The domain of the given function would be x > 0.
What is a function?
In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.
The function f(x) = log is the natural logarithm function, also known as ln(x). The domain of this function is the set of all positive real numbers x such that x > 0, because the natural logarithm of a non-positive number is undefined.
Hence, the domain of the given function would be x > 0.
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The domain of the given function would be x > 0.
What is a function?
In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.
The function f(x) = log is the natural logarithm function, also known as ln(x). The domain of this function is the set of all positive real numbers x such that x > 0, because the natural logarithm of a non-positive number is undefined.
Hence, the domain of the given function would be x > 0.
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An isosceles trapezoid has a perimeter of 38 ft and a leg measuring 8 ft. A similar trapezoid has a leg measuring 3ft. Find its perimeter.
The perimeter of a trapezoid is 28ft.
An isosceles trapezoid is a trapezoid whose non-parallel sides (the legs) are equal in length.
The perimeter of an isosceles trapezoid (P) = a + b+ 2c
where a is the top, b is the bottom, and c is the leg of the trapezoid
According to the question,
perimeter = 38ft
leg of an isosceles trapezoid = 8ft
38 = a +b +2 × 8
⇒ 38 = a+b +16
⇒a +b = 38 -16
⇒a +b = 22
Another similar trapezoid has a leg measuring 3ft.
Perimeter of this trapezoid is =( 22 + 2× 3) ft
= (22 +6)ft
= 28 ft
So, the perimeter of a trapezoid is 28ft.
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Define negative and positive numbers. Explain.
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Negative Numbers :-⟹ Numbers that are less than zero are known as negative numbers (or integers). They fall on the left side of the number line.
Positive Numbers :-⟹ Numbers that are greater than zero are known as positive numbers (or positive integers). They fall on the right side of the number line.
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꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐
Consider the line x+5y=6
What is the slope of a line perpendicular to this line?
What is the slope of a line parallel to this line?
Answer:
[tex]x + 5y = 6[/tex] is perpendicular to [tex]y = 5x + \frac{6}{5}[/tex] and parallel to [tex]y = -\frac{1}{5}x + 2\\[/tex]
Step-by-step explanation:
First, convert the equation to standard form so that y is isolated.
x + 5y = 6 --> x - 6 = -5y (divide both sides by -5) --> [tex]y = -\frac{1}{5}x + \frac{6}{5}[/tex]
A perpendicular line will have a slope that is the opposite reciprocal of the original slope (meaning you flip the numerator and denominator then make it negative).
[tex]-\frac{1}{5}[/tex] is perpendicular to [tex]-(\frac{-5}{1} )[/tex] which simplifies to 5.
A parallel line will have the same slope, but the y-intercept will be different. It can be pretty much any number as long as the original slope is used in the new equation.
[tex]y = -\frac{1}{5}x + \frac{6}{5}\\[/tex] is parallel to [tex]y = -\frac{1}{5}x + 2\\[/tex] just like [tex]y = -\frac{1}{5}x - \frac{100}{23}[/tex].
Brent has goldfish that quadruple (become four times as many) every month, and Gretel has goldfish that double every month. If Brent has 4 goldfish at the same time that Gretel has 128 goldfish, then in how many months from that time will they have the same number of goldfish
On solving the provided question, we can say that by fraction they will have the same amount of fish in 5 months.
what is fraction?Any number of equal portions, or fractions, can be used to represent a whole. Fractions in standard English indicate how many units of a certain size there are. 8, 3/4. A whole includes fractions. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. True fractions have numerators that are less than their denominators. A fraction is a sum that constitutes a portion of a total. By breaking the entire up into smaller bits, you can evaluate it. Half of a full number or item, for instance, is represented as 12.
Month / Brent / Gretel
0/4/ 128
1/ 16 / 256
2 / 64 / 512
3 / 256 / 1024
4 / 1024 / 2048
5 / 4096 / 4096
They will have the same amount of fish in 5 months.
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A farm brings 15 tons of watermelon to market. Find a 90% confidence interval for the population mean cash value of this crop. What is the margin of error
The margin of error is $148.89. The upper limit is $2215 and lower limit is $1914.
What is a confidence interval with an example?In statistics, confidence is another word for probability. If you create a confidence interval, for instance, with a 95% level of confidence, you can be sure that 95 out of 100 times, the estimate will fall between the upper and lower values indicated by the confidence interval.
First we need to name some of the variables we are given:
n = 38 the sample size
x = 6.88 the sample mean
= 1.86 the population standard deviation
We need to find a 90% confidence interval for the mean price per 100 lbs of watermelon:
= 1-.90 = .10
/2 = .05
z(/2) = -1.64
-z(/2) = 1.64
This can give us a probability expression:
P(-1.645 < z < 1.645) = .90
The margin of error is calculated with the formula: E = z(/2)(/√n)
E = 1.645(1.86/√38) = $.4963(300) = $148.89
Then to calculate the upper and lower limit we add and subtract E from x:
lower limit = 6.88 - .4963 = $7.38(300) = $2214
upper limit = 6.88 + .4963 = $6.38(300) = $1914
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At a fancy dinner party, the number of courses that will be served determines how many forks will be set out by the hostess.
c = the number of courses served during dinner
f = the number of forks set out by the hostess
Which of the variables is independent and which is dependent?
Answer:
c is the independent variable and f is the dependent variable
Step-by-step explanation:
Pls answer question number 1 pls it’s for my math that is due tomorrow
Answer:
Total cost =3over8 x 48 x0. 55=9.9
Answer:
$9.90
Step-by-step explanation:
First, we need to find the number of vanilla cupcakes.
The question tell us that 3/8 of the 48 cupcakes are Vanilla flavored, so we can start by dividing 48 by 8 to find what 1/8 of 48 is:
48/8 = 6
1/8 of 48 = 6
Now to find 3/8, we just need to multiply that number by 3:
6 x 3 = 18
3/8 of 48 = 18
So now we know that she bought 18 vanilla cupcakes.
Finally to find the price, we just need to multiply the price per cupcake by the number of cupcakes:
$0.55 per cupcake x 18 cupcakes = 0.55 x 18 = $9.90
The total cost of the vanilla cupcakes was $9.90
Hope this helped!
Mrs. Freeman is trying to determine if her new desk will fit through her classroom door. Her desk of her is 59 inches wide. She knows that the height of the door is 80 inches and the diagonal measure of the door is 100 inches. Determine the width of her door de ella and whether or not her new desk will fit. Justify your conclusion.
Answer: x = 60
Step-by-step explanation:
the equation is a^2 + b^2 = c^2.
If you draw out the problem, you plug in the information into the formula, so it would be...
x^2 + 80^2 = 100^2.
80^2 = 6,400 and 100^2 = 10,000.
x^2 + 6,400 = 10,000.
You subtract 6,400 from itself and 10,000 and then you get...
x^2 = 3,600.
You square both of those and your final answer will be x = 60.
Jill and beth are sisters. Jill is 1/3 of beth's age. Let b represent beth's age.Write an algebraic expression to show jill's age.
The algebraic expression to show Jill's age will be;
Jill = 1/3 x b
What is an Algebraic Expression?Algebraic expressions are the mathematical statements that are derived when operations such as addition, subtraction, multiplication, division, etc. are operated upon on variables and constants.
There are different parts of an algebraic expression and they are; Variables - a symbol that doesn't have a fixed value is called a variable. It can take any value assigned to it.
Constants - a symbol that has a fixed numerical value is called a constant. All numbers are constants.
Terms - A term is a variable alone (or) a constant alone (or) it can be a combination of variables and constants and the operation of multiplication or division with it.
Coefficients - the numbers that are multiplying the variables are called coefficients.
Beth's age = b
Jill's age = 1/3 of Beth's age
Jill's age = 1/3 x b
Jill's age = 1/3b
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I really need help with this answer pls help fast
Step-by-step explanatio
Solve the simultaneous equations by substitution
2 + y = 16
x = 2y + 1
Answer:
x=29, y= 14
Step-by-step explanation:
y=16-2(move the 2 over to isolate y.) y=14. now input 14 in the bottom equation. x= 2(14)+1, 2×14=28, 28+1=29. x=29, y=14
5. Find the perimeter of this figure.
Answer:
40
Step-by-step explanation:
Perimeter of sqaure:
= 4 × side
= 4 × 10
= 40 m
What is the degree of the polynomial 2x² 5x³ 7 *?
The degree of the polynomial 2x² 5x³ 7 is 5.
The degree of a polynomial is the highest exponent of the variable in the polynomial. In this case, the highest exponent of the variable is 5, which appears in the term 5x³. The degree of a polynomial is a whole number that tells us how many times the variable is multiplied by itself. The degree of the polynomial is 5.
It's worth noting that polynomials can be constant or non-constant, meaning they don't have to have a variable in them, in that case the degree is 0. And also a polynomial with only one term, the degree of that polynomial is the exponent of that term.
In this case, we only have one term with variable x in it, 5x³, and the degree is the exponent of that term which is 5.
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in a photograph alison stands next to her brother caleb. alison is 4cm tall in the photograph her actual height is 60in cale is 3.2cm tall in the photograph, whats his actual height
How do you write an equation for a parabola with the vertex and Y intercept?
To write an equation for a parabola with the vertex and y-intercept, the equation of vertex form y=a(x-h)^2+k is used.
What is a parabola?
A parabola is an approximately U-shaped, mirror-symmetrical plane curve in mathematics. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves.
Consider an example where vertex is (2,1) and y-intercept is (0,-3).
The equation of parabola needs to be deduced using these points.
The equation of a parabola in vertex form is -
y=a(x-h)^2+k
Here, a is a constant and (h ,k) are the coordinates of the vertex.
So, (h,k)=(2,1)
⇒y=a(x−2)^2+1
To obtain the value of a, substitute (0,−3) into the equation -
-3=4a+1
4a=-4
a=-1
⇒y=-1(x−2)^2+1
Now, distribute and simplify -
y=-1(x−2)^2+1
y=-(x^2-4x+4)+1
y=-x^2+4x-4+1
y=-x^2+4x-3
On, graphing this equation a parabola is obtained.
Therefore, to write an equation of parabola vertex form is used.
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HELP ME I am not really sure how to explain this !!!
Answer:
I'm not good with math lol
236 divided by 44 pls
Answer:it’s 5.36
Step-by-step explanation:
Evaluate the expression if x = 6
X3 – 10 =
Answer:
8
Step-by-step explanation:
3x6 = 18
18-10 = 8
Use 10% to find 40% of 40
Is math hard to study?
Joe has 10 marbles . Ken has fewer marbles than joe witch inequality represent the number of marbles m that ken has
Answer:
k < 10
Step-by-step explanation:
An inequality is a statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers.
Let k represent Ken. The closed side of < is the side the smaller number is going to be on. Ken has fewer marbles then Joe, therefore, k < 10 because Joe has 10 marbles.
I’ll brainliest you please help me
Answer:
x = 62°
y = 118°
Step-by-step explanation:
Since the sum of interior angles of any quadrilateral is 360°, all of the interior angles in this image will add up to 360°.
Since the shape of the trapezoid is symmetrical, x is equivalent to 62°.
This means 62 + 62 + x + x = 360°
(360-(62+62))/2 = 118°
118 + 118 + 62 + 62 = 360°
x = 62°
y = 118°
What is the equation of the circle?
Answer:
(x - 3)^2 + (y + 2)^2 = 2^2
Step-by-step explanation:
The center is at x = 3 and y = 2: (3, 2). The radius is 2. Starting with the standard equation of a circle with radius r and center (h, k), we get:
(x - 3)^2 + (y + 2)^2 = 2^2
Ratio, proportion and percent unit 4 homework 3 wages hours 1 wage is $9.50 2 $19.00 3 $28.50 4 $38.00
Answer:
(a) The complete table
[tex]\begin{array}{cccccc}Hours & {1} & {2} & {3} & {4} &{5}\ \\ {Amount} & {\$9.50} & {\$19.00} & {\$28.50} & {\$38.00} & {\$47.50} \ \end{array}[/tex]
(b) $38.00
(c) 3 hours
Step-by-step explanation:
Given
[tex]Earnings = \$9.50[/tex] per hour
See attachment for complete question;
Solving (a): Complete the table
To complete the table, we simply multiply the earnings by the number of hours.
So, we have:
[tex]Hours = 2 \to Earnings = \$9.50 * 2 = \$19.00[/tex]
[tex]Hours = 3 \to Earnings = \$9.50 * 3 = \$28.50[/tex]
[tex]Hours = 4 \to Earnings = \$9.50 * 4 = \$38.00[/tex]
[tex]Hours = 5 \to Earnings = \$9.50 * 5 = \$47.50[/tex]
Solving (b): Earnings, if Megan works for 4 hours
In (a) above, we have:
[tex]Hours = 4 \to Earnings = \$9.50 * 4 = \$38.00[/tex]
This implies that Megan will earn $38.00
Solving (c): Hours to earn $28.50
In (a) above, we have:
[tex]Hours = 3 \to Earnings = \$9.50 * 3 = \$28.50[/tex]
This implies that Megan will work for 3 hours to earn $28.50
Mr. Garcia purchased twelve watermelons for the school picnic. Each watermelon cost $4.95. How much did he pay for the watermelons?
Answer:
$59.40
Step-by-step explanation:
Multiply the amount of watermellon (12) by the price (4.95) giving you 59.40
Answer:
$59.40
Step-by-step explanation:
take $4.95 and times it by twelve to get $59.40
ASAP NEED HELP THX !! Look at picture
Answer:
66
Step-by-step explanation:
Replace t with 9 in the equation.
[tex]28(1.1)^9[/tex]
Simplify.
[tex]28(2.358)[/tex]
[tex]66.023[/tex]
Rounded, it equals 66
3 divided by 3/4 (three divided by three fourths) | HELP ASAP!
Answer:
[tex]3 \div \frac{3}{4 } \\ = 3 \times \frac{4}{3} \\ = 4[/tex]
Use the graph of the equation to answer the question.
What is the domain of the equation?
What is the range of the equation?
As per the graph, there is no restrictions for the domain but the range has a minimum value at y = - 4.
The domain is any real number:
x ∈ ( - ∞, + ∞)The range is any real number not less than - 4:
y ∈ [ - 4, + ∞)A company is loading recliners and sofas onto a trailer that has a volume of about 3800 cubic feet. Each recliner takes up about 40 cubic feet and each sofa takes up about 80 cubic feet. The company wants the shipment to have at least 30 recliners and more than 25 sofas. Identify and interpret the ordered pair in the solution region.
The ordered pair that would be needed by the company for shipment can be loaded in the trailer as the pair will take only 3200ft³ of the volume of the trailer which is 3800 cubic feet.
How to calculate the ordered pair for shipment?The total volume of the trailer = 3800 cubic feet
The volume of each recliner = 40 cubic feet
The volume of each sofa = 80 cubic feet
The number of recliner needed = 30
The number of sofas needed = 25
The volume that the sofa will cover = 25 × 80 = 2000
The volume that the recliner will cover= 30 × 40 = 1200
Therefore the total volume both will take = 3200 cubic feet.
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on a restaurant menu there are 22 main dishes of which 4/11 are gluten free 7 rice dishes which are all gluten free 5 naan breads of which 40% are gluten free. this meal deal is on the menu 'choose one main dish, one rice dish and one naan bread' how many of these possible meal deals are gluten free
Answer:
56
Step-by-step explanation:
Gluten-free choices:
Main dishes: 4
Rice dishes: 7
Bread: 2 (40% of 5 is 2) 0.40 x 5 = 2
Multiply numbers of choices together: 4 x 7 x 2 = 56
There are a total of 112 meal deals.
What is a fraction?'In mathematics, a fraction is a number that represents a part of a whole. It consists of a numerator and a denominator. The numerator represents the number of equal parts of a whole, while the denominator is the total number of parts that make up said whole.'
According to the given problem,
For gluten free choices,
Main dishes = 22 × [tex]\frac{4}{11}[/tex]
= 8
Bread choices = [tex]\frac{40}{100}[/tex] × 5
= 2
Total possible meal deals = 8 × 7 × 2
= 112
Hence, we can conclude, 112 possible meal deals are gluten free.
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