will see a meteor in the next 10 minutes. The probability that this event will occur is 0.56. Therefore, the odds in favor of this event occurring are:
Odds in favor = 0.56 / (1 - 0.56)
= 0.56 / 0.44
= 1.27
So, the odds in favor of Adam seeing a meteor in the next 10 minutes are 1.27 to 1.
It means that Adam is 1.27 times more likely to see a meteor in the next 10 minutes than not seeing one.
Step-by-step explanation:
The odds in favor of Adam seeing a meteor in the next 10 minutes are 14 : 11
I WILL MARK BRAINLYIST
Describe a meal that you could put together that provides 4 servings of both a main
course and a side dish. Explain how you know that it will not exceed the weight limit of the box
A meal that you could put together that provides 4 servings of both a main
course and a side dish and not exceeding the weight limit is 4 servings of
chicken and 4 servings of baked beans.
What are the types of representing data?Data refers to the elements that make up persons, things, events, and ideas. It could be an integer, a title, or anycast. Data must be tabulated after collection in order to study their prominent characteristics. The presentation of data is the name given to such a configuration.
Bar Chart, Histogram, Line Graph, Pie Chart, Frequency Distribution Table.
Given, Each box can hold a maximum of 44 ounces.
By observing the given table we see 4 servings of chicken would weight
2×12.6 oz = 25.2 oz.
And 4 serves of baked beans weigh 14.2 oz.
Therefore, The total serving would weigh (25.2 + 14.2) oz.
= 39.4 oz.
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What is the circumference of a circle with sector area 9π and arc measure 90 degrees?
By using the area of circle formula, the solution of the given problem of circle comes out to be 6 + π cm
Describe the circle.Every location in the plane of a circle is equally separated from the center and is a closed, as double object. Each line tracing the circle contributes to the formation of a line of reflection symmetry. Additionally, each angle has axis of symmetry around the center.
Here,
A 9 Pi square centimeter circle's sector has a 60 degree center angle. The sector's exterior border is
Circle area is equal to. πR² = 9π
Circumference =2πR
=> 2π*3 = 6π cm
Arc length equals (60/360)*6 to cm
Arc's perimeter is calculated as follows: Radius + Length of Arc + Radius = π +3 + 3 = 6 + π cm
Therefore , the solution of the given problem of circle comes out to be
6 + π cm.
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By using the area of circle formula and circumference of a circle formula, the solution of the given problem of circle comes out to be 12π cm
Describe the circle.Every location in the plane of a circle is equally separated from the center and is a closed, as double object. Each line tracing the circle contributes to the formation of a line of reflection symmetry. Additionally, each angle has axis of symmetry around the center.
Here,
sector area of circle = 9π
arc measure = 90°
Area of sector = (arc/360°)*πr²
⇒ 9π = (90°/360°)πr²
⇒ 9π = (1/4)πr²
⇒ 4*9π = πr²
⇒ 36 = r²
⇒ 6² = r²
r = 6
and Circumference of circle = 2πr
=> 2π*6 = 12π cm
Therefore , the solution of the given problem of circle comes out to be
12π cm.
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How do you solve 2 polynomial equations?
The steps to solve two polynomial equations are given below.
What is polynomial?
A polynomial is a mathematical expression made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables.
x^2 + 4x + 7 is an illustration of a polynomial with a single indeterminate x.
Apply the Zero Factor Property to an Equation Solving.
ZERO. FACTOR, write the equation with one side equal to zero. the expression by a factor.
PROPERTY. Solve the equation by setting each factor to zero.
Check by adding substitutes to the initial equation.
Write a polynomial equation in standard form before attempting to solve it. Factor it, then set each variable factor to zero once it has reached zero. The original equations' solutions are the solutions to the resulting equations. Factoring cannot always be used to solve polynomial equations.
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Which expression is equivalent to
Answer:
4 ^ -8
Step-by-step explanation:
How do you find the zero’s algebraically?
To find the zeros of a polynomial algebraically, you can use the following steps:
Write the polynomial in standard form, with the terms arranged in descending order of the degree of the term. For example, if the polynomial is 3x^2 - 2x + 5, it is already in standard form.
Set the polynomial equal to zero. For example, if the polynomial is 3x^2 - 2x + 5, you would set the equation equal to zero like this:
3x^2 - 2x + 5 = 0
Use the quadratic formula to find the solutions (i.e., the zeros) of the equation if the polynomial is a quadratic (degree 2). The quadratic formula is:
x = (-b +/- sqrt(b^2 - 4ac)) / (2a)
where a, b, and c are the coefficients of the polynomial, and sqrt represents the square root.
For example, if the polynomial is 3x^2 - 2x + 5, the solutions would be:
x = (-(-2) +/- sqrt((-2)^2 - 4 * 3 * 5)) / (2 * 3)
x = (2 +/- sqrt(4 - 60)) / 6
x = (2 +/- sqrt(-56)) / 6
Since the square root of a negative number is not a real number, there are no real solutions (zeros) for this polynomial.
Use the Rational Root Theorem to find the solutions of the equation if the polynomial is not a quadratic. The Rational Root Theorem states that if a polynomial of degree n has a rational root p/q (where p and q are integers and q is not equal to zero), then p must be a divisor of the constant term and q must be a divisor of the coefficient of the term of highest degree.
For example, if the polynomial is x^3 - 2x^2 + x - 6, the constant term is -6 and the coefficient of the term of highest degree is 1. The divisors of -6 are -6, -3, -2, -1, 1, 2, 3, and 6. The divisors of 1 are 1 and -1. Therefore, the possible rational roots of this polynomial are -6, -3, -2, -1, 1, 2, 3, and 6.
To find the actual roots, you can try each of these numbers as a root and see if it works. For example, if you try -6 as a root, you would get:
(-6)^3 - 2(-6)^2 + (-6) - 6 = 0
(-216) - (-72) + (-6) - 6 = 0
-144 - 6 - 6 = 0
-156 = 0
This equation is not true, so -6 is not a root of the polynomial. You can repeat this process for each of the other possible rational roots until you find all of the roots of the polynomial.
a forest covers 59,000 acres. A survey finds that 0.6% of the forest is old oak trees How many are acres of old oak trees are there?
Answer:
354acres
Step-by-step explanation:
Total acre = 59000
Percentage of old oak acre trees is 0.6%
Therefore, the acres of old trees are calculated:
59000 * (0.6÷100) = 354acres
An elliptical mirror measures 16 inches wide and 20 inches high. The ellipse is centered at (0, 52) on a coordinate plane, where units are in inches. Which equation represents the mirror?
(y - 52)²/400 + x²/256 = 1
(y – 52)²/100+ x²/64 = 1
X²/400+ (y-52)²/256 = 1
x²/100+(y-52)²/64 = 1
Equation of ellipse is x²/400 + (y-52) ²/256 =1
What is ellipse?An ellipse is an oval shaped close geometrical figure. Ellipse has two radius, one is horizontal, and the other is vertical. An ellipse can be stretched either horizontal direction or vertical direction.
Which equation represent the mirror?given, width of elliptical mirror = 16 inches
height of elliptical mirror = 20 inches
the center of ellipse = (0, 52)
as the width of elliptical mirror is less than height so the ellipse has vertical major axis.
vertical radius is denoted by b.
and horizontal radius is denoted by a.
as per the question, a = 16 inches and b = 20 inches.
we know the equation of ellipse whose major axis is vertical and center at the origin is shown by
x² / b² + y²/ a² = 1
we are given information about an ellipse having center (0, 52) and vertical radius 20 and horizontal radius 16.
the equation of this ellipse is.
x² / (20) ² + (y -52) ²/ (16)² = 1
x²/400 + (y - 52) ² /256 = 1
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HELP BRAINLIEST FOR FASTEST AND CORRECT NO NEED TO EXPLAIN
Answer:
The answer is 48
Step-by-step explanation:
Answer:
48 students
4*12=48
Bilquis finds some nickels and quarters in her piggy bank. How much money (in
cents) does she have if she has 7 nickels and 5 quarters? How much money
does she have if she has n nickels and q quarters?
Answer:Bilquis finds some nickels and quarters in her piggy bank. How much money (in
cents) does she have if she has 7 nickels and 5 quarters? How much money
does she have if she has n nickels and q quarters?
Step-by-step explanation:
Answer: 157 cents ($1.57)
Step-by-step explanation: Nickels are worth 5 cents each, so 5 cents times 7 nickels equals a total of 35 cents. After that, we have 5 quarters which cost 25 cents each, so 25 cents times 5 quarters equals a total of 125 cents. Combine these two products, and you get 157 cents. Or, if you want it in dollars, you can divide 157 by 100 cents (there are 100 cents in a dollar) and end up with $1,57.