Repeating decimals are never rational numbers. Hence the statement of enrique that "0.44444 is a rational number" is incorrect.
Rational numbers are those which can be expressed as the ratio of two integers, but the denominator should not be zero. Rational numbers can be expressed in p/q form. Rational numbers are never repeating decimals. For example 10/2, 3/2, 2/1 are rational numbers.
Irrational number are those which cannot be written in the form of p/q. They are repeating decimal and recurring decimals. The best example of irrational number is the value of π(pie). The value of π is 3.1415...with no repeating pattern of decimals.
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Which is the common difference for this arithmetic series? 8, 30, 52, 74, 96, 118 a. d = 8 b. d = 22 c. d = 32 d. d = 38
Answer:
d = 22
Step-by-step explanation:
you add 22 to a number in the sequence to get the next number
8 + 22 = 30
30 + 22 = 52 and so on...
Given f(x) = 3x^3+kx-13, and x-1 is a factor of f(x), then what is the value of k?
Answer: k=10
Step-by-step explanation:
Which operation results in a binomial
A. -
B. +
C. •
Answer:
answer is d
Step-by-step explanation:
because of binomials connect to the plus sign but which solves the equations of the multiplicationsThe dashed triangle is the image of the solid triangle for a dilation centered at the origin. What is the scale factor?
Option(c) is the correct answer i.e. the scale factor of the given triangle is 4/9.
What is Scale factor?
The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor.
Let's take the measurement of one side of the original triangle and dashed triangle.
The side of Original triangle is 18 units and,
The side of dashed(new) triangle is 8 units
We know that,
Scale factor = dimension of new figure ÷ dimension of original figure
= 8 units / 18 units
= 4/9.
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Emily was offered a job after college earning a salary of $35,000. She will get a raise
of $2,000 after each year working for the company. Answer the questions below
regarding the relationship between salary and the number of years working at the
company.
, and the
The independent variable, x, represents the
dependent variable is the
depends on the
because the
A function relating these variables is C(x)
So C(4)
meaning 4
Answer:
The independent variable, x, represents the number of years working at the company. The dependent variable, C(x), represents the salary. The salary depends on the number of years working at the company because the salary increases by $2,000 for each year of work. A function relating these variables is C(x) = 35,000 + 2,000x, where x is the number of years working at the company and C(x) is the salary. So C(4) = 35,000 + 2,000(4) = $43,000 meaning that if Emily works for 4 years, her salary will be $43,000.
pls help me
Josh is the owner of CranBog, a Cranberry Bog in Massachusetts. Cranberry production at CranBod can be represented by the inequality y ≤ 150x - 3100
under normal climate conditions, where y
is the annual production of cranberries at CranBog, in thousands of pounds, and x
is the number of acres of land that produce cranberries.
The TRUE statements about the inequality y ≤ 150x - 3100 are:
A) For a solution to be viable, both x and y must be integers.E) The ordered pair (40, 2900) is a solution to the inequality and means that with 40 acres of land, CranBog can produce 2,900 (in thousands of) pounds of cranberries.What is inequality?Inequality is a mathematical statement showing that two or more mathematical expressions are unequal or not equivalent.
Inequalities are represented by the following types and inequality symbols:
Less than (<)Greater than (>)Not equal to (≠)Less than or equal to (≤)Greater than or equal to (≥).Check:
Ordered pairs (40, 2900)
y ≤ 150x - 3100
y ≤ 150(40) - 3100
y ≤ 6,000 - 3100
y ≤ 2900
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my grade depends on this, help!!
Answer:
x ≥ - 3-----------------------
We observe on the graph:
The relation is not a function because it fails the vertical line test. You can see the graph intersects with the y-axis twice.The domain is restricted at x = -3 and unrestricted on the positive side.The domain is:
x ≥ - 3The graph below represents the distance of a dog from a trainer after a command is given.
A graph titled Dog Obedience School. The horizontal axis shows Time (seconds), numbered 1 to 10, and the vertical axis shows Distance (yards) numbered 4 to 40. The line shows an increase, then decrease, then constant distance.
Which statement could describe the dog’s movement at 5 seconds once the command was given?
The dog stopped to lie down and obey the trainer’s command.
The dog was running towards the trainer.
The dog was running away from the trainer.
The dog was stopped but began running towards the trainer.
The correct statement regarding the dog’s movement at 5 seconds once the command was given is given as follows:
The dog was running towards the trainer.
How to obtain the correct statement regarding the graph?The input and output variables for the function graphed are given as follows:
Input: time.Output: distance.At a time of 5 seconds, the distance between the dog and the trainer is decreasing, meaning that the dog was moving towards the trainer, and thus the second option is the correct option.
Missing InformationThe graph is given by the image presented at the end of the answer.
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Answer:
The dog was running towards the trainer.
Is x = 6 a solution to the equation x + 13 = 18?
A. No, because 6 + 13 = 18 is not true.
B. Yes, because 6 + 13 = 18 is not true.
C. No, because 6 + 13 = 18 is true.
D. Yes, because 6 + 13 = 18 is true.
On solving the provided question, we can say that x = 6 a solution to the equation x + 13 = 18, no, because 6 + 13 = 18 is not true, as 6 + 13 = 19
What is equation?A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.
x = 6 a solution to the equation x + 13 = 18
No, because 6 + 13 = 18 is not true, as 6 + 13 = 19
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Distributive property c3/c when c=3
Answer: The answer is 9
Step-by-step explanation: 3^3/3=9
1) Differentiate following equations with respect to x.
a) x² + xy + y² = 0
b) 1/x + 1/y =e^y
The differential equations are dy/dx = -x/y and dy/dx = e^y * (-1/x² + 1/y²).
What is the differential equation?
A solution of a differential equation is an expression for the dependent variable in terms of the independent one(s) which satisfies the relation. The general solution includes all possible solutions and typically includes arbitrary constants (in the case of an ODE) or arbitrary functions (in the case of a PDE.)
a) To differentiate x² + xy + y² = 0 with respect to x, we can use the power rule and the chain rule.
The power rule states that the derivative of x^n is nx^(n-1)
The chain rule states that if y = f(u) and x = g(u) then dy/dx = dy/du * du/dx
x² + xy + y² = 0
dx/dx (x² + xy + y²) = dx/dx (0)
2x + y = 0
dy/dx = -x/y
b) To differentiate 1/x + 1/y = e^y with respect to x, we can use the chain rule and the reciprocal rule.
The chain rule states that if y = f(u) and x = g(u) then dy/dx = dy/du * du/dx
The reciprocal rule states that the derivative of 1/x is -1/x²
1/x + 1/y = e^y
dy/dx = dy/dx (e^y)
dx/dx (1/x + 1/y) = dx/dx (e^y)
-1/x² - 1/y² = e^y
dy/dx = e^y * (-1/x² + 1/y²)
Hence, the differential equations are dy/dx = -x/y and dy/dx = e^y * (-1/x² + 1/y²).
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what is the slope of the line through the points (-2,9) and (-4,6) ?
Answer:
The slope is [tex]\frac{3}{2}[/tex]
Step-by-step explanation:
The slope formula would be: [tex]\frac{y2-y1}{x2-x1}[/tex]
So for (-2,9) and (-4,6), we can plug in the variables: (x1, y1) and (x2, y2)
Let's use the numbers in the equation provided above:
[tex]\frac{6-9}{-4-(-2)}[/tex]
= [tex]\frac{-3}{-2}[/tex]
= [tex]\frac{3}{2}[/tex]
Answer:
3/2
Step-by-step explanation:
[tex]\frac{y2-y1}{x2-x1} = \frac{6-9}{-4-(-2)} = \frac{-3}{-2} =\frac{3}{2}[/tex]
Please help!! I can’t figure this out
Answer:
$3213
Step-by-step explanation:
You want to know the total spent on rent and food if rent is 7/20 of your budget and food is 1/2 of your budget of $3780 per month.
AmountsThe amount spent on each item is the product of the fraction of the budget it is and the total amount being budgeted (your income).
rent = 7/20 × 3780 = 1323
food = 1/2 × 3780 = 1890
The total spent on these items is the sum of these amounts:
rent + food = 1323 +1890 = 3213
A total of $3213 is budgeted for rent and food.
__
Additional comment
Your calculator can figure this handily.
You can factor out the income amount and add the fractions first:
(7/20·3780) +(1/2·3780) = 3780(7/20 +1/2) = 3780(7/20 +10/20)
= 3780(17/20) = 3213
The baker made a batch of chocolate chip, oatmeal raisin, and sugar cookies. If P(chocolate chip) = 0.25, interpret the likelihood of randomly selecting a chocolate chip cookie from the batch.
A. Equally likely and unlikely
B. Likely
C. Unlikely
D. This value is not possible to represent probability of a chance event.
The baker made a batch of chocolate chips, oatmeal raisin, and sugar cookies. If P(chocolate chip) = 0.25, the likelihood of randomly selecting a chocolate chip is B. Likely.
What is probability?Generally, Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, with 0 indicating that an event is impossible and 1 indicating that an event is certain.
A probability of 0.5, for example, would indicate that an event has a 50% chance of occurring. Probability can be used to make predictions and inform decision-making in a wide range of fields, including statistics, finance, and engineering.
A probability of 0.25 represents a 25% chance of a randomly selected cookie from the batch being a chocolate chip cookie, which is considered "likely" to occur.
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The graph shows the number of gallons of water in a large tank as it is being filled. Based on the trend line, predict how long it will take to fill the tank with gallons of water.
The required time it will take to fill the tank with gallons of water is 18 minutes.
What is a line?A line is a straight curve connecting two points or more showing the shortest distance between the initial and final points.
Here,
From the figure, the equation of the trend line is given as,
y = 20.83x
Where y = gallons of water and x is time in minutes
Now, put y = 375
375 = 20.83x
x = 18 min
Thus, the required time it will take to fill the tank with gallons of water is 18 minutes.
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Complete question,
Make Sense and Persevere The graph shows the number of gallons of water in a large tank as it is being filled. Based on the trend line, predict how long it will take to fill the tank with 375 gallons of water.
a child's toy harp is in the shape of a trapezoid as shown. in square inches, what is the area of the harp?
The area of a trapezoid is given by the formula A = 1/2(b1 + b2)h. In this case, b1 = 4, b2 = 3, and h = 8.
The area of a trapezoid can be determined using the formula A = 1/2h(b1 + b2), where A is the area, h is the height, and b1 and b2 are the lengths of the top and bottom bases of the trapezoid, respectively. To determine the area of a child's toy harp in square inches, we need to know the length of the top and bottom bases and the height of the trapezoid.
Therefore, the area of the harp is 1/2(4 + 3)8 = 20 square inches. To find the area of the harp, we first need to know the measurements of the base lengths, b1 and b2, as well as the height, h. Once we have these measurements, we can plug them into the formula for the area of a trapezoid and solve for A. In this case, the area of the harp is 20 square inches.
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Answer:
20 square inches
Correct Answer 100%. Pls, give me brainliest. Thank You.
Dr. Chandler wants to print copies of
his thesis in hardcover book format. He
could use Washington Printing, paying a
setup fee of $41 and $6 for every book
printed. Or, he could go through Fairfax
University, paying an up-front fee of
$32 and $9 per book. For how many
books will the costs be the same? How
much is that?
Answer:
For 3 books, costs are the same
$59
Step-by-step explanation:
x = number of books
$41 + ($6/book)(x) = $32 + ($9/book)(x)
41 - 32 = 9x - 6x
9 = 3x
x = 9/3 = 3
41 + 6(3) = 32 + 9(3) = $59
Please Help ASAP - 100pts + Brainliest!
Answer:
g(x) = e^(x+2) -3
Step-by-step explanation:
You want the transformed function g(x) of the parent function f(x) = e^x given that g(x) has a horizontal asymptote of -3 and goes through the point (-2, -2).
TranslationThe parent function goes through the point (0, 1), which has apparently been translated to (-2, -2) by the transformation. That translation looks like ...
g(x) = f(x -h) +k . . . . . . . . f(x) translated h units right and k units up
ApplicationOur function has been translated from 0 to -2 in the horizontal direction, or left 2 units: h = -2.
It has been translated from 1 to -2 in the vertical direction, or down 3 units: k = -3.
Then the translated function is ...
g(x) = f(x +2) -3
g(x) = e^(x+2) -3
can you include the full picture?
Determine whether the sequence converges or diverges. If it converges, find the limit. an=(1+2/n)^n
This sequence converges to e. The sequence (1 + 2/n)^n is a geometric sequence in which each successive term is found by multiplying the previous term by a constant.
This sequence is an example of a geometric sequence where each successive term is found by multiplying the previous term by a constant. In this case, the constant is equal to (1 + 2/n).
By using the limit definition of a geometric sequence, we can see that the limit of this sequence is given by lim n→∞ (1 + 2/n)^n = e. Therefore, the sequence converges to e.
The sequence (1 + 2/n)^n converges to e.
The sequence (1 + 2/n)^n is a geometric sequence in which each successive term is found by multiplying the previous term by a constant. By using the limit definition of a geometric sequence, it can be determined that the limit of this sequence is given by lim n→∞ (1 + 2/n)^n = e. As a result, the sequence converges to e.
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The article "Kids Digital Day: Almost 8 Hours" (USA Today, January 20, 2010) summarized results from a national survey of 2002 Americans age 8 to 18. The sample was selected in a way that was expected to result in a sample representative of Americans in this age group.
a. Of those surveyed, 1321 reported owning a cell phone. Use this information to construct and interpret a 90% confidence interval estimate of the proportion of all Americans age 8 to 18 who own a cell phone.
b. Of those surveyed, 1522 reported owning an MP3 music player. Use this information to construct and interpret a 90% confidence interval estimate of the proportion of all Americans age 8 to 18 who own an MP3 music player.
c. Explain why the confidence interval from Part (b) is narrower than the confidence interval from Part (a) even though the confidence level and the sample size used to compute the two intervals was the same.
The confidence interval from Part (b) is narrower than the confidence interval from Part (a) because the proportion of Americans age 8 to 18 who own an MP3 music player is higher than the proportion of Americans age 8 to 18 who own a cell phone.
a. 90% confidence interval estimate of the proportion of all Americans age 8 to 18 who own a cell phone:
(1321/2002) ± (1.645*sqrt( (1321/2002)*(1-(1321/2002)) / 2002)) = (0.6608 ± 0.0402)
Interpretation: We are 90% confident that the true proportion of all Americans age 8 to 18 who own a cell phone is between 0.6206 and 0.7010.
b. 90% confidence interval estimate of the proportion of all Americans age 8 to 18 who own an MP3 music player:
(1522/2002) ± (1.645*sqrt( (1522/2002)*(1-(1522/2002)) / 2002)) = (0.7610 ± 0.0346)
Interpretation: We are 90% confident that the true proportion of all Americans age 8 to 18 who own an MP3 music player is between 0.7264 and 0.7956.
c. The confidence interval from Part (b) is narrower than the confidence interval from Part (a) because the proportion of Americans age 8 to 18 who own an MP3 music player is higher than the proportion of Americans age 8 to 18 who own a cell phone. This means that the sample size is more likely to result in a more accurate estimation of the true population proportion for the MP3 music player than for the cell phone.
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URGENT PLEASE HELP!!!!!!
Answer:
یه گل یک گل بام میی مه فیلم بام حس بام حس فمس یکم باشگاه هی یک گل یه حس سیم هی فکریه خشک پیل هر یک حس صب زی صب هم گچ نی بلن هر بر قل هم بی دو حس قیین
Step-by-step explanation:
سبک حس بام نی شیک حس
یا کمی سیم حس او
نی یک حس بکشم یک حس بام نی که خیلی تنیام که اما الا دیه انجام نمییم ای موضوع که دعوا خیلی تخفیف خیلی خوعه ای موضوع که اما الا دیمش خوش
۳ خشک هی یک هی بام نی با که اما ۷غ هه بام نی بلن کف بام نی بکر
به نمییم هی بام میی لاک حس بام
بلن هی یک
حالم ای زبونه فراموش که
فخ بیم فک
Need help with this equation
4x⁴ +12x³ +15x² +9x −6 is the expression which can represent function f(g(x)). Thus, option D is correct.
What is function?A rule that transforms one number into another is called a function. However, not every rule outlines an appropriate function. In addition to introducing some of the mathematical terms related to functions, this unit explains how to determine if a given rule describes a valid function.
Given
f(x) = x² + 3x - 6
g(x) = 2x² +3x
To find expression for f(g(x))
Put the value of g(x) place of x, f(x)
f(x) = x² + 3x - 6
(2x² +3x)² + 3(2x² +3x) - 6
4x⁴ +12x³ +15x² +9x −6
Thus, 4x⁴ +12x³ +15x² +9x −6 is the expression which can represent f(g(x)).
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State the domain and range for the following relation. Then determine whether the relation represents a function. {( -4,6), (-4,7), (6,5), (7,9)} The domain of the relation is __. (Use a comma to separate answers as needed.) The range of the relation is ___ (Use a comma to separate answers as needed.) Does the relation represent a function? Choose the correct answer below. A. The relation is a function because there are no ordered pairs with the same second element and different first elements. B. The relation is a function because there are no ordered pairs with the same first element and different second elements. C. The relation is not a function because there are ordered pairs with 5 as the second element and different first elements. D. The relation is not a function because there are ordered pairs with - 4 as the first element and different second elements.
Since the input value of domain -4 has two different output values (7 and 6), the relation is not a function.
By definition, a relation is a function if each input value has only one output value.
Given the relation:
(-4,6)
(-4,7)
(6,5)
(7,9)
The domain is the set of the x-coordinates of each ordered pair (You do not need to write 4 twice):
domain ={-4 ,6,5}
The range is the set of the y-coordinates of each ordered pair :
range= {6,7,5,9}
Since the input value 4 has two different output values (7 and 6), the relation is not a function.
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Please Hurry!
A box of apples sells for $17. At this rate, which expression represents the cost, in dollars, of 100 apples?
A) 5/17•20
B) 5/20•17
C) 100/17•20
D) 100/20•17
E) 17•5•20
Answer: D
Step-by-step explanation:
20 apples cost $17
100 apples = 100/20 * 17 = D
three friends went to an icecream store and tried a new flavor the store was testing. After
trying the flavor, they were asked to rate the icecream on 9-point rating scale ranging from
1-Hate it to 9-Love it. The friends ratings were: Destiny 9, Taylor 6, Jeremiah 5. What is the
mean of their ratings?
The mean of their ratings is 7.
How to calculate the mean of their ratings?
Mean (also called the average) is used to describe the central tendency of a set of numerical data. It is calculated by summing up all the values in the data set and dividing by the number of values.
Since We have the ratings:
Destiny 9, Taylor 6, Jeremiah 5
Mean = (9 + 6 + 5)/3 = 20/3 = 7
Note: we divide by 3 because there are 3 people
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the first three steps for completing the square to solve a quadratic equation are shown. x squared minus 8 x plus 2 equals 0. x squared minus 8 x equals negative 2. x squared minus 8 x plus box equals negative 2 plus box.questionwhat number goes in the boxes to complete the third step?
The number that goes in the box is 4, since 4 + (-2) = 2, which is the coefficient of x^2 in the equation. The third step is to add the same number to both sides of the equation, so the box needs to contain 4.
To complete the third step in solving a quadratic equation using the completing the square method, the number that goes in the box is 4. This is because the goal is to make the coefficient of x^2 on the left side of the equation equal to the coefficient of x^2 on the right side. The equation is x^2 - 8x + 2 = 0, so the coefficient of x^2 on the left side is 1, and the coefficient of x^2 on the right side is 2. Therefore, the number that needs to be added to the left side is 1, and the number that needs to be added to the right side is also 1. This means that 4 needs to be added to both sides of the equation, so 4 is the number that goes in the box.
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describe your sketch. the solid has no negative x-values. the solid has both positive and negative y-values. the solid has no negative z-values. the solid has a straight side and a curved side in the x y-plane. the solid has ---select--- in the x z-plane. the solid has ---select--- in the y z-plane.
The solid has a straight side in the x y-plane and a curved side in the x y-plane. In the x z-plane, the solid has a curved side, and in the y z-plane, the solid has a straight side.
The solid has no negative x-values, meaning all x-values are positive. It has both positive and negative y-values, indicating that it is symmetrical around the x-axis. The solid has no negative z-values, meaning all z-values are positive. In the x y-plane, the solid has a straight side and a curved side. In the x z-plane, the solid has a curved side and in the y z-plane, the solid has a straight side.
The solid has a straight side in the x y-plane and a curved side in the x y-plane. In the x z-plane, the solid has a curved side, and in the y z-plane, the solid has a straight side.
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Find the equation of the ellipse with the following properties.
The ellipse with foci at (4, 0) and (-4, 0); y-intercepts (0, 3) and (0, -3)
Step-by-step explanation:
The equation of the ellipse
[tex]\displaystyle\\\boxed {\frac{x^2}{a^2} +\frac{y^2}{b^2} =1}[/tex]
[tex]F^2=a^2-b^2[/tex]
Given: F₁(-4,0) F₂(4,0) b₁(0,-3) b₂=(0,3)
[tex]\displaystyle\\a^2=F^2+b^2\\\\a^2=4^2+3^2\\\\a^2=16+9\\\\a^2=25\\\\a_{1,2}=б5\\\\So,\ a_1(-5,0)\ \ \ \ a_2(5,0)\\\\Thus,\ \frac{x^}{(б5)^2} +\frac{y^2}{(б3)^2} =1\\\\\frac{x^2}{25}+\frac{y^2}{9} =1\ \ \ \ -\ the\ equation \ of\ the\ ellipse[/tex]
k2 is 11,194.21 feet higher than mt. kenya. enter and solve an equation to find the elevation of mt. kenya. use x to represent the elevation of mt. kenya.
The elevation of mountain mt.kenya is, x = 17,057.1 feet by substitution method from the elevation of mountain K2 given.
Given that,
K2 is 11,194.21 feet higher than mt.Kenya, write and solve an equation to find the elevation of mt.Kenya.
x = mt. Kenya ( since given that x represents the elevation of mt.kenya)
Let us consider/assume ,
y = K2 (say)
Therefore, the relation between x and y:
x = y - 11,194.21 ( or )
y = x + 11,194.21
( since given that K2 is 11,194.21 more than mt.Kenya )
The elevation of K2 Mountain = 28251.31 feet
= y
substitute the value of y in x = y - 11,194.21
x = 28251.31 - 11,194.21
∴ x = 17,057.1 feet.
Therefore the elevation of mt.kenya found to be, x = 17,057.1 feet by substitution method.
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The complete question is :
K2(Which is 28251.31) is 11,194.21 feet higher than Mt.Kenya Write and solve an equation to find the elevation of Mt.Kenya. use x to represent the elevation of mt. kenya.
Highway Design A section of highway connecting two hillsides with grades of 6% and 4% is to be built between two points that are separated by a horizontal distance of 2000 feet (see figure). At the point where the two hillsides come together, there is a 50-foot difference in elevation.
(a) Design a section of highway connecting the hillsides modeled by the function {eq}f(x) = ax^3 + bx^2 + cx + d (-1000 \le x \le 1000) {/eq}. At the points A and B, the slope of the model must match the grade of the hillside.
(b) Use a graphing utility to graph the model.
(c) Use a graphing utility to graph the derivative of the model.
(d) Determine the grade at the steepest part of the transitional section of the highway.
You need to find the four constants, a, b, c, and d. At x = -1000, you have a value for f(x).
A)Outline it:
f(-1000) = -1000 = a (-1000)^3 b(-1000)^2 + c (-1000) + d
At x = 1000, you have a value for f(x).
B)Outline it:
f(+1000) = a (1000)^3 + b (1000)^2 + c (1000) + d
You know the slope's value, f'(x), and when x = -1000, f'(-1000) equals 3 a (-1000)2 + 2 b (-1000) + c.
At x = + 1000 f'(1000), you have a value for the slope: 3 a (1000)2 + 2 b (1000) + c
C) That is four linear equations with a, b, c, and d as the four unknowns.
When you simultaneously solve all four equations, you will get the function and its derivative, which you may graph.
D) The steepest part is where the derivative's absolute value is at its highest.
You can find that extreme by setting the derivative of the derivative equal to zero.
6 a x + 2 b = 0
solve for x and calculate the slope at that point.
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