A young sumo wrestler decided to go on a special diet to gain weight rapidly. He gained weight at a constant rate.
The table compares the wrestler's weight (in kilograms) and the time since he started his diet (in months).
Time (months) Weight (kilograms)
1.5
1.51, point, 5
85.8
85.885, point, 8
3.0
3.03, point, 0
93.6
93.693, point, 6
4.5
4.54, point, 5
101.4
101.4101, point, 4
What was the wrestler's weight before he went on his diet?
The wrestler's weight before he went on his diet was 78.0 kilograms.
What is y-intercept?
In the context of a graph of a function, the y-intercept is the point where the graph intersects the y-axis. It is the value of the dependent variable (y) when the independent variable (x) is zero. Geometrically, the y-intercept is the value of the function at the point where it crosses the y-axis.
To determine the wrestler's weight before he went on his diet, we need to find the y-intercept of the linear function that represents his weight gain over time. This is because the y-intercept corresponds to the initial weight of the wrestler, i.e., his weight before he started his diet.
We can use the two data points where the time is 0 (i.e., at the start of the diet) to find the slope of the linear function:
(1.5, 85.8) and (3.0, 93.6)
The change in weight over the time interval of 1.5 to 3.0 months is:
93.6 - 85.8 = 7.8
The change in time over that interval is:
3.0 - 1.5 = 1.5
So the slope of the linear function is:
7.8 / 1.5 = 5.2
Now we can use the point-slope form of a linear function to write an equation for the wrestler's weight gain over time:
y - 85.8 = 5.2(x - 1.5)
where y represents the wrestler's weight and x represents the time in months.
To find the wrestler's weight before he went on his diet, we need to evaluate this equation at x = 0:
y - 85.8 = 5.2(0 - 1.5)
y - 85.8 = -7.8
y = 78.0
Therefore, the wrestler's weight before he went on his diet was 78.0 kilograms.
To learn more about y-intercept, visit the link:
https://brainly.com/question/29501432
#SPJ9
Part D
The table in part C did not have a row for 10°. Look at the values of other powers of 10 in the table. Given the pattern of the values, what would
the value of 10° be?
Therefore, we can assume that the value of 10⁰ would be 1, based on the pattern of the other values in the table.
What is Celsius?Celsius (symbol: °C) is a temperature scale used in the metric system. It is named after the Swedish astronomer Anders Celsius, who first proposed it in 1742. The Celsius scale is based on the properties of water, with 0°C defined as the freezing point of water, and 100°C defined as the boiling point of water at standard atmospheric pressure. Celsius is widely used in many countries around the world as a unit of temperature measurement, including in scientific and everyday contexts.
Given by the question.
In the table from part C, we see that as the power of 10 decreases by 1, the value of 10 raised to that power also decreases by a factor of 10. For example, we see that 10² = 100, 10¹ = 10, and 10⁰ = 1.
To learn more about factor:
https://brainly.com/question/14209188
#SPJ1
Each year, the school has a goal to have a third as many students in remedial mathematics courses as the year before. Currently the school has 1,200 students in remedial math. Approximately how many students will be enrolled in four years?
(a) 44 (b)15 (c) 32,400 (d) 1
Answer:
44 students
Step-by-step explanation:
1200 for the first year
a third of that is 400
400 for the second year
a third of that is 133.4
133.4 for the third year
a third of that is 44
please please please help i’ll give brainlist
The scale factor of PQRS to JKLM is 4/5.
The scale factor of JKLM to PQRS is 5/4.
The value of w, x, and y are 20, 12.5, and 20 respectively.
The perimeter ratio is 4:5.
What is scale factor?In Mathematics and Geometry, the scale factor of a geometric figure can be calculated by dividing the dimension of the image (new figure) by the dimension of the pre-image (original figure):
Scale factor = Dimension of image (new figure)/Dimension of pre-image(actual figure)
Substituting the given parameters into the scale factor formula, we have the following;
Scale factor of PQRS to JKLM = 15/12
Scale factor of PQRS to JKLM = 5/4 or 1.25.
Scale factor of JKLM to PQRS = 12/15
Scale factor of JKLM to PQRS = 4/5 or 0.8.
For the value of w;
15/12 = 25/w
15w = 12 × 25
w = 20
For the value of x;
15/12 = x/10.
12x = 150
x = 12.5
For the value of y:
15/12 = y/16
12y = 15 × 16
y = 20
Perimeter ratio = 12 : 15 = 4:5
Read more on scale factor here: https://brainly.com/question/20795321
#SPJ1
The surface area of a cylinder is given by the formula SA = 2r2 + 2rh. A cylinder has a radius of 12 cm and a surface area of 1,632 cm^2 . Find the height of the cylinder.
A. 52 cm
B. 56 cm
C. 59 cm
D. 34 cm
Which two statements best describe Michael’s height while on the two roller coasters?
It switches between negative and positive every 40 seconds. it switches between positive and negative every 80 seconds. So correct statements are B and E.
Describe Algebra?Mathematics' branch of algebra deals with symbols and the formulas used to manipulate them. It is an effective tool for dealing with issues involving mathematical expressions and equations. In algebra, variables—which are typically represented by letters—are used to represent unknowable or variable quantities.
Equations represent mathematical relationships between variables in algebra. An equation is made up of two expressions, one on either side of an equal sign, separated by an equation. Algebraic expressions can involve constants, variables, and mathematical operations such as addition, subtraction, multiplication, and division.
As we can see from the first roller coaster's graph, Michael's height changes from positive to negative after 40 seconds, whereas it was positive for the first 40. It remains negative between 40 and 80 seconds. It continues to be positive from 80 to 120, and so forth.
As a result, every 40 seconds it alternates between negative and positive.
B is accurate.
We can see from the second roller coaster's table that it stays positive from 0 to 80. It continues to be negative from 80 to 160, and so forth.
As a result, every 80 seconds it alternates between positive and negative.
E is accurate.
The complete question is:
To know more about height visit:
https://brainly.com/question/17045372
#SPJ1
please help, thank you!
Answer:
To find all values of x for which f(x) = 26, we can set up the equation:
8x + 15/x = 26
Multiplying both sides by x, we get:
8x^2 + 15 = 26x
Bringing all the terms to one side, we get:
8x^2 - 26x + 15 = 0
We can factor this quadratic equation using the factoring method or by using the quadratic formula. Here, we will use the factoring method:
8x^2 - 26x + 15 = 0
(4x - 3)(2x - 5) = 0
Setting each factor equal to zero and solving for x, we get:
4x - 3 = 0 OR 2x - 5 = 0
4x = 3 OR 2x = 5
x = 3/4 OR x = 5/2
Therefore, the values of x for which f(x) = 26 are x = 3/4 or x = 5/2.
Reflect on why you think guitar tabs are easier or harder to read than regular musical notation.
This will have to be in paragraph form. :)
Guitar tabs are generally considered easier to read than regular musical notation because they are written in a language that most guitarists are familiar with.
What is Guitar?Guitar is a stringed musical instrument played with the fingers or a pick. It is one of the most popular instruments in the world and is widely used in genres such as rock, jazz, blues, country, folk, and classical.
Unlike traditional notation, guitar tabs do not require any knowledge of music theory to understand. Instead, they are laid out in a straightforward format that conveys the pitch of a note and the timing of when it should be played. This makes it easier for most guitarists to quickly learn a new piece of music without having to spend time studying the complexities of traditional notation. Additionally, guitar tabs also offer an easy way to determine the fingering of certain chords or techniques.
While guitar tabs are easier to read than traditional notation, they do have some drawbacks. For one, guitar tabs cannot convey the same level of detail about a piece of music as traditional notation can. Additionally, it can be difficult for some to distinguish between rhythm and lead parts when reading guitar tabs. Finally, guitar tabs do not easily convey the dynamics or expression of a piece of music, which are important to consider when playing music.
To learn more about Guitar
https://brainly.com/question/31185326
#SPJ1
Domain is now called the ____________ which means before a change
Answer:
Step-by-step explanation:
Domain is now called the "source" which means before a change or transformation. In mathematics, the term "source" is often used to refer to the set of all possible inputs or values that can be fed into a function or transformation, before any changes or transformations take place. The set of all possible outputs or resulting values from the function or transformation is called the "range" or "codomain".
- 1 and combining like terms
(x² - 4x+9)-(3x² - 6x-9)
Combining the like terms of the expressions (x² - 4x+9)-(3x² - 6x-9) gives -2x² + 2x + 36
What are algebraic expressions?Algebraic expressions are simply described as those mathematical expressions that are known to consist of certain variables, coefficients, terms, factors and constants.
Algebraic expressions are also identified with arithmetic operations. These arithmetic operations are;
SubtractionBracketDivisionParenthesesMultiplicationAdditionFrom the information given, we have;
(x² - 4x+9)-(3x² - 6x-9)
First, expand the bracket
x² - 4x + 9 - 3x² + 6x + 27
Now, collect the like terms
x²- 3x² - 4x + 6x + 9 + 27
Add or subtract
-2x² + 2x + 36
Learn about algebraic expressions at: https://brainly.com/question/4344214
#SPJ1
Simplify 1/cos x + 1/cos x -1
Answer:
-2cotxcscx
Step-by-step explanation:
Step 1: Find a common denominator
Step 2: Simplify
A solid metal cone has radius 1.65 cm and slant height 4.70 cm. Find the angle the, slant height makes with the base of the cone.
Answer:
Step-by-step explanation:
We can use trigonometry to find the angle between the slant height and the base of the cone.
The base of the cone is a circle with radius 1.65 cm. The slant height is the hypotenuse of a right triangle whose other two sides are the height (which we don't know) and the radius (1.65 cm).
Using the Pythagorean theorem, we can find the height of the cone:
height^2 = (slant height)^2 - (radius)^2
height^2 = (4.70 cm)^2 - (1.65 cm)^2
height^2 = 19.96 cm^2 - 2.72 cm^2
height^2 = 17.24 cm^2
height = sqrt(17.24) cm
height = 4.15 cm (rounded to two decimal places)
Now we can use trigonometry to find the angle between the slant height and the base of the cone.
tan(angle) = opposite / adjacent
tan(angle) = height / radius
tan(angle) = 4.15 cm / 1.65 cm
tan(angle) = 2.515
Taking the inverse tangent (or arctan) of both sides, we get:
angle = arctan(2.515)
angle = 70.32 degrees (rounded to two decimal places)
Therefore, the angle between the slant height and the base of the cone is 70.32 degrees.
Can someone please help me!!!
The graph of f(x) is a parabola that opens downward and has a vertex at (-3/2, 3/4), while the graph of g(x) is a parabola that opens upwards and has a vertex at (-1/2, 7/4). They both intersect at the point (-3/2, -5/4).
What is vertex?Vertex is a mathematical term used to describe the point where two lines or line segments meet. It is the point of intersection for two or more lines. In a two-dimensional plane, a vertex is the point that marks the beginning and end of a line segment. In a three-dimensional plane, a vertex is the point of intersection of three or more lines. A vertex can also refer to a corner, such as the vertex of a triangle or a cube. In graph theory, a vertex is a node, or point, in a graph. Vertex can also refer to the highest point of a graph, such as the vertex of a parabola.
To learn more about vertex
https://brainly.com/question/21185651
#SPJ1
The radius of a cylindrical water tank is 4 ft, and its height is 6 ft. What is the volume of the tank?
Use the value 3.14 for it, and round your answer to the nearest whole number.
Be sure to include the correct unit in your answer.
0
4 ft
6 ft
In response to the stated question, we may state that Therefore, the cylinder volume of the tank is approximately 301 cubic feet.
what is cylinder?A cylinder is a three-dimensional polyhedron made up of two congruent parallel circular bases but a curving surface linking the two bases. The bases of a cylinder are all equal to its axis, which is an artificial straight line across the centre of both bases. The volume of a cylinder is the composite of its base area and length. The volume of a cylinder is computed as V = r2h, where "V" represents the volumes, "r" represents the circle of the base, and "h" is the height of the cylinder. The formula to find the volume of a cylinder is:
[tex]V = \pir^2h[/tex]
Where V is the volume, r is the radius, h is the height, and π is a constant value that approximates to 3.14.
[tex]V = 3.14 * 4^2 * 6\\V = 3.14 * 16 * 6\\V = 301.44\\V = 301 ft^3[/tex]
Therefore, the volume of the tank is approximately 301 cubic feet.
To know more about cylinder visit:
https://brainly.com/question/16134180
#SPJ1
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
The correct option is 1 and 4 of the given inequality –3(2x – 5) < 5(2 – x)
The correct representations of the inequality –3(2x – 5) < 5(2 – x) are:
-6x + 15 < 10 – 5x
x < 5
Therefore, options 1 and 4 are correct. The other options do not correctly represent the inequality.
To Know more about inequality visit :
https://brainly.com/question/31278109
#SPJ9
In a restaurant, there are 5 managers, 15 servers, 10 cooks and 15 other personnel. If a person is selected at random, what is the probability that the person is either a manager or a cook?
Answer:
0.33
Step-by-step explanation:
There are a total of 5 + 15 + 10 + 15 = 45 people in the restaurant.
The probability of selecting a manager or a cook is the sum of the probabilities of selecting a manager and selecting a cook, since these events are mutually exclusive (a person cannot be both a manager and a cook at the same time).
The probability of selecting a manager is 5/45, since there are 5 managers out of 45 people in total.
The probability of selecting a cook is 10/45, since there are 10 cooks out of 45 people in total.
Therefore, the probability of selecting either a manager or a cook is:
P(manager or cook) = P(manager) + P(cook)
P(manager or cook) = 5/45 + 10/45
P(manager or cook) = 15/45
P(manager or cook) = 1/3
So, the probability that the person selected at random is either a manager or a cook is 1/3 or approximately 0.333
leave a comment
What is the area of the real object that the scale drawing models? Scale factor. 1:5 Area = 10 square cm Scale drawing Real object
Answer:
D. 50 square centimeters
Rachel ran 3 miles when she was training for a race. How many feet did she run?
15,840 feet
5,280 feet
10,560 feet
14,840 feet
To convert miles to feet, we need to multiply the number of miles by the number of feet in one mile. There are 5,280 feet in one mile. So, to find out how many feet Rachel ran, we can multiply 3 miles by 5,280 feet/mile:
3 miles x 5,280 feet/mile = 15,840 feet
Therefore, Rachel ran 15,840 feet. Answer: 15,840 feet.
If you place a 26-foot ladder against the top of a building and the bottom of the ladder is 20 feet from the bottom of the building, how tall is the building? Round to the nearest tenth of a foot. help please now.
Answer: The building is approximately 16.6 feet tall.
Step-by-step explanation:
Use Pythagorean theorem (a²+b²=c²) to solve this.
We know that the ladder is 26 feet long so that would be our hypotenuse (c²). and the distance between the ladder and the building is 20 feet. So, this is the base. The remaining side is x.
Your equation would be: 20²+x²=26²
subtract 20² from 26² --> 276=x²
then take the square root --> 16.6=x
In ΔLMN, n = 27 inches, l = 70 inches and ∠M=149°. Find ∠N, to the nearest degree.
Using trigonometric functions, we can find that the value of the angle N is 3°.
What are trigonometric functions?The six fundamental trigonometric operations make up trigonometry. Trigonometric ratios are useful for describing these methods. The sine, cosine, secant, co-secant, tangent, and co-tangent functions are the six fundamental trigonometric functions. On the ratio of a right-angled triangle's sides, trigonometric identities and functions are founded. Trigonometric formulas are used to determine the sine, cosine, tangent, secant, and cotangent values for the perpendicular side, hypotenuse, and base of a right triangle.
Here, using the cosine theorem:
CosM = n² + l² - m²/2nl
⇒ Cos 149° = 27² + 70² - m²/2 × 27 × 70
⇒ -0.981 = 729 + 4900 - m²/3780
⇒ 5629 - m² = -3708
⇒ m² = 9337.
Now Cos N = m² + l² - n²/2ml
= (9337 + 4900 - 729) / (2 × √9337 × 70)
= 0.9985
Cos N = 0.9985
Putting [tex]Cos^{-1}[/tex] on both sides:
[tex]Cos^{-1}[/tex] Cos N = [tex]Cos^{-1}[/tex] 0.9985
⇒ N ≈ 3°
To know more about trigonometric functions, visit:
https://brainly.com/question/6904750
#SPJ1
The complete question is:
In ΔLMN, n = 27 inches, l = 70 inches and ∠M=149°. Find ∠N, to the nearest degree.
How many total blocks does Ben need to walk north and east to get from his home to the playground and home again?
75909931 rounded to the nearest hundred thousand
Answer:
the answer is supposably 75900000
23 x _ = 23 x 4
(help me)
Answer:
4
Step-by-step explanation:
To solve for the missing value in 23 x _ = 23 x 4, you can use the property of equality to divide both sides by 23. This will give you _ = 4. Therefore the missing value will be 4.
Hope this helped :)
Answer: the answer is 4
Step-by-step explanation: u can divide both sides with 23 and that leaves u with x=4
Someone please help me answer this question
The two statements that are both true are as follows: line
AC is perpendicular to line HB and line AC is parallel to FG. That is option A.
What is a perpendicular line?A perpendicular line is defined as the line that forms angle 90° where it meets with another line in a plane.
A line is said to be parallel to each other when they do not intercept as they are both on the same plane.
From the given diagram, line AC is perpendicular to line HB because they form angle 90° at the point of intersection.
Also, line AC is parallel to FG, because they can never intersect till infinity.
Learn more about parallel lines here:
https://brainly.com/question/24607467
#SPJ1
PLEASE HELP WILL GIVE BRAINLIEST!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
The notation Σ-2 (3η + 5) is incorrect for representing the arithmetic series 8 + 11+ ... + 29.
The correct notation for the arithmetic series 8 + 11 + ... + 29 should be:
Σ_{i=1}^{11} (6i + 2)
The series has 11 terms, and each term can be found by adding 3 to the previous term, starting with the first term 8. Therefore, the general form of the series is 6i + 2, where i represents the index of the term in the series.
In contrast, the notation Σ-2 (3η + 5) appears to have multiple errors. The use of a negative index (-2) is not valid, as the index should start from 1 or 0. Also, the use of the Greek letter eta (η) instead of i as the index variable is unconventional and likely to cause confusion. Finally, the expression inside the parentheses does not appear to correspond to the terms of the arithmetic series.
The correct notation for the arithmetic series 8 + 11 + ... + 29 should be:
Σ_{i=1}^{11} (6i + 2)
To explain the error in the given notation Σ-2 (3η + 5), we can break it down as follows:
The use of a negative index (-2) is incorrect. The index of summation should always be a non-negative integer.
The use of the Greek letter eta (η) instead of i as the index variable is unconventional and may cause confusion or errors.
The expression inside the parentheses, 3η + 5, does not represent the terms of the arithmetic series. In particular, it does not involve the index variable i or the common difference 3.
Therefore, the correct notation for the given arithmetic series is Σ_{i=1}^{11} (6i + 2).
The sum of twice a number,n, and 14 is 30. Write an equation that models this statement.Then explain how you might use reasoning to find the value of n.
Answer:
2n + 14 = 30
Step-by-step explanation:
Since you know that 2n + 14 = 30, we can determine the values by first subtracting 14 from 30. Our equation would then be 2n = 16. Divide 2 from both sides and n = 8.
This model represents the total on the top and the 2 parts on the bottom.
Is ∆PQR a right triangle? Explain
Answer:
Yes, ∆PQR is a right triangle.
Step-by-step explanation:
A right triangle has one right angle, which is 90°. This triangle has one right angle, so it is a right triangle.
Trevor used about half of a 5-lb bag of potatoes (2 lb 6 oz). How much did the remaining potatoes weigh?
Answer:
Step-by-step explanation:
f Trevor used 2 lb 6 oz of a 5-lb bag of potatoes, then the weight of the remaining potatoes is:
5 lb = 80 oz (since 1 lb = 16 oz)
Remaining potatoes = Total potatoes - Used potatoes
Remaining potatoes = 80 oz - 2 lb 6 oz
Remaining potatoes = 80 oz - (2 × 16 oz + 6 oz)
Remaining potatoes = 80 oz - 38 oz
Remaining potatoes = 42 oz
Therefore, the remaining potatoes weighed 2 lb 10 oz (or 42 oz).
Polly's sister-in-law is going to have a baby! For the baby shower, Polly decided to sew pillow to give as a gift. She is using a flower-printed rectangular piece of fabric that is 26 inches long and 22 inches wide.
Answer:
The answer is 96
Step-by-step explanation:
2*(26+22)
2*48
96
Natalie invests $2,000 into a savings account
which earns 11% per year. In 20 years, how
much will Natalie's investment be worth if
interest is compounded monthly? Round to the
nearest dollar.
Answer:
We can use the formula for compound interest to find the future value (FV) of Natalie's investment:
FV = P * (1 + r/n)^(n*t)
Where:
P is the principal amount (the initial investment), which is $2,000 in this case
r is the annual interest rate as a decimal, which is 11% or 0.11
n is the number of times the interest is compounded per year, which is 12 since interest is compounded monthly
t is the number of years, which is 20
Substituting the values into the formula, we get:
FV =
2
,
000
∗
(
1
+
0.11
/
12
)
(
12
∗
20
)
�
�
=
2,000 * (1.00917)^240
FV = $18,255.74
Therefore, after 20 years of compounded monthly interest at a rate of 11%, Natalie's investment of 2,000 will be worth approximately 18,256.
Answer:
$17,870
Step-by-step explanation:
You must use the formula for compound interest.
A = P(1 + r/n)^nt
I suggest you look it up at some point so that you can do these more easily in the future!