Answer:
Mean of given observations = Sum of given observations Total number of observations
∴11=x+(x+2)+(x+4)+(x+6)+(x+8)÷5
⇒55=5x+20
5x=55-20
5x=35
x=35/5
x=7
Hence, the value of x is 7.
help me please! thanks bud
Answer:
Steps:
1. Draw a 3 x 3 table
2. Place the titles on the left and top of the table (play sports and don't play sports on left for example and instruments on top)
3. Place the numbers inside accordingly
Hope this helped! Please mark brainliest!
a jury has 12 jurors. a vote of at least 10 of 12 for guilty is necessary for a defendant to be convicted of a crime. assume that each juror acts independently of the others and that the probability that anyone juror makes the correct decision on a defendant is .80. if the defendant is guilty, what is the probability that the jury makes the correct decision? round your answer to 4 decimal places.If the defendant is guilty, the probability that the jury makes the correct decision is ____
The probability that the jury makes the correct decision is 0.9999
This is a binomial distribution problem where the event of interest is a juror making a correct decision (voting guilty) and the number of trials is 12 (the number of jurors).
The probability of a single juror making the correct decision is 0.80. Therefore, the probability of a single juror making the incorrect decision (voting not guilty) is 1 - 0.80 = 0.20.
To calculate the probability that at least 10 out of 12 jurors make the correct decision (voting guilty) if the defendant is guilty, we can use the binomial distribution formula:
P(X ≥ 10) = 1 - P(X < 10)
where X is the number of jurors who make the correct decision.
Since the probability of a single juror making the correct decision is 0.80, we can use the binomial probability formula to calculate the probability of X jurors making the correct decision
P(X = x) = (12 choose x) * 0.80^x * 0.20^(12-x)
where (12 choose x) is the number of ways to choose x jurors out of 12.
Using this formula, we can calculate the probability of fewer than 10 jurors making the correct decision:
P(X < 10) = P(X = 0) + P(X = 1) + ... + P(X = 9)
We can use a calculator or software to calculate this probability:
P(X < 10) = 0.00000436
Therefore, the probability of at least 10 out of 12 jurors making the correct decision if the defendant is guilty is:
P(X ≥ 10) = 1 - P(X < 10) = 1 - 0.00000436 = 0.99999564
Rounding to four decimal places, the probability is 0.9999.
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1
1
About of a fruit punch is pineapple juice. About of the punch is orange juice. Write and solve an equation to find the
10
fraction of the punch that is pineapple juice or orange juice.
Select the correct equation below, and fill in the answer box to complete your choice.
An equation to find the fraction of punch that is either pineapple juice or orange juice is 1/6 + 1/9 = 5/8.
What is a fraction?In Mathematics, a fraction simply refers to a numerical quantity (numeral) which is not expressed as a whole number. This ultimately implies that, a fraction is simply a part of a whole number.
Based on the information provided about the pineapple juice and orange juice, an equation that can be used for determining the fraction of punch that is either pineapple juice or orange juice is as follows;
Fraction = 1/6 + 1/9
Fraction = 3/18 + 2/18
Fraction = 5/18
In this context, we can reasonably infer and logically deduce that exactly 5/18 of the punch is either pineapple juice or orange juice.
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Complete Question:
About 1/6 of a fruit punch is pineapple juice. About 1/9 of the punch is orange juice. Write and solve an equation to find the fraction of the punch that is pineapple juice or orange juice.
a newsletter publisher believes that 71% 71 % of their readers own a rolls royce. a testing firm believes this is inaccurate and performs a test to dispute the publisher's claim. after performing a test at the 0.02 0.02 level of significance, the testing firm fails to reject the null hypothesis. what is the conclusion regarding the publisher's claim?
We cannot claim that the newsletter publisher's statement is incorrect. Hence, the conclusion is uncertain.
The newsletter publisher's claim is uncertain after performing a test at the 0.02 level of significance as the testing firm fails to reject the null hypothesis.
In this case, we cannot claim that the publisher's statement is incorrect without additional tests and proof. Here is an explanation of the above statement.
A hypothesis test is conducted to find out whether or not there is sufficient evidence to contradict a hypothesis. In this case, the hypothesis test's null hypothesis claims that the newsletter publisher's statement is correct.
The alternate hypothesis claims that the newsletter publisher's claim is incorrect. As a result, the null hypothesis is represented by [tex]H_0[/tex]:
p = 0.71 (71%) and
the alternate hypothesis is represented by [tex]H_a[/tex]:
p ≠ 0.71 (71%).
Where 'p' denotes the percentage of newsletter readers who own a Rolls Royce.
The test statistic for a sample proportion can be calculated by
z = (p - P) / √(P(1 - P) / n)
Where 'p' denotes the sample proportion,
P denotes the population proportion, and
n denotes the sample size.
A two-tailed test is used because the alternate hypothesis is written as [tex]H_a[/tex]:
p ≠ 0.71 (71%).
At a 0.02 significance level, the test statistic's critical value is ±2.58 (round off) Because the test statistic does not fall in the rejection region, we fail to reject the null hypothesis.
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AUGH WHAT EVEN IS!!PLEASE HELP
The length of the base of the given parallelogram is 2 feet.
The area of a parallelogram is all the square units that fit inside, measured in square units (cm2, m2, in2, etc.). It is the area surrounded or enclosed by parallelograms in two places. The elements of a parallelogram. Since a rectangle and a parallelogram have the same properties, the area of the rectangle is the same as that of the parallelogram.
Given us the area in sq. feet but height in yards, So let's convert the height in feet instead.
We know, 1 yard = 3 feet
∴ Height = 5 feet.
Now, We know
⇒ Area = Base × Height
⇒ 10 = Base × 5
⇒ Base = 2 feet
Hence, The length of the base of the given parallelogram is 2 feet.
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Evaluate the expression: |8| - 2 x |-3| + 4
22
10
42
6
Answer:
6
Step-by-step explanation:
The work, W (in joules), done when lifting an object is jointly proportional to the product of the mass, m (in kilograms), of the object and the height, h (in meters), that the object is lifted. The work done when a 100-kilogram object is lifted 1.5 meters above the ground is 2116.8 joules.
The constant of proportionality for the work done when lifting an object is given as follows:
k = 14.78.
What is a proportional relationship?A proportional relationship is a type of relationship between two quantities in which they maintain a constant ratio to each other. This means that if one quantity is multiplied by a certain factor, the other quantity will also be multiplied by the same factor.
The equation that defines the proportional relationship is given as follows:
y = kx.
In which k is the constant of proportionality, representing the increase in the output variable y when the constant variable x is increased by one.
The work, W (in joules), done when lifting an object is jointly proportional to the product of the mass, m (in kilograms), of the object and the height, h (in meters), that the object is lifted, hence the equation is given as follows:
W = khm.
The work done when a 100-kilogram object is lifted 1.5 meters above the ground is 2116.8 joules, the the constant is given as follows:
150k = 2216.8
k = 2216.8/150
k = 14.78.
Missing InformationThe problem asks for the constant of the proportional relationship.
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A bird travels 71. 2 kilometers after 2 hours of flying. Complete the equation to represent the number of hours, t, the bird will take to fly d kilometers at this rate
the equation to represent the number of hours, t, the bird will take to fly d kilometers at this rate is t = 2d / 71.2
We can use the formula for distance, rate, and time:
distance = rate x time
We can rearrange this formula to solve for time:
time = distance / rate
If we substitute the given distance of 71.2 km and rate of (71.2 km / 2 hours) into this formula, we can find the time it took the bird to fly 71.2 km:
time = 71.2 km / (71.2 km / 2 hours) = 2 hours
Now, we can use the same formula to find the time it will take the bird to fly d kilometers:
time = d km / (71.2 km / 2 hours) = 2d / 71.2 hours
Therefore, the equation to represent the number of hours, t, the bird will take to fly d kilometers at this rate is t = 2d / 71.2
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Find the frequency with the largest amplitude Find the frequency w for which the particular solution to the differential equation dạy dy 2- + dt2 + 2y = eiwt dt has the largest amplitude. You can assume a positive frequency w > 0. Probably the easiest way to do this is to find the particular solution in the form Aeiwt and then minimize the modulus of the denominator of A over all frequencies w. W= number (rtol=0.01, atol=1e-08) ?
The frequency with largest amplitude for the particular solution to the differential equation is w = 0.707 (approximately).
To find the frequency with the largest amplitude, we can assume that the particular solution to the given differential equation is of the form:
y(t) = Aeiwt
Taking the first and second derivatives of y(t), we get:
dy/dt = iwtAeiwt
d2y/dt2 = -w2Aeiwt
Substituting these into the differential equation, we get:
-w2Aeiwt + 2Aeiwt = eiwt
Simplifying, we get:
A = 1 / (1 - 2iw2)
The amplitude of y(t) is given by |A|, which is:
|A| = 1 / |1 - 2iw2|
To find the frequency w for which |A| is largest, we need to minimize the modulus of the denominator of A over all frequencies w. We can do this using numerical optimization methods. So, frequency is 0.707.
Therefore, the frequency with the largest amplitude is w = 0.707 (approximately).
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21.
Ada Mae bought a pen for $1.50 and 3 DVDs that each cost the same amount. She spent $22.50
in all. Which equation models the situation?
A, 1.5+3d=22.5
B. 3(1.5) +d=22.5
C. 3d-1.5=22.5
D. 1.5=22.5+3d
Items: 1 Pen: 1.50
3 DVDS: ???
Total : 22.50
It is A, 1.5+3d=22.5.
Hope this helps!!!
It is not B because you are not multiplying the number and cost of 3 DVDS by the cost of one pen.
It is not C because you are not subtracting to find the total cost. You are adding.
It is not D because 3d is part of the total cost so that option just doesn't make sense.
please help i have until saturday
After answering the provided question, we can state that As a result, the equation shortcut is approximately 72.1 metres long. The length is 72.1 metres, rounded to the nearest tenth.
To calculate the length of the shortcut, we must apply the Pythagorean theorem, which states that the square of the hypotenuse (the longest side) in a right triangle is equal to the sum of the squares of the other two sides. The hypotenuse in this case is the shortcut PQ, and the other two sides are the distances from P to the park's corner (which we'll call A) and from Q to A.
shortcut length2 = 402 + 602
shortcut length2 = 1600 + 3600
shortcut length2 = 5200 = 72.1 metres
As a result, the shortcut is approximately 72.1 metres long. The length is 72.1 metres, rounded to the nearest tenth.
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A tangent segment is a line segment that has a point on the tangent line and on the center of the circle.
It is a true statement that tangent segment is a line segment that has a point on the tangent line and on the center of the circle.
What does tangent segment means on a Circle?In geometry, a tangent segment is a line segment that intersects a circle at exactly one point, known as the point of tangency. This line segment is called a tangent because it touches the circle at a single point and does not cross through the circle.
The tangent segment's length is determined by the distance between the point of tangency and a point on the line that is outside the circle, known as the external point. This distance is equal to the radius of the circle, as the radius is the distance between the center of the circle and any point on the circle's circumference.
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Which of the following is closest to the circumference of a circle that has a diameter of 8 inches?
Answer: The formula for the circumference of a circle is C = πd, where d is the diameter of the circle.
If the diameter of the circle is 8 inches, then:
C = πd
C = π(8)
C = 8π
Using an approximation of π as 3.14, we can estimate the circumference:
C ≈ 8 × 3.14
C ≈ 25.12
Therefore, the answer closest to the circumference of the circle is 25.12 inches.
Step-by-step explanation:
The larger leg of a right triangle is 3 cm longer than its smaller leg. The hypotenuse is 6 cm longer than the? smaller leg. How many centimeters long is the smaller leg
Answer:
3cm or 1.5
Step-by-step explanation:
Long leg = radical of 3
Short leg = 1
Hypotenuse= 2
A town in the shape of a trapezoid
is shown below. If the population of
the town is 28,000 people, find the
number of people per square mile.
14 mi
12 mi
21 mi
16.6 mi
In Linear equation, 121 the number of people per square mile.
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) component, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables. Equations with variables of power 1 are known as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.
A = (12 + 21) * 14 * 1/2
= 33 * 14 * 1/2
= 231 mi²
28000 ÷ 231 = 121 people
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The function f(x)=x^3 is expanded vertically by a factor of 2, translated down 2 unitsWrite the equation of the transformed function.
To vertically expand a function by a factor of 2, we multiply the function by 2. Thus, the transformed function becomes g(x) = 2f(x) = [tex]2(x^3)[/tex].
To translate a function down 2 units, we subtract 2 from the original function. Thus, the transformed function becomes h(x) = g(x) - 2 = 2[tex](x^3)[/tex] - 2.
So the equation of the transformed function is h(x) = 2[tex](x^3)[/tex] - 2.
Graphically, the transformation of the function f(x) = [tex]x^3[/tex] into h(x) = 2[tex](x^3)[/tex] - 2 means that the graph of h(x) is twice as tall as the graph of f(x) and shifted 2 units downwards. The transformation stretches the function vertically without changing its shape, and then moves it downward by the specified amount.
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Consider parallelogram QRST below.
Use the information given in the figure to find mZR, m/RSQ, and x.
3x
66°
53°
S
12
R
m/R =
m/RSQ =
X =
X
The answers of following questions are given as follows:- m∠R = 114°
m∠RSQ = 13°
TQ = SR = 3x
What is parallelogram?Quadrilateral which is made up of 2 pairs of parallel sides. The opposite sides are parallel and equal in length in a parallelogram.
Since QRST is a parallelogram, opposite angles are congruent. Therefore, we have:
m∠R = m∠T = 180° - m∠QTS = 180° - 66° = 114°
Also, since QRST is a parallelogram, opposite sides are congruent. Therefore, we have:
SR = TQ = 3x
Finally, we can use the fact that the sum of the angles in a triangle is 180° to find m∠RSQ:
m∠RSQ = 180° - m∠QST - m∠T = 180° - 53° - 114° = 13°
Note that we cannot solve for x since we have only one equation and two unknowns.
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What is the equivalent?
Drag the answer into the box to match the fragative.
The equivalent decimal of a fraction of 6/11 is given as follows:
0.5454.
How to obtain the equivalent decimal of a fraction?To obtain the equivalent decimal of a fraction, divide the numerator (the top number) by the denominator (the bottom number) using a calculator or long division.
The fraction for this problem is given as follows:
6/11.
The numerator and the denominator of the fraction are given as follows:
Numerator of 6.Denominator of 11.The division of 6 by 11 has a result of 0.5454, hence the equivalent decimal of the fraction is given as follows:
0.5454.
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weight loss x runs a number of weight reduction centers within a large city. from the historical data it was found that the weight of the participants is normally distributed with a mean of 175 lbs and a standard deviation of 35 lbs. calculate the standard error of the average sample weight when 15 participants are randomly selected for the sample? enter your answer rounded to two decimal places. for example, if your answer is 12.345 then enter as 12.35 in the answer box.
The standard error of the average sample weight when 15 participants are randomly selected for the sample is 9.05 (rounded to two decimal places).
The standard error of the average sample weight when 15 participants are randomly selected for the sample can be calculated using the formula given below:SE = σ/√nWhere,σ = standard deviation of the populationn = sample sizeSE = standard error of the meansubstituting the given values,SE = 35/√15 = 9.05
Note:When using the given formula, it is important to note that it assumes a normal distribution of sample means. The standard error is used to estimate the true value of the mean from the sample data. The larger the sample size, the smaller the standard error. The smaller the standard error, the more precise the estimate of the true value of the mean.
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What is the measure of the indicated (?) angle?
a
68 degrees
b
112 degrees
c
136 degrees
d
144 degrees
Answer:
c 136 degrees
Step-by-step explanation:
The function F is defined by F(x) = 12/x+1/2. Find each value of the function.
F(k) =
Each values of the function are;
[tex]F(3) = \frac{9}{2} , F(-12) = -\frac{1}{2} , F(\frac{1}{3}) = \frac{73}{2} , F(\frac{3}{4}) =\frac{33}{2}[/tex]
Define the term function?A function is a relationship between two sets of numbers, called the domain and the range, such that each input value from the domain corresponds to exactly one output value from the range. A function can be thought of as a rule that assigns to each input value a unique output value. The most common way to represent a function is by using an equation or formula that defines the relationship between the input values and the output values. The variable in a function represents the input values from the domain.
Given function;
[tex]F(x) = \frac{12}{x} + \frac{1}{2}[/tex]
We need to find the values of function [tex]F(3) , F(-12) , F(\frac{1}{3}) , F(\frac{3}{4})[/tex]
Put the values of x = 3, -12, 1/3, 3/4 one by one in the given function of [tex]F(x) = \frac{12}{x} + \frac{1}{2}[/tex]
1. If x= 3; [tex]F(3) = \frac{12}{3} + \frac{1}{2} = \frac{9}{2}[/tex]
2. If x= -12; [tex]F(-12) = \frac{12}{(-12)} + \frac{1}{2} = -1 + \frac{1}{2}[/tex] [tex]= -\frac{1}{2}[/tex]
3. If [tex]x=\frac{1}{3}[/tex]; [tex]F(\frac{1}{3} ) = \frac{12}{(\frac{1}{3}) } + \frac{1}{2} = 36+\frac{1}{2}[/tex] [tex]= \frac{73}{2}[/tex]
4. If [tex]x=\frac{3}{4}[/tex]; [tex]F(\frac{3}{4} ) = \frac{12}{(\frac{3}{4}) } + \frac{1}{2} = 16 +\frac{1}{2}[/tex] [tex]= \frac{33}{2}[/tex]
Therefore the values are; [tex]F(3) = \frac{9}{2} , F(-12) = -\frac{1}{2} , F(\frac{1}{3}) = \frac{73}{2} , F(\frac{3}{4}) =\frac{33}{2}[/tex]
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Complete question-
Britney is mapping out a new running path around her local park. She is going to run west for 2.1 km, before turning 105" to the night and running another 3.3 km From there, she will run in a straight line back to her starting position. How far will Britney run in total? Give your answer correct to the nearest meter.
Answer:
Britney will run approximately 9,090 meters in total.
Step-by-step explanation:
To solve the problem, we can use the Law of Cosines to find the distance of the final straight line back to her starting position.
Let A be the starting position, B be the end of the first leg, and C be the end of the second leg. Then, we have:
AB = 2.1 km BC = 3.3 km ∠ABC = 180° - 105° = 75°
Using the Law of Cosines, we have:
AC² = AB² + BC² - 2(AB)(BC)cos(∠ABC)
AC² = (2.1)² + (3.3)² - 2(2.1)(3.3)cos(75°) AC ≈ 3.69 km
Therefore, Britney will run a total distance of approximately:
2.1 km + 3.3 km + 3.69 km ≈ 9.09 km
So, Britney will run approximately 9,090 meters in total.
R(55, -75) W(-15,-40)
Find the slope
Answer:
- 1/2
Step-by-step explanation:
We can use the slope formula to find the slope.
m = ( y2-y1)/(x2-x1)
= ( -40 - -75)/(-15 - 55)
= (-40+75)/( -15-55)
=35/-70
=- 1/2
Answer:
m = -0.5
Step-by-step explanation:
Given that, ( Coordinates of a line )
( 55, - 75 ) ⇒ ( x₁ , y₁ )
( - 15 , - 40 ) ⇒ ( x₂ , y₂ )
The formula to find the slope of a line is:
[tex]\sf m =\frac{y_1-y_2}{x_1-x_2}[/tex]
Let us find it now.
[tex]\sf m =\frac{y_1-y_2}{x_1-x_2} \\\\\sf m =\frac{-75-(-40)}{55-(-15)} \\\\\sf m =\frac{-75+40}{55+15} \\\\\sf m =\frac{-35}{70} \\\\m = -0.5[/tex]
Find the perimeter of the shaded region. Round your answer to the nearest hundredth.
The perimeter is about _ units
The perimeter of the shaded region is 22.58 units.
What is perimeter of rectangle?
Perimeter of a rectangle is 2×(Length+Breadth).
Here in this figure we have three part. They are a rectangle and two semicircles.
Length of the rectangle is 13 unit and breadth is 6 unit
So, perimeter of the rectangle part = 2×(length+breadth) = 2×(13+6) = 38 unit
Again, diameter of two semicircles is 6 unit
So, radius of two semicircles will be [tex] \frac{6}{2} = 3 \: unit[/tex]
So, perimeter of one semicircle
[tex] = \pi \: r + 2r \\ = \pi \times 3 + 2 \times 3 \\ = 3\pi + 6[/tex]
Now, perimeter of two semicircles will be
[tex]2 \times (3\pi + 6) = 3(\pi + 2) \: unit[/tex]
If we subtract perimeter of two semicircles from the perimeter of rectangle then we will get perimeter of the shaded portion.
So, required perimeter of shaded region
[tex] = 38 - 3(\pi + 2) = (32 - 3\pi) = 22.58 \: unit[/tex]
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What is the axis of symmetry?
x=
7.3.AP-5
Question content area top
Part 1
Find the area of the shape.
10 ft
7 ft
11 ft
10 ft
Question content area bottom
Part 1
The area is
enter your response here
▼
ft cubed .
ft.
ft squared .
(Type a whole number or a decimal.)
The area of the given shape is 73.5 ft squared
The question content area indicates that we need to find the area of a shape with dimensions of 10 ft, 7 ft, and 11 ft. However, the units are not specified, so it is assumed that we are dealing with a two-dimensional shape and the units are in feet.
To find the area of this shape, we need to use the appropriate formula for the shape.
Since the question does not provide any further information about the shape, we cannot determine the formula for certain. However, based on the dimensions given, we can assume that this is a trapezoid.
The shape can be divided into a rectangle and a triangle.
Calculate the area of the rectangle.
The dimensions of the rectangle are 7 ft by 10 ft.
To find the area, multiply the length by the width:
Area of rectangle = length × width = 7 ft × 10 ft = 70 ft²
Calculate the area of the triangle.
The base of the triangle is 10 ft, and its height is the difference between the 11 ft and 7 ft sides of the shape, which is 4 ft.
Multiply the base by the height and then divide by 2:
Area of triangle = (base × height) / 2 = (10 ft × 4 ft) / 2 = 20 ft²
Total area = area of rectangle + area of triangle = 70 ft² + 20 ft² = 90 ft²
The formula for the area of a trapezoid is:
Area = ((b1 + b2) / 2) * h
where b1 and b2 are the lengths of the two parallel sides, and h is the height (or perpendicular distance between the parallel sides).
Using the given dimensions, we can plug them into the formula:
Area = ((10 + 11) / 2) * 7
Area = (21 / 2) * 7
Area = 147 / 2
Area = 73.5 ft squared
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Determine whether the function is a polynomial function. Check by setting in standard from, identifying leading coefficient, constant, Highest degree, and type of function
The function is not a polynomial function,
Leading coefficient, Constant, Highest degree, is not possible with a rational function, Type of function: Rational function
What is an expression?An expression is a mathematical equation that combines variables, numbers, and other mathematical operations to represent a value or a set of values. It can be simple or complex, and it is often used in algebra to solve problems and represent mathematical relationships.
We have the given function is, [tex]f(x)= 5x - 12 + x^3 + 9x^{-4} + x^2[/tex]
The standard form, means arranging the terms in descending order of degree; So,
[tex]f'(x) = x^3 + x^2 + 5x - 12 + 9x^{-4}[/tex]
No, the function f'(x) is not a polynomial function because it contains a term with a negative exponent, which makes it a rational function rather than a polynomial function.
To find the leading coefficient, constant, highest degree, and type of function of a polynomial function, we would put it in standard form, but this is not possible with a rational function.
Instead, we can identify that the term 9[tex]x^{-4}[/tex] is a rational term, which means it contains a variable raised to a negative exponent. Polynomial functions, by definition, cannot have terms with negative exponents, so f(x) is not a polynomial function.
In summary, the function [tex]f'(x) = x^3 + x^2 + 5x - 12 + 9x^{-4}[/tex] is a rational function, not a polynomial function, because it contains a term with a negative exponent.
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please help.!!!!!!!!!!!!!!!!!!!!!!!!!!
The expressions are matched as;
5³· 5³ add the exponents
(4x³)⁵. write as the product of the powers
6⁹ ÷ 6⁵. subtract the exponents
(7²)³. multiply the exponents
What are index forms?Index forms are described as those mathematical models that are used to represent numbers too small or large in more convenient forms.
They are represented as variables or numbers that are being raised to an exponent.
Other names for index forms are;
Scientific notationStandard formsThe rules of the index forms are;
Add the exponents when the bases are similar and being mulitiplied.Subtract the exponents when the bases are similar and being divided.From the information given, we have that;
5³· 5³ multiply the exponents
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On the grid draw the graph of y=2x-3 for values of x from -2 to 4
A graph of the equation y = 2x - 3 is shown in the image attached below.
How to graph the given linear equation?In order to to graph the solution to the given linear equation on a coordinate plane, we would use an online graphing calculator to plot the given linear equation and then take note of the point that lie on it;
y = 2x - 3
In this scenario and exercise, we would use an online graphing calculator to plot the given linear equation as shown in the graph attached below.
Based on the graph shown in the image attached below, we can reasonably infer and logically deduce that the domain for this linear equation is -2 < x < 4.
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The graph of h(x) = -log(x + 5).
-6
d
h(x)
9
7
6
5
4
3
2
1
3 -2 -1 0
-2
دی
-4
-5
-6
1
2
3 4 5 6
What are the intercepts and asymptote of h(x)? Explain how to find these using the graph. Please help
Answer:
The function h(x) = -log(x + 5) has a vertical asymptote at x = -5, since the logarithm of a non-positive number is undefined. To find the intercepts of this function, we can set h(x) equal to zero and solve for x:
h(x) = 0
-log(x + 5) = 0
x + 5 = 1
x = -4
So the function has an x-intercept at (-4, 0). To find the y-intercept, we can set x equal to zero and evaluate h(x):
h(0) = -log(0 + 5) = -log(5)
So the function has a y-intercept at (0, -log(5)).
To verify these intercepts using the graph, we can look for the points where the graph intersects the x and y axes. The x intercept is where the graph crosses the x-axis, which in this case is at x = -4. The y-intercept is where the graph crosses the y-axis, which is at y = -log(5) or approximately -1.609. The vertical asymptote is the vertical line where the graph approaches but never touches. From the graph, we can see that this occurs at x = -5.
It is important to note that when graphing logarithmic functions, it is recommended to plot a few points, including the intercepts and vertical asymptote, to help visualize the graph accurately.