The approximate zero of P(x) is 1.87, and the polynomial is P(x) = x5 − 2x2 − 12.
When finding the real zero in the interval [1,2] using the Intermediate Value Theorem and polynomial P(x) = x5 − 2x2 − 12, there are several steps to follow. We will outline them below. Step 1: State the Intermediate Value Theorem (IVT)The Intermediate Value Theorem (IVT) states that if a function is continuous on an interval [a,b], then it takes on every value between f(a) and f(b) at least once. This means that if f(a) and f(b) have opposite signs, the function has at least one real zero between them. This is useful when the function cannot be solved explicitly. Step 2: Determine the values of f(1) and f(2)Plugging in 1 and 2 to the polynomial P(x) = x5 − 2x2 − 12, we get: f(1) = (1)5 − 2(1)2 − 12 = −13f(2) = (2)5 − 2(2)2 − 12 = 8Hence, f(1) and f(2) have opposite signs, so by the Intermediate Value Theorem, the polynomial P(x) = x5 − 2x2 − 12 has at least one real zero in the interval [1,2]. Step 3: Approximate the real zero to two decimal placesTo approximate the real zero of P(x), we can use a graphing calculator or an iterative method such as Newton's method. Using a graphing calculator, we find that the real zero of P(x) in the interval [1,2] is approximately 1.87 (rounded to two decimal places).Therefore, the approximate zero of P(x) is 1.87, and the polynomial is P(x) = x5 − 2x2 − 12.
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The quadratic functions f(x) and g(x) are described in the table. x f(x) g(x) −2 4 36 −1 1 25 0 0 16 1 1 9 2 4 4 3 9 1 4 16 0 5 25 1 6 36 4 In which direction and by how many units should f(x) be shifted to match g(x)? Left by 4 units Right by 4 units Left by 8 units Right by 8 units
By inspecting the table, it can be seen that f(x) must be shifted left by 4 units in order to match g(x). Thus, Left by 4 units is the answer.
What is quadratic function?A quadratic function is a function of the form f(x) = ax² + bx + c, where a, b, and c are real numbers and a ≠ 0.
The standard form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are real numbers and a ≠ 0. The solutions of the equation are the points at which the graph of the function intersects the x-axis.
The functions, that are quadratic, f(x) and g(x) are described in the table. From the table, it can be seen that f(x) and g(x) are not equal to each other, as the values for each x are different. To match f(x) and g(x), one of the functions must be shifted.
By inspecting the table, it can be seen that f(x) must be shifted left by 4 units in order to match g(x).
This can be calculated by subtracting the g(x) values from the f(x) values for each x.
For example, at x = -2, the difference between f(x) and g(x) is -32.
This difference is the same for all x values, meaning that f(x) must be shifted left by 4 units to match g(x). Thus, the correct answer is Left by 4 units.
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Kendall washes 10 1/2 windows in 3/4 hours. At this rate, how many windows can she wash in one hour?
Answer:
To find out how many windows Kendall can wash in one hour, we can divide the number of windows washed by the time taken:
Number of windows washed per hour = (Number of windows washed) / (Time taken)
We can first convert the mixed number 10 1/2 to an improper fraction:
10 1/2 = (10 x 2 + 1) / 2 = 21/2
Substituting the given values:
Number of windows washed per hour = (21/2) / (3/4) hours
To divide by a fraction, we can multiply by its reciprocal:
Number of windows washed per hour = (21/2) x (4/3) = 28 windows/hour
Therefore, Kendall can wash 28 windows in one hour at this rate.
Answer:
14 windows
Step-by-step explanation:
All you have to do is a simple equation 10 1/2÷3 which equals 14
A company that records and sells rewritable DVDs wants to compare the reliability of DVD fabricating machines produced by two different manufacturers. They randomly select 500 DVDs produced by each fabricator and find that 484 of the disks produced by the first machine are acceptable and 480 of the disks produced by the second machine are acceptable. Let 1 and 2 = the proportions of acceptable DVDs produced by the first and second machines, respectively.
Are the conditions for calculating a confidence interval for 1−2 met?
Random: met
10%: does not apply
Large Counts: met
Random: met
10%: not met
Large Counts: met
Random: met
10%: does not apply
Large Counts: not met
Random: not met
10%: does not apply
Large Counts: met
Random: met
10%: met
Large Counts: met
If 484 of the disks produced by the first machine are acceptable and 480 of the disks produced by the second machine are acceptable, random , 10% and large counts are met. Correct option is E.
To calculate a confidence interval for the difference between the proportions of acceptable DVDs produced by two different fabricating machines, we need to ensure that the following conditions are met:
Random: The sample of DVDs from each machine should be selected randomly, without any bias. This is important to ensure that the sample is representative of the population of all DVDs produced by each machine.
The sample size should be no more than 10% of the population of DVDs produced by each machine. This is important to ensure that the sampling distribution of the sample proportions is approximately normal.
Large counts: The number of acceptable and unacceptable DVDs in each sample should be large enough to satisfy the normal approximation to the sampling distribution of the sample proportions.
Therefore, the correct answer is (e) Random: met, 10%: met, Large Counts: met. All conditions for calculating a confidence interval for the difference between the proportions of acceptable DVDs produced by two different fabricating machines are met in this scenario.
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Ashley bought stock in a company two years ago that was worth x dollars. During the first years that she owned the stock it decreased by 7%. During the second year the value of the stock decreased by 23%. Wrote an expression in terms of x that represents the value of the stock after two years
After answering the presented question, we can conclude that As a result, the equation that reflects the stock's value after two years in terms of x is: 0.7161x
What is equation?An equation is a mathematical statement that proves the equality of two expressions connected by the equal symbol '='. 2x - 5 Equals 13, for example. Expressions include 2x-5 and 13. The character '=' joins the two expressions. A mathematical formula with two algebraic expressions on either side of an equal sign (=) is known as an equation. It demonstrates the relationship of equivalence between the left and right formulas. In every formula, LHS = RHS (left side = right side).
Because the stock's value fell by 7% after the first year, it is now worth:
x - 0.07x = 0.93x
The stock's value dropped by 23% after the second year, therefore it would be worth:
0.93x - 0.23(0.93x) = 0.93x - 0.2139x = 0.7161x
As a result, the expression that reflects the stock's value after two years in terms of x is:
0.7161x
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There are 16 girls and 20 boys who want to participate in a Trivia Challenge. Each team must have the same ratio of girls and boys.
A. What is the greatest number of teams that can enter? (2 points)
B. Find how many boys and girls would be on each team. (2 points)
Each squad has to have an equal amount of men and women. The maximum number of teams that can participate is 8.
A location in mathematics where a function has its maximum value. The value is an absolute maximum if it exceeds or is equal to all other function values. It is a relative or local maximum if it is simply greater than any neighboring point.
Number of girls = 16.
Number of boys = 20.
In order to calculate the maximum number of teams that can enter, we must determine the most prevalent criteria for both boys and girls based on the information provided. As follows:
Factors of 18 [tex]= 1, 2, 4, 8[/tex] and 16.
Factors of 24 = [tex]1, 2, 3, 4, 6, 8, 12[/tex] and 24.
Highest common factor = 8
Therefore, the greatest number will be 8.
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An invasive species of carp is introduced to Lake Freshwater. Initially there are 100 carp in the lake and the population varies by 20 fish seasonally. If by year 5 , there are 625 carp, find a function modeling the population of carp with respect to t , the number of years from now
modeling function the population of carp with respect to time is: P(t) = 100 * [tex]e^{0.707t}[/tex]
To model the population of carp with respect to time, we can use the following exponential growth formula:
P(t) = P(0) * [tex]e^{rt}[/tex]
where P(0) is the initial population, r is the annual growth rate, and t is the number of years from now.
We know that initially there are 100 carp in the lake, so P(0) = 100.
We also know that the population varies by 20 fish seasonally, so the annual growth rate is:
r = ln(625/100) / 5 = 0.707
Thus, the function modeling the population of carp with respect to time is:
P(t) = 100 * [tex]e^{0.707t}[/tex]
where t is the number of years from now.
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PLEASE HELP WILL GIVE BRAINLIEST
Answer:
Uhm i think its ABD weeweee
Step-by-step explanation:
Because monkeys wooowooo not weewee so the commentary would be weeeweee
Geometry
> P. 11 Similarity and altitudes in right triangles CE7
If FG = 10 and GH=7 what is EG
Therefore , the solution of the given problem of triangle comes out to be EG = 23.14.
What is triangle?A triangle is a hexagon because it has two or more extra polygon sections. Its form is a simple rectangular one. A and B are the only 2 different edges of a form that can set it apart from a regular triangular. When bounds are still not precisely collinear, Euclidean geometry produces a single section rather than a full cube. Three edges and three angles make up a triangle.
Here,
The length of EG can be determined as follows if EF = 24:
First, we calculate the length of FG using the Pythagorean theorem:
=> FG² = EF² - EG²
=> 10² = 24² - EG²
=> EG² = 24² - 10²
=> EG² = 536
=> EG = √536 ≈ 23.14
Consequently, EG 23.14 when FG = 10 and GH = 7 if E is the right angle apex of a right triangle EFG and EF = 24.
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Find X.
A: 78
B: 81
C: 109
D: 95
E: 99
The value of the angle X is 99 degrees. Option E
How to determine the value of the angleTo determine the value of the angle, we need to note that the sum of the interior angles of a given regular polygon is determined with the formula;
(n -2)180
Such that 'n' is the number of sides of the polygon
From the information given, we have that;
The value of n = 6
Then, the sum of interior angles = (6-2)180 = 4(180)
Multiply the values
= 720
Equate the angles
x + 108 + 146 + 101 + 113 + 153 = 720
Add the values
x = 720 - 621
subtract the values
x = 99 degrees
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PLEASE HELP!!!! ASAP
The side length x is given as follows:
[tex]x = \frac{7}{\sqrt{3}}[/tex]
The number that belongs in the green box is of 7.
What are the trigonometric ratios?The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:
Sine of angle = length of opposite side to the angle divided by the length of the hypotenuse.Cosine of angle = length of adjacent side to the angle divided by the length of the hypotenuse.Tangent of angle = length of opposite side to the angle divided by the length of the adjacent side to the angle.For the side x, we have that:
It is opposite to the angle of 30º.The other side is of 7.Hence the tangent can be applied, as follows:
tan(30º) = x/7
x = 7 x tangent of 30 degrees
[tex]x = 7 \times \frac{1}{\sqrt{3}}[/tex]
[tex]x = \frac{7}{\sqrt{3}}[/tex]
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The measure of the length of x is equal to 7/√2 using the trigonometric ratio of tangent for angle 60°.
What are trigonometric ratiosThe trigonometric ratios involves the relationship of an angle of a right-angled triangle to ratios of two side lengths. Basic trigonometric ratios includes; sine cosine and tangent.
recall that tan 60° = √2
tan 60° = 7/x {opposite/adjacent}
√2 = 7/x
by cross multiplication
x = 7/√2.
Therefore, the measure of the length of x is equal to 7/√2 using the trigonometric ratio of tangent for angle 60°.
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in a study of breast cancer, a mother was considered exposed if she first gave birth at 30 years of age or older. among 1,628 mothers who were exposed, 31 subsequently developed breast cancer. among the 4,450 mothers who first gave birth before the age of 30, 65 subsequently developed breast cancer. what type of study design was used for this investigation of the association age at first birth and breast cancer?
The compared to mothers who gave birth for the first time at the age of under 30 to determine the incidence of breast cancer.
The study design used for this investigation of the association between age at first birth and breast cancer is Cohort Study.What is a cohort study?A cohort study is an analytical research approach in which a group of people with a shared trait or experience are followed over time. Cohort studies are used to determine the incidence of a disease, changes in morbidity and mortality rates, and to recognize risk factors for a disease. In this study of breast cancer, the mothers who gave birth for the first time at the age of 30 or older were considered exposed, and they were compared to mothers who gave birth for the first time at the age of under 30 to determine the incidence of breast cancer.
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Order the parts from least to greatest, with 1 being the smallest mass and 5 the greatest mass. 1. Atmosphere
2. 3. 4. 5. 6
the atmosphere has the smallest mass, followed by the oceans, inner core, crust, outer core, and mantle having the largest mass.
Based on the given masses, the order from least to greatest for the parts of the Earth would be:
Atmosphere (5.1 × 10¹⁸ kg)
Oceans (1.4 × 10²¹ kg)
Inner core (9.675 × 10²² kg)
Crust (2.6 × 10²² kg)
Outer core (1.835 × 10²⁴ kg)
Mantle (4.043 × 10²⁴ kg)
Therefore, the atmosphere has the smallest mass, and the list goes according oceans, inner core, crust, outer core, and mantle having the largest mass. The Earth is composed of several layers, including the crust, mantle, outer core, and inner core. The mass of the Earth is distributed unevenly among these layers, with the mantle being the most massive layer, accounting for about 84% (percentage) of the Earth's total mass. The core of the Earth is made up of the outer core and the inner core, which are predominantly composed of iron and nickel. The crust is the thin, outermost layer of the Earth, while the atmosphere is the layer of gases that surround the planet. Despite the atmosphere being the layer with the smallest mass, it plays a critical role in regulating the Earth's climate and sustaining life on the planet.
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Complete question
The mass of Earth is made up of these parts.
oceans 1.4 × 1021kg
crust 2.6 × 1022kg
atmosphere 5.1 × 1018kg
mantle 4.043 × 1024kg
outer core 1.835 × 1024kg
inner core 9.675 × 1022kg
What is the order, from least to greatest, of the masses of each part of Earth? Order the parts from least to greatest, with 1 being the smallest mass and 5 the greatest mass.
CONNECTING CONCEPTS Find the missing dimension of the figure.
The length of the other parallel side of the parallelogram (b2) is 8.3m with the area of the parallelogram 100m².
What is a parallelogram?It is a four-sided shape that has two pairs of parallel lines with all sides equal in length.
The area of the parallelogram is 100m² and the height is 10m, so the base of the parallelogram is 13m. This forms a right triangle with one side of the parallelogram. To calculate the length of the other non-parallel side (b²), we can use the squaring method.
This can be expressed as:
a² + b² = c²
Where a and b are the two shorter sides of the triangle, and c is the longest side.
Substituting in the values given, we get:
x² + 10² = 13²
x²=13²-10²
x= √169-100
x = √69
x = 8.3m
Therefore, the length of the other non-parallel side of the parallelogram (b2) is 8.3m.
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Please help it’s due today Solve x+2/3=9/10
Answer:
[tex]x=\frac{7}{30}[/tex]
Step-by-step explanation:
Solve for x:
[tex]x+\frac{2}{3}=\frac{9}{10}[/tex]
Subtract [tex]\frac{2}{3}[/tex] on both sides
[tex]x=\frac{7}{30}[/tex]
Answer:
X= 7/30
Step-by-step explanation:
subtract 2/3 from both sides.
X+ 2/3 = 9/10
X +2/3 -2/3 =9/10 -2/3
simplify the expression
X + 2/3 -2/3 =9/10 -2/3
X=7/30
Write an exponential function that passes through (0,3) and (1,6). Write your answer in the form f(x) = ab^x
Answer:
[tex]\boxed{f(x)=(3)(2)^x}[/tex]
Step-by-step explanation:
First, we need to substitute the coordinates of the two given points in the ecuation [tex]f(x)=ab^x[/tex]:
[tex]3=ab^{0} \qquad \textbf{ec.1}\\6=ab^{1} \qquad \textbf{ec.2}[/tex]
Remember that any number raised to the power 0 is equal to 1. So:
[tex]3=a \qquad \textbf{ec.3}[/tex]
now, we can substitute in ec.2 and solve for b:
[tex]6=3b\\ b=2[/tex]
Finally:
[tex]f(x)=(3)(2)^x[/tex]
Therefore, we have found the solution to the exercise
[tex]\text{-B$\mathfrak{randon}$VN}[/tex]
please help me with my maths work
The parts of the algebraic expression 3x - 2 are:
3 is the coefficient of x.
x is the variable
2 is the constant term
How to describe an algebraic expression?The algebraic Expression is given as:
3x - 2
Now, some parts of algebraic expressions are coefficients, variables and constant.
Coefficient is defined as the figure or number that is attached to the variable in an algebraic expression.
The variable is the letter that can change because different numbers are used for it.
The constant is the number that stands alone and doesn't change.
Thus, in 3x - 2:
3 is the coefficient of x.
x is the variable
2 is the constant term
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A container in the shape of a triangular prism is used to hold a slice of pizza. The dimensions of the container are shown in the diagram.
Pizza, 10.8 inches, 7.2 inches, 1.5 inches, 9 inches
What is the volume of the container in cubic inches?
For the pizza box shaped in triangular prism, the volume is obtained as 58.32 cubic inches.
What is volume?
Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.
The volume of a triangular prism is given by the formula:
V = (1/2) × base × height × length
where the base and height are the dimensions of the triangular base and the length is the height of the prism.
In this case, the base of the prism is a right-angled triangle with base 10.8 inches and height 7.2 inches.
The area of the base can be found as -
Area = (1/2) × base × height
= (1/2) × 10.8 × 7.2
= 38.88 square inches
The length of the prism is given as 9 inches.
Therefore, the volume of the container can be calculated as -
V = (1/2) × base × height × length
= 38.88 × 1.5
= 58.32 cubic inches
Hence, the volume of the container is 58.32 cubic inches.
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please please please please help me with this question
Answer:
See attached image
Step-by-step explanation:
This is how I did it
I made point A as (0,0)
Point B is 12 units right and 4 units up from A. So B is(12,4)
Point C is 8 units right and 8 units down from A so it is at (8, -8)
When dilated by 1/4 with point A as center of dilation, B coordinates are reduced by 1/4 so the image B' coordinates are (12/4, 4/4) = (3,1)
C coordinates are reduced by 1/4 so C' coordinates of image are (8/4, -8/4) = (2, -2)
The A' coordinates are unchanged at A'(0,0)
So the image is A'B'C' as shown in the blue triangle
I do not know what that other triangle is for, it plays no role in the dilation
I also realize you may have been given some other strategy for solving but this is the way I did it
I hope that works for you.
An airplane can fly with either one engine or both. Each engine has a 0.21 chance of failing. What is the probability that during a 10-hour flight the plane will fail to reach its intended destination or crash?
The probability that during a 10-hour flight an airplane will fail to reach its intended destination or crash is
To solve this problem, we can use the binomial distribution, which gives the probability of k successes in n independent trials, each with the same probability of success p. In this case, a "success" is defined as the engine not failing, and a "failure" is defined as the engine failing.
Let X be the number of engines that fail during the flight. Since each engine can fail independently of the other engine, X follows a binomial distribution with n = 2 (the number of engines) and p = 0.21 (the probability of a single engine failing). The probability of X failures is:
P(X = 0) + P(X = 1) + P(X = 2)
where P(X = k) = (n choose k) * p^k * (1 - p)^(n - k), and (n choose k) is the binomial coefficient.
Using this formula, we can calculate the probability of each possible value of X and add them up:
P(X = 0) = (2 choose 0) * 0.21⁰* 0.79²= 0.6241
P(X = 1) = (2 choose 1) * 0.21¹* 0.79¹= 0.32994
P(X = 2) = (2 choose 2) * 0.21² * 0.79⁰ = 0.04689
Therefore, the probability of the plane failing to reach its intended destination or crashing is:
P(X >= 1) = P(X = 1) + P(X = 2) = 0.32994 + 0.04689 = 0.37683
So the probability of the plane not making it to its destination is about 37.7%.
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Is 96 grater less than or equal to one
Answer: Greater than
Step-by-step explanation: 96 is a larger number than 1
Answer: 96 is greater than one
Step-by-step explanation:
96 is greater than one because if you plot it on a number line in would be far more than zero
Which situation is linear?
Responses
A the population of a town in increasing by ten people each yearthe population of a town in increasing by ten people each year
B the number of cars each hour on a road for a weekthe number of cars each hour on a road for a week
C a sample of bacteria is doubling every daya sample of bacteria is doubling every day
D the cost of a movie ticket increases five percent each yearthe
The linear relation is (a) A the population of a town in increasing by ten people each year
How to determine the linear relationFrom the question, we have the following parameters that can be used in our computation:
The list of options that represent the situations
Situation A is linear because the increase in population is constant and can be represented by a linear equation (y = mx + b),
where y is the population, x is the number of years, m is the slope (10 people per year), and b is the initial population.The equation would be y = 10x + b, where b is the population at year 0.
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Please ASAP Help
Will mark brainlest due at 12:00
Answer:
1
Step-by-step explanation:
we just find the middle of the 2 places
For the problems below, consider the rational function:
x³+x² - 6x/2x²5x+3
c) What are the vertical asymptotes?
Explain/show how you can find them using
the equation.
d) What are the holes?
Explain/show how you can find them using
the equation
e) What are the zeros?
Explain/show how you can find them using
the equation
f)
What is the horizontal/slant
asymptote?
Explain/show how you can find them
using the equation
g) What is the domain?
Explain what you did to find the domain.
Use desmos to check your answers:
Answer:
c) The vertical asymptotes are x = (-5 + √(13))/4 and x = (-5 - √(13))/4. To find them, set the denominator equal to zero and solve for x.
d) There are no holes in the function.
e) The zeros are x = 0, x = 2, and x = -3. To find them, set the numerator equal to zero and solve for x.
f) The slant asymptote is y = x + 2 - (3.5x + 1.5)/(2x^2 + 5x + 3). To find it, use long division to divide the numerator by the denominator. To find the slant asymptote of the given rational function, we use long division to divide the numerator by the denominator. The quotient of the division gives the equation of the slant asymptote.
g) The domain is (-∞, (-5 - √(13))/4) U ((-5 + √(13))/4, ∞). To find it, set the denominator not equal to zero and solve for x. To find the domain of the given rational function, we set the denominator not equal to zero and solve for x. The domain is all real numbers except the values of x that make the denominator equal to zero.
I hope this helps you! I'm sorry if it's wrong! If you need more help, ask me! :]
com S ch Akosua Example 4 Mr. Asiedu and Mr. Amoako run a small business assembling two types of product. The cost of components and the labour needed for each product is shown in the table below. Type A Type B Cost of component 36 24 Labour man- hours 16 24 The business has $156.00 available to buy components each week. The total labour available each week is 96 man-hours. How many products of each type can they assemble each week to maintain maximum production? The y = 3 o Ex Ti- pe W a b What is the equation for production where cost of component and labour man hours is involved.
The number of products of each type that they can assemble each week to maintain maximum production are 3 Type A and 2 Type B.
How to write the required linear equation?In order to write a system of linear equations that could be used to model the situation, we would assign variables to the cost of component and the labour man-hours respectively as follows:
Let the variable c represent the cost of component.Let the variable a represent the labour man-hours.Next, we would translate the word problem into system of linear equations as follows. Since the business has $156.00 available to buy components each week, a linear equation that models the situation is given by;
36x + 24y = 156 .....equation 1.
Additionally, the total labour man-hours available each week is 96 man-hours;
16x + 24y = 96 .....equation 2.
Subtracting equation 2 from equation 1, we have:
20x = 60
x = 3.
y = (96 - 16x)/2
y = (96 - 16(3))/24
y = 48/24
y = 2.
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Solve for x. Round to the nearest tenth, if necessary.
[tex]cos \beta = \frac{adjuscent}{hypotenuse} \\ cos15 = \frac{47}{x} \\ x = \frac{47}{cos15} \\ x = 48.7[/tex]
Which fraction looks same way even if you turn it upside down
Answer:
Question is not asked properly. Details missing. The data is not given.
The plan for a new football stadium calls for the stands to be in a region defined by two concentric ellipses (Figure ). The outer ellipse is to be 240 yd long and 200 yd wide. The inner ellipse is to be 200 yd long and 100 yd wide. A football field of standard dimensions, 120 yd by 160 ft, will be laid out in the center of the inner ellipse.
a. Find particular equations of the two ellipses.
b. Find the eccentricities of the two ellipses.
c. How much clearance will there be between the corner of the field and the inner ellipse in the direction of the end line?
d. The area of an ellipse is where and are the major and minor radii, respectively. To the nearest square yard, what is the area of the stands? If each seat takes about 0.8 square yards, what will be the approximate seating capacity of the stadium?
e. Show that the familiar formula for the area of a circle is a special case of the formula for the area of an ellipse.
The particular equation of the outer ellipse is therefore: 1002x2 + 2402y2 - 2402 * 1002 = 0, the inner ellipse is therefore:502x2 + 2002y2 - 2002 * 502 = 0, Clearance= 343.29 yd and Approximate seats= 47124 seats
The plan for a new football stadium calls for the stands to be in a region defined by two concentric ellipses. The outer ellipse is to be 240 yd long and 200 yd wide. The inner ellipse is to be 200 yd long and 100 yd wide. A football field of standard dimensions, 120 yd by 160 ft, will be laid out in the center of the inner ellipse.
To find the particular equations of the two ellipses, we can make use of the following: standard form of equation of an ellipse:x2/a2 + y2/b2 = 1 The outer ellipse: Major axis = 240 yd = 480 yd/2a = 480/2 = 240 yd Minor axis = 200 yd/2b = 100 yd Now, substituting the values in the standard equation of an ellipse, we have:x2/2402 + y2/1002 = 1Multiplying both sides by 2402 * 1002, we have: 1002x2 + 2402y2 = 2402 * 1002
The particular equation of the outer ellipse is therefore: 1002x2 + 2402y2 - 2402 * 1002 = 0 The inner ellipse: Major axis = 200 yd = 400 yd/2a = 400/2 = 200 yd Minor axis = 100 yd/2b = 50 yd Now, substituting the values in the standard equation of an ellipse, we have: x2/2002 + y2/502 = 1 Multiplying both sides by 2002 * 502, we have:502x2 + 2002y2 = 2002 * 502The particular equation of the inner ellipse is therefore:502x2 + 2002y2 - 2002 * 502 = 0
The eccentricity of an ellipse is given by the formula: e = √(1 - b2/a2)For the outer ellipse: a = 240, b = 100∴ e = √(1 - 1002/2402) = √0.694 = 0.833 For the inner ellipse: a = 200, b = 50∴ e = √(1 - 502/2002) = √0.9375 = 0.968
To find the clearance between the corner of the field and the inner ellipse in the direction of the end line, we need to find the distance between the foci of the inner ellipse, which is given by: d = 2 * √(a2 - b2)where a = 200 yd and b = 50 yd. Substituting the values, we have: d = 2 * √(2002 - 502)≈ 387.29 yd The clearance between the corner of the field and the inner ellipse in the direction of the end line is approximately 387.29 - 120/2 = 343.29 yd.
The area of the stands is the area between the two ellipses. Using the formula given in the question, A = πab, where a = 240 yd/2 and b = 200 yd/2, the area is: A = π * 120 * 100 = 37,699.1 sq yd Approximate seating capacity of the stadium will be number of seats = 37,699.1 / 0.8 = 47123.88 ≈ 47124 seats.
A circle is a special case of an ellipse, where both radii are equal. In the case of a circle with radius r, the formula for the area of an ellipse is reduced to the formula for the area of a circle: A = πab = πr2 = area of a circle
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if there are 850 newborn babies and 335 are boys, what is the probability of randomly selecting a girl? a. 515 b. 0.500 c. 0.606 d. 0.394
The probability of randomly selecting a girl is 0.606. the correct option is (C).
Given that, Total newborn babies = 850
No. of boys = 335
We need to find the probability of randomly selecting a girl baby from this population of 850 babies.
Let G be the no. of girls in the population. Then, G + 335 = 850=> G = 850 - 335=> G = 515
Therefore, the number of girls in the population is 515. Hence, the probability of randomly selecting a girl from the population is:
P (girl) = No. of girls / Total newborn babies= 515 / 850= 0.606
Thus, the correct option is (c) 0.606.
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Zack wheeler had a war of 7. 8 in the 2021 season what does this mean
Zack wheeler had a war of 7. 8 in the 2021 season this means that He scored an average of 7.8 runs per game.
This means that Zack scored an average 7.8 runs per game.
An average is a single number represented as a list of numbers, usually the sum of the numbers divided by the number of numbers in the list (arithmetic mean). For example, the numbers 2, 3, 4, 7, and 9 (for a total of 25) have an average of 5. Depending on the context, the average can be another statistic, such as the median or the mode. Average personal income, for example, is often given as the median – a figure below 50% of personal income and above 50% of personal income – because the average would be higher if some personal income of billionaires were included. Therefore, it is recommended to avoid using the word "average" when referring to measures of central tendency.
Complete Question:
Zack Wheeler had a WAR of 7.8 in the 2021 season. What does this mean?
A. He scored an average of 7.8 runs per game.
B. His team won an average of 7.8 more games than other teams in MLB.
C. His team won around 7.8 more games than it would have with a replacement player.
D. He scored around 7.8 more runs than a replacement player would have.
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Points P,Q,S appear in that order on a line. The ratio PQ:QR is 3:4. The ratio QR:RS is 2:5. The length PQ is 6 in. Find the length PS
Based on according to the ratio given for PQ:QR, The length of side PS on the line is 34 inches.
What is an equation?We can use the ratios given to find the lengths of the other segments and then add them up to get the length of PS.
Let x be the length of QR. Then, according to the ratio given for PQ:QR, we have:
PQ:QR = 3:4
6:x = 3:4
Multiplying both sides by 4x, we get:
24 = 3x
x = 8
So, QR is 8 inches long. Now, using the ratio given for QR:RS, we have:
QR:RS = 2:5
8:y = 2:5
Multiplying both sides by 5y, we get:
40 = 2y
y = 20
So, RS is 20 inches long. Finally, we can add up the lengths of PQ, QR, and RS to get the length of PS:
PS = PQ + QR + RS
PS = 6 + 8 + 20
PS = 34
Therefore, the length of PS is 34 inches.
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