The equation and value of x , the distance of 1 lap around the path at the park is 4.8x + 1.2 = 3.6.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
Florian ran 1.2 miles and walked 4.8 laps around the path at the park for a total distance of 3.6 miles.
As, we know the number of them (4.8) would be multiplied by the variable (x). We also know that 1.2 is the constant.
So, the equation can be framed as
4.8x + 1.2 = 3.6
4.8x = 2.4
x = 0.5
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The question attached here seems to be incomplete the remaining portion is given below:
3.6 x + 1.2 = 4.8; x = 1 mile
4.8 x + 1.2 = 3.6; x = 1 mile
3.6 x + 1.2 = 4.8; x = 0.5 mile
4.8 x + 1.2 = 3.6; x = 0.5 mile
5 x = negative 58
16÷8
Like as an equivalent multiplication expression
Answer: 16*(1/8)
Step-by-step explanation:
25 points! Multiply and simplify. Show all steps to earn full credit. Circle your final answer (or highlight final answer in yellow if typing). (4 points)
(2x−3)(4x^2−5x+2)
Answer: [tex]8x^{3}-22x^{2} +19x-6[/tex]
Step-by-step explanation:
I need help with problem
Answer:
Below
Step-by-step explanation:
Since all of the lines are parallel and cut by a transversal .... the
corresponding angles are equal
8x - 11 = 7x +8
x = 19
A backcountry airport has a runway that is 150 feet long. Approximately 75 feet past the runway is a large
grove of trees that average in height around 100 feet tall. What angle of elevation must a pilot take in
order to avoid crashing into the trees? Round to the nearest hundredths.
Select an answer
Question Help: Message instructor
To find the angle of elevation, we need to determine the height of the plane relative to the trees, and then use the tangent function to find the angle. Let's call the height of the plane "h".
We can set up a right triangle with the height of the plane, the distance from the runway to the trees, and the height of the trees.
We have:
h / (150 + 75) = 100 / h
Solving for h, we find that:
h = 125
So the height of the plane relative to the trees is 125 feet.
Now we can use the tangent function to find the angle:
tan(angle) = 100 / 125
angle = tan^-1(100 / 125)
angle = approximately 53.13 degrees
Rounding to the nearest hundredths, the angle of elevation that the pilot must take to avoid crashing into the trees is 53.13 degrees.
If g(x) = x², what is the value of g(a + 2)?
Answer:
[tex](a+2)^2[/tex]
Step-by-step explanation:
Substitute [tex]x=a+2[/tex] into [tex]g(x)[/tex].
Jimmy is an accountant who also works part-time as a museum tour guide. Information from his tax worksheet is wages from accounting job, $75,937.84; wages from museum job, $14,937.92; interest, $839.40; and dividends, $123.45. What is Jimmy’s total income?
Jimmy’s total income is $91838.61
How to determine Jimmy's income?You should understand that total income' refers to the sum of certain incomes (in cash and, in some circumstances, in kind) of the statistical unit during a specified reference period
The given parameters that will help us to determine the income are
wages from accounting job, $75,937.84;
interest, $839.40
wages from museum job, $14,937.92;
dividends, $123.45.
Therefore Jimmy's total income is the sum of all the incomes
$(75,937.84 + 839.40 + 14,937.92 + 123.45)
Total income = $91838.61
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Of the three important sources of resistance, which ones remain relatively constant?1.Blood viscosity 2.Blood vessel length
The blood viscosity and vessel length remain relatively constant, the regulation of vessel radius becomes the primary mechanism for controlling resistance in the body.
Blood viscosity refers to the thickness or stickiness of blood, which is determined by the number and size of red blood cells, as well as the concentration of proteins and other substances in the plasma.
Blood viscosity affects resistance because the thicker the blood, the more difficult it is for it to flow through the blood vessels.
Blood vessel length refers to the distance that blood has to travel through the vessels, which affects resistance because the longer the vessel, the more difficult it is for blood to flow through it.
However, vessel length remains relatively constant in the body because it is determined by the body's anatomy and does not change significantly over time. Therefore, the only time when vessel length can change is during a surgical procedure or injury that alters the anatomy of blood vessels.
Mathematically, the resistance to blood flow (R) can be calculated using the formula R = (8 x viscosity x length) / (π x radius⁴).
This formula shows that blood viscosity and vessel length are directly proportional to resistance, while vessel radius is inversely proportional.
Therefore, any increase in blood viscosity or vessel length will increase resistance, while any decrease in vessel radius will increase resistance.
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When an integer is subtracted from 6 times the next consecutive integer, the difference is 41. Find the value of the greater integer.
The value of the greatest integer such that the smaller integer subtracted from 6 times the greater integer, difference is 41 is 8.
What is an Equation?An equation is a mathematical statement containing two expressions on either sides which are connected with an equal to sign.
Either sides of an equation is called as left hand side and right hand side.
Given that,
When an integer is subtracted from 6 times the next consecutive integer, the difference is 41.
Let the integer be x.
Then the next consecutive integer will be x + 1
6 times the next consecutive integer means 6 (x + 1).
an integer is subtracted from this means 6 (x + 1) - x.
The difference of this is 41.
6 (x + 1) - x = 41
By distributive property,
6x + 6 - x = 41
5x + 6 = 41
5x = 41 - 6
5x = 35
x = 7
Hence the value of the integer is 7 and the value of next consecutive integer is 8.
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A spinner is divided into six equal parts numbered 1, 2, 3, 4, 5, and 6. In a repeated experiment, Ryan spun the spinner twice. The theoretical probability of both spins being odd numbers is 9 over 36.
If the experiment is repeated 140 times, predict the number of times both spins will be odd numbers.
140
70
36
35
So, based on the theoretical likelihood, we anticipate that 35 times out of 140 repeats, both spins will be odd numbers.
What is probability?Probability is a branch of mathematics that deals with the study of random events and the likelihood of their occurrence. Probability is expressed as a number between 0 and 1, with 0 indicating that an event is impossible to occur and 1 indicating that an event is certain to occur. The probability of an event A, denoted by P(A), is calculated as the number of favorable outcomes for the event divided by the total number of possible outcomes. For example, if a fair six-sided die is rolled, the probability of rolling a 3 is 1/6 because there is only one favorable outcome (rolling a 3) out of the total 6 possible outcomes. Probabilities can be used to make predictions about the likelihood of future events and to make decisions under uncertainty. Probabilities can also be used to describe the distribution of random variables and to quantify the relationship between different events. Probability theory is widely used in many fields, such as statistics, engineering, finance, physics, and biology, among others.
Here,
The theoretical probability of both spins being odd numbers is 9 over 36, which means that for every 36 times the experiment is repeated, we expect 9 of those times to result in both spins being odd numbers.
If the experiment is repeated 140 times, we can use the theoretical probability to estimate the number of times both spins will be odd numbers as follows:
140 * (9/36) = 35
So, based on the theoretical probability, we predict that both spins will be odd numbers 35 times out of 140 repetitions.
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27. Table 2 show rates of tax on salary per month for certain country. Table 2. Salary per month Tax rate First K9000.00 % (tax free) Next K10000.00 15% Next K12000.00 25% Next K15000.00 35% If a worker earns K30000.00 per month, calculate the worker's monthly tax. 25%
The amount of the worker monthly tax will equals to K4,850.
What are worker income tax?An income tax refers to the tax imposed on individuals or entities in respect of the income earned by them. It is computed as the product of a tax rate times the taxable income. They may vary by type or characteristics of the taxpayer and the type of income
To calculate the worker's monthly tax, we need to determine the amount of salary that falls into each tax bracket and then calculate the tax owed for each bracket:
For a monthly salary of K30,000, the first K9,000 is tax-free, leaving K21,000 to be taxed. Of this K21,000, the first K10,000 is taxed at 15%, which gives a tax of K1,500. The next K12,000 is taxed at 25%, which gives a tax of K3,000.Finally, the remaining K-1,000 is taxed at 35%, which gives a tax of K350.The worker's monthly tax is then computed as:
= K1,500 + K3,000 + K350
= K4,850.
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what day is 75 days from now?
The date that is 75 days from now, if today is February 22, 2023, is May 8, 2023.
To find the date that is 75 days from now, we can start with the current date and add 75 days to it. This can be done by adding the number of days to the day of the month, and if necessary, advancing to the next month or year.
For example, if today is February 22, 2023, we can count forward 75 days on a calendar to find the date that is 75 days from now. This would take us to May 8, 2023.
Here is the mathematical calculation:
Current date + 75 days = (February 22, 2023) + 75 days
= February 22, 2023 + 75 days
= (February 22, 2023 + 31 days) + (44 days)
= March 25, 2023 + 44 days
= (March 25, 2023 + 30 days) + (14 days)
= April 24, 2023 + 14 days
= (April 24, 2023 + 14 days)
= May 8, 2023
Therefore, the date that is 75 days from now, if today is February 22, 2023, is May 8, 2023.
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Noah would like to cover a rectangular tray with rectangular tiles. The tray has a width of 2 1/2 and an area of 4 3/4. What is the length of the tray?
The length of the rectangular tray is 1 9/10
What is a Rectangle?
Rectangle is a four-sided flat shape where every angle is a right angle (90°).
Area of a Rectangle = Length * Width
where,
Area = 4 3/4
Length = ?
Width = 2 1/2
To find the length of the tray,
Length = Area/Width
Length = 4 (3/4) / (2 1/2)
Length = (19/4) / (5/2)
Length = 19/4 * 2/5
Length = 19/10
Length = 1 9/10
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Part E
If you’re a frequent flyer who travels to many different airports, and you have the choice between SkyWest Airlines (OO) and Southwest Airlines (WN) for all your flights, which carrier should you choose if your primary concern is arriving on time?
Answer:
Щоб визначити, яка авіакомпанія має кращий досвід прибуття вчасно, ми можемо переглянути їхню статистику ефективності вчасності. Згідно з даними Міністерства транспорту США, у 2020 році показник своєчасних прильотів у SkyWest Airlines становив 85,8%, а у Southwest Airlines – 83,5%. Це означає, що у 2020 році SkyWest Airlines мала кращий досвід прибуття вчасно, ніж Southwest Airlines.
Однак варто зазначити, що своєчасна продуктивність може змінюватися залежно від низки факторів, включаючи погоду, управління повітряним рухом і проблеми з обслуговуванням. Також важливо врахувати інші фактори, які можуть бути для вас важливими, наприклад вартість авіаквитків, наявність рейсів у бажані пункти призначення та якість обслуговування під час польоту. Таким чином, незважаючи на те, що оперативність є важливим фактором, який слід враховувати при виборі авіакомпанії, це може бути не єдиним фактором, який вам слід враховувати.
Step-by-step explanation:
Please help! I will mark you "brainliest" if you write an answer.
The correct statement regarding the solution to the system of equations is given as follows:
b. (1,2) is a solution to both the lines A and B.
How to obtain the solution to the system of equations?We want to obtain the graphic solution for the system of equations, hence we obtain the point of intersection of the two equations.
This point of intersection is a solution to both of the equations, hence it is the solution to the system of equations.
The coordinates of the point of intersection in this problem are given as follows:
(1,2).
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Explain how to find answers please help!!!
A fiction novel series that costs the seller $38 has a markup rate of 62%. What is the selling price
of the fiction novel series?
on solving the provided question we can say that the selling price of the fiction novel series is $61.56.
What is selling price?Cost: The cost price is the amount paid for an item at the time of purchase or the cost for producing it. Costs are identified by the notation C.P. Selling price: The selling price is the price at which a thing is sold. The amount that the seller really receives when the sale is complete is known as the selling price. The price a seller pays for a good or service is really called the cost. A profit percentage is then added.
markup rate is 62%,
t the seller is adding 62% of the cost to the price to make a profit.
Markup = 62% of Cost = [tex]0.62 * $38 = $23.56[/tex]
Selling price = [tex]Cost + Markup = $38 + $23.56 = $61.56[/tex]
the selling price of the fiction novel series is $61.56.
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The ratio of men to women working for a company is 5 to 6. If there are 95 men working for the company, what is the total number of employees
Answer:
114
Step-by-step explanation:
5 : 6
5 + 6 =11
5/6 x y = 95
y = 95 / 5/6
= 95 x 6/5
= 114
Therefore total number of employees is 114 :)
Find the value of sin S rounded to the nearest hundredth, if necessary.
Answer:
Step-by-step explanation:
sin angle S = [tex]\frac{opposite}{hypotenuse}[/tex]
sin S = [tex]\frac{30}{hypotenuse}[/tex]
To complete the ratio we need to find the hypotenuse:
a² + b² = c²
16² + 30² = c²
256 + 900 = c²
1156 = c²
√1156 = √c²
34 = c
Now substitute 34 in the sin ratio:
[tex]\frac{30}{34}[/tex] = .8824
nearest hundredth = .88
Mike wrote a pattern starting at 15 and following the rule "add 5." What is the missing term in the pattern?
15, 25, 30, 35...
O 10
40
30
O 20
Answer:
40
Step-by-step explanation:
X, Y, Z Axis. What do they stand for?
The X, Y, and Z axes define a three-dimensional coordinate system, which is commonly used to represent physical objects or mathematical functions in space.
The X, Y, and Z axes are terms commonly used in mathematics, physics, engineering, and computer graphics to refer to the three dimensions in a three-dimensional coordinate system.
The X-axis is the horizontal axis and is used to represent values along the horizontal plane. It is often called the "abscissa" and is typically drawn as a horizontal line that intersects with the Y-axis at the point where they meet, which is called the origin.
The Y-axis is the vertical axis and is used to represent values along the vertical plane. It is often called the "ordinate" and is typically drawn as a vertical line that intersects with the X-axis at the origin
.The Z-axis is the third axis and is used to represent values along the depth or height plane. It is often called the "applicate" and is typically drawn as a line that is perpendicular to both the X and Y axes, intersecting with both at the origin.
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Hi can someone help please this is due tomorrow
a. Two out of every 3 seniors at Lewis High apply for college, so the number of seniors who apply for college is 2/3 (or approximately 0.67) times the total number of seniors at Lewis High.
How to calculate the valuesb. The number of seniors who apply for college is one-third (or approximately 0.33) less than the number of seniors who don't apply.
c. One-third (or approximately 0.33) of the graduating seniors at Lewis High do not apply to college.
d. Three out of every 5 seniors who apply for college are female students, so two out of every 5 seniors who apply for college are male students. Therefore, the fraction of seniors who are males who apply for college is 2/5 (or approximately 0.4).
The number of males who apply for college is 2/3 of the total number of seniors who apply for college, which is (2/3) * (2/5) = 4/15 (or approximately 0.27) times the total number of graduating seniors at Lewis High.
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A marine biologist wants to determine the impact of warming oceans on the coral in Great Barrier Reef. Which option below best describes the population he will study?
Answer:All the oceans in the world
Only the ocean in which the Great Barrier Reef is found
Coral in all the oceans of the world
Only coral found in the Great Barrier Reef
Step-by-step explanation:
Answer: all oceans
Step-by-step explanation:
For number 8 find the variable using the properties of a parallelogram
Applying one of the properties of a parallelogram, the value of x is 10°, then 6x=60° and 12x=120°.
QuadrilateralsThere are different quadrilaterals, for example square, rectangle, rhombus, trapezoid, and parallelogram. Each type is defined accordingly to its length of sides and angles. For example, a parallelogram presents some properties that are presented below.
the opposite sides are equal and parallelthe opposite angles and the diagonals are equal.the adjacent angles are supplementary.The figure of the exercise shows two adjacent angles. From the property: the adjacent angles are supplementary, you have:
6x+12x=180
18x=180
x=10°
Therefore, 6x= 6*10=60° and 12x=12*10=120°.
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Decide which of the given units would be the most appropriate to use for
a) the height of a building: kilometres, metres or centimetres?
b) the mass of a pen: grams, tonnes or kilograms?
c) the capacity of a paddling pool: millilitres or litres?
The measurement units along with the measured quantities are given as -
The height of a building : metersThe mass of a pen : gramsThe capacity of a paddling pool : litersWhat are measurement units?Measurement units are used to measure the total amount of any specific quantity.
Given are the units to measure the various quantities as given.
{a} -
Height of building is measured in meters.
The height of a building : meters
{b} -
Small quantities of mass is measured in grams.
The mass of a pen : grams
{c} -
The capacity of a paddling pool : liters
Therefore, the measurement units along with the measured quantities are given as -
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What is the result when the number 76 is decreased by 39%? Round your answer to the nearest tenth?
Answer:
46.4
Step-by-step explanation:
lets use a multiplier instead
100-39=61
so 76 x 0.61 = 61% of 76
76 x 0.61 = 46.36
rounded to the nearest tenth would be rounded up
46.4
Leo Gandolfi takes out a short-term loan of $1,800 at 12 percent
for 6 months. The monthly payment is $310.50. The balance of the loan after 4 payments is
$612.34. How much does he save by paying off the loan when the next payment is due?
A $6.12
R2 $18.00
C
2,353
SCIO
In a linear equation, 9.14 does he save by paying off the loan when the next payment is due .
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) term, 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.
Jan 293 18 311 1,507 16.25%
Feb 296 15 311 1,212 32.67%
Mar 298 12 311 913 49.25%
Apr 301 9 311 612 66.00%
May 304 6 311 308 82.92%
Jun 308 3 311 0 100.00%
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A cylinder has a volume of 1 and one third in3 and a radius of one third in. What is the height of a cylinder? Approximate using pi equals 22 over 7.
42 over 6 inches
42 over 9 inches
42 over 11 inches
42 over 22 inches
Answer:
42/11!
Step-by-step explanation:
So first, you need to make sure you have the formula which is V= Base X height. The base is the area of 1 circle, so you multiply the radius X radius X PI.
1/3 x 1/3 is 1/9. 22/7 is used as pi so multiply 1/9 by 22/7 and you get 22/63. Now you divide that by 4/3. When dividing fraction, you keep the first decimal (4/3) the same, turn the division symbol into a multiplication one, and flip the last fraction (so 22/63 is now 63/22!).
Now you just solve 4/3 x 63/22, which will give you 252/66. Now simplify that by dividing both numbers by 3 until you get the smallest answer, which is 42/11!
The height of the cylinder is approximately 42/11 inches. The answer is option C.
Here, we have,
we know that,
The formula for the volume of a cylinder is V = πr²h,
where V is the volume, r is the radius, and h is the height.
We are given that the volume of the cylinder is 1 and one-third in^3 and the radius is one-third in. Substituting these values into the formula, we get:
1 and one-third = 4/3
V = π(1/3)²h = 4/3
Simplifying the equation, we get:
h = (4/3) / (π(1/3)²)
= (4/3) / (π/9)
= (4/3) * (9/π)
= 12/π
Approximating π as 22/7, we get:
h ≈ (12/π)
≈ (12/(22/7))
= 42/11 inches
Therefore, the height of the cylinder is approximately 42/11 inches. The answer is option C.
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Ennis wants to make a border for a triangular-shaped vegetable garden. He has 4 pieces of wood that measure 8 inches, 10 inches, 12 inches, and 18 inches. How many different triangular borders can ennis make?.
After considering all the combinations of three pieces of wood, we can conclude that Ennis can make 2 different triangular borders for his vegetable garden.
A triangle is a shape with three sides, and each side can be considered as a side length. In order to form a triangle, the sum of the lengths of the two shorter sides must be greater than the length of the longest side.
To find the number of different triangular borders that Ennis can make, we need to consider all the combinations of three pieces of wood as the sides of the triangle. There are four pieces of wood, so the number of combinations of three pieces is 4 choose 3, which is 4.
Now, we need to determine if each combination of three pieces of wood forms a triangle. If the sum of the lengths of the two shorter sides is greater than the length of the longest side, it forms a triangle. If not, it does not form a triangle.
If Ennis uses the 8-inch and 10-inch pieces as two sides, he can use the 12-inch or 18-inch piece as the third side, and it forms a triangle.
If he uses the 8-inch and 12-inch pieces as two sides, he can only use the 10-inch piece as the third side, and it forms a triangle. If he uses the 8-inch and 18-inch pieces as two sides, it does not form a triangle.
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I hate these kind of questions. I forgot how to do it :)
The length of the right triangle x is 2√5 units.
How to find the side of a right triangle?A right triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.
Therefore, the sides of the right triangle can be found using Pythagoras's theorem,
Hence,
c² = a² + b²
where
a and b are the legsc = hypotenuse sideTherefore,
x² = 6² - 4²
x² = 36 - 16
x² = 20
square root both sides
x = √20
x = 2√5
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The function f(x)=90(16)x describes an exponential growth function, where x is the time in years. How long does it take the initial value to double?
Answer: 1440x or 1440
Step-by-step explanation:
find the unit tangent vector T and the curvature k for the following parameterized curver(t) = <9 cos t, 9 sin t, sqrt(3) t>
The unit tangent vector T and the curvature k is √2/3
Unit Tangent Vector and Curvature are two important concepts in vector calculus that are used to describe the behavior of curves in space.
To find the Unit Tangent Vector, we must first find the derivative of the curve. The curve is defined as (t) = <9 cos t, 9 sin t, √(3) t>, so taking the derivative with respect to t, we get:
d(t) / dt = < -9 sin t, 9 cos t, √(3) >
Next, we want to normalize this vector to get the Unit Tangent Vector, T. To do this, we divide the vector by its magnitude, which is given by:
=> √((-9 sin t)² + (9 cos t)² + (√(3))²)
=> √(81 + 81 + 3) = 9 √(3)
So, the Unit Tangent Vector is given by:
T = d(t) / dt / |d(t) / dt|
T = < -9 sin t / 9 √(3), 9 cos t / 9 √(3), √(3) / 9 √(3) >
T = < -sin t / √(3), cos t / √(3), 1 / 3 √(3) >
To find the Curvature, we use the formula:
k = |dT / dt|
where T is the Unit Tangent Vector and dT / dt is the derivative of the Unit Tangent Vector. To find dT / dt, we take the derivative of T with respect to t:
dT / dt = < cos t / √(3), -sin t / √(3), 0 >
Finally, the magnitude of dT / dt gives us the Curvature:
=> √((cos t / √(3))² + (-sin t / √(3))² + (0)²)
=> √(1 / 3 + 1 / 3) = √(2 / 3) / √(3)
So, the Curvature is given by:
k = √(2 / 3) / √(3)
k = √2 / 3
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