Answer:
Paul is 70 kg, John is 62 kg and David is 65 kg.
Step-by-step explanation:
Let x the mass for each person.
Paul = x
John is lighter than Paul, so John = x-8
David's mass is 5 kg less than John's, so David = x-5
Solution:
Make an equation.
x + (x-8) + (x-5) = 197
3x -13 = 197
3x = 197 + 13
3x= 210, then divide both side by 3, to get 70.
Do substitution to get a correct answer.
70+62+65= 197
197= 197
find the value of the polygon. the polygon has 6 interior angles 2 of them are y and 4 of them are (2Y-20)
The cost of producing x units of a product is C dollars, where C is given by the function C = 0.25x2 - 80x + 300. What is the cost if no units are produced?
A)
$0
B)
$100
C)
$200
D)
$300 ...?
Answer:
D) $ 300
Step-by-step explanation:
Here, the cost ( in dollars ) of x products is defined by the function,
[tex]C=0.25x^2-80x+300[/tex]
Since, if the no units are produced,
x = 0,
Hence, the cost would be,
[tex]C=0.25(0)^2-80\times 0+300[/tex]
[tex]=0-0+300[/tex]
[tex]=\$ 300[/tex]
Option D is correct.
The cost is $300 if no units are produced.
To find the cost when no units are produced, which are shown by x and we need to evaluate the cost function C at x = 0. The cost function is given by [tex]C = 0.25x^2 - 80x + 300.[/tex]
Let's substitute x = 0 into the function:
[tex]C(0) = 0.25(0)^2 - 80(0) + 300[/tex]
[tex]C(0) = 0 - 0 + 300[/tex]
[tex]C(0) = 300[/tex]
Therefore, the cost when no units are produced is $300.
This corresponds to the constant term in the cost function, which represents the fixed costs that are incurred regardless of the number of units produced.
HELP! Which two-dimensional shape can be rotated about the y-axis to create a cone?
Answer:
Its a triangle
Tell whether the sequence is arithmetic. If it is, what is the common difference?
A. -6,2,10,18, ...
B. 1,2,4,8, ...
Write an equation ;
you have cable plan that costs $39 a month for a basic plan plus one movie channel . Your friend has the same basic plan plan plus two movies channels for $45.50 . What is the basic plan change that you both pay ?
What is 490% written as a decimal? 4.9 0.0049 49 490
Answer:
the answer is A
Step-by-step explanation:
James has 6 stamps in his stamp collection. Roy has 12 stamps in his stamp collection. James adds 2 stamps to his stamp collection. After James adds these stamps, what is the ratio of the number of stamps in James's collection to the number of stamps in Roy's collection
height of a table tennis net: 6 in. height of a tennis net: 3ft
Explain how using equivalent ratios is like adding fractions with unlike denominators?
Final answer:
Using equivalent ratios is like adding fractions with unlike denominators as it involves finding a common value to work with.
Explanation:
Using equivalent ratios is similar to adding fractions with unlike denominators because both involve finding a common value to work with. When adding fractions, we look for a common denominator so that we can add the numerators. With equivalent ratios, we find a common multiplier to scale the ratios, which allows us to compare or combine the quantities represented by the ratios.
Here's a step-by-step process:
Convert the given ratios to fractions by writing them as a fraction with the given quantities as the numerator and denominator.
Find a common denominator for the fractions. This involves identifying the least common multiple (LCM) of the denominators.
Multiply the numerators and denominators of the fractions by the appropriate multiples to get equivalent fractions with the same denominator.
Compare or combine the quantities represented by the equivalent fractions.
What are the sine, cosine, and tangent of Θ = 3 pi over 4 radians?
sin Θ = square root 2 over 2; cos Θ = negative square root 2 over 2; tan Θ = -1
sin Θ = negative square root 2 over 2; cos Θ = square root 2 over 2; tan Θ = 1
sin Θ = square root 2 over 2; cos Θ = negative square root 2 over 2; tan Θ = 1
sin Θ = negative square root 2 over 2; cos Θ = square root 2 over 2; tan Θ = -1
43/14 as a decimal rounded to the nearest hundredth
Answer:
The decimal of the fraction rounded to the nearest hundredth is
[tex]\frac{43}{14}=3.07[/tex]
Step-by-step explanation:
Given : Expression [tex]\frac{43}{14}[/tex]
To find : What is the decimal of the fraction rounded to the nearest hundredth?
Solution :
Step 1 - Write the fraction
[tex]\frac{43}{14}[/tex]
Step 2 - Divide the numerator by denominator,
[tex]\frac{43}{14}=3.071[/tex]
Step 3 - Convert to the nearest hundredth,
[tex]3.071\approx 3.07[/tex]
Therefore, The decimal of the fraction rounded to the nearest hundredth is
[tex]\frac{43}{14}=3.07[/tex]
To date, Jay Ward has cumulative earnings of $107,600. This week he is paid $3,000. What is the total amount of Social Security tax for this week? Assume a rate of 6.2% on $110,100 for Social Security and 1.45% for Medicare. A. $186.00 B. $155.00 C. $57.66 D. $180.00
Answer:
Option B. $155
Step-by-step explanation:
Jay Ward has already been taxed on his earning on $107,600.
So on this paycheck only ($110,100 - $107,600) = $2,500 of his earnings are taxable for social security tax.
Social security tax rate = 6.2%
Hence, social security tax amount = 6.2% × 2500
= 0.062 × 2500
= $155
Option B. $155 is the answer.
To go to dance class at 6:45 pm bus, kelly needs 35 minutes to walk home from a friends house, 30 minutes for dinner, and 20 minutes to drive to the class. to make class on time, what is the latest time she should leave her friends house
What is the volume of a cylinder with a radius of 1.5 inches and a height of 19 inches? use 3.14 for pi. round your answer to the nearest hundredth. 28.5 cubic inches 100.25 cubic inches 134.24 cubic inches 156.73 cubic inches
134.235 cube inches is the volume of a cylinder with a radius of 1.5 inches and a height of 19 inches.
What is volume?Volume is simply defined as the space occupied by any three-dimensional solid. These solids can be a cube, cuboid, cone, cylinder or sphere.The volume of a solid is measured in cubic units. For example, if the dimensions are given in meters, the volume is in cubic meters. It is a standard unit of volume in the International System of Units (SI). Similarly, other units of volume are cubic centimetres, cubic feet, cubic meters, etc.The formula to calculate the volume of a solid in three-dimensional space is to find the product of the dimensions. Basically, volume is equal to the product of the surface area and the height of the shape.Volume = base area x height
Radius of cylinder (r) = 1.5 inches
Height of cylinder (h) = 19 inches
Value of π = 3.14
To Find :
The volume of a cylinder.
Explanation :
Let, volume of a cylinder be "R".
We know that,
Volume of a cylinder = πr²h
[ Put the values ]
↪ R = 3.14 × (1.5)² × 19
↪ R = 3.14 × 2.25 × 19
↪ R = 7.065 × 19
↪ R = 134.235 cube inches
Therefore,
The volume of a cylinder is 134.235 cube inches.
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how do you Write 432,000 in scientific notation
...?
4.32*10^5
To write scientific number must be greater than one but less than 10
air is being pumped into a spherical balloon at a rate of 100 cm^3/sec. How fast is the diameter increasing when the radius is 5 cm?
The diameter is increasing at a rate of approximately 100 / 300π cm/s when the radius is 5 cm.
Explanation:To find the rate at which the diameter is increasing, we need to differentiate the formula for the volume of a sphere with respect to time:
V = (4/3)πr^3
Where V is the volume and r is the radius.
Let's differentiate V with respect to t:
dV/dt = (4/3)π(3r^2)(dr/dt)
We know dV/dt = 100 cm^3/s and r = 5 cm, so plug in these values:
100 = (4/3)π(3(5^2))(dr/dt)
Simplifying the equation gives us:
dr/dt = 100 / (4π(3(5^2)))
dr/dt ≈ 100 / 300π
So, the diameter is increasing at a rate of approximately 100 / 300π cm/s when the radius is 5 cm.
James has $120 in his saving account and plans to have $x each month for 6 months. the expression $6x $120 represents the total amount in the account after 6 months. factor the expression 6x 20
Answer:
6(x+20)
Step-by-step explanation:
6x: 2*3
120: 2*2*3*5
The GCF of 6x*120 is 2*3
so the factored expression is 6(x+20)
An adult meerkat weighs 776 grams. This is o.747 kilograms more than the weight of a baby meerkat. how much does a baby meerkat weigh ?
The baby meerkat weighs 29 grams.
First, we need to ensure our units are the same, so we'll convert 776 grams to kilograms.
There are 1,000 grams in a kilogram, so 776 grams is equivalent to 0.776 kilograms.
Given that the adult meerkat is 0.747 kilograms heavier than the baby meerkat, we can calculate the baby meerkat's weight by subtracting.
Baby meerkat weight = Adult meerkat weight - Additional weight
Baby meerkat weight = 0.776 kg - 0.747 kg
Baby meerkat weight = 0.029 kg
To express this in grams, we multiply by 1,000:
Baby meerkat weight in grams = 0.029 kg × 1000
= 29 grams
A bag contains 5 red marbles, 3 green marbles, 2 purple marbles, 2 orange marbles, and 1 blue marble.
Which color marble is less likely to be picked than purple?
The answer is blue i just took the test.
find an expression for the width of a rectangle who's length is represented by x-2 and whos's width is represented by 2x^3-8x^2+2x+12
The expression for the width of a rectangle when the width is given by the algebraic expression 2x3 - 8x2 + 2x + 12.is already stated in its complete form.
Explanation:The student is asking about finding an expression for the width of a rectangle with given algebraic expressions for length and width. Since the student has provided the expressions for both length and width, we do not need to perform any calculations or manipulations to answer the question directly. The length of the rectangle is given as x-2, and the width of the rectangle is given by the expression 2x3 - 8x2 + 2x + 12. There are no further instructions to simplify or modify, so the expression for the width as provided is complete.
A dog's weight increased by 50% in three years. by the end of the 3 years, the dog weighed 45 pounds. how much did the dog weigh three years ago?
How can i find the factors of 12 and 15,explain?
The factors of 12 are 1, 2, 3, 4, 6, and 12, while the factors of 15 are 1, 3, 5, and 15.
To find the factors of 12 and 15, you need to identify the numbers that can evenly divide these two numbers without leaving a remainder. Here's how you can find the factors:
Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 15: 1, 3, 5, 15.
write this 15 is 12 less than 2 times a number.
WILL UPVOTE PLS HELP
The area of a rectangle is 48 square centimeters and the length of the rectangle is 8 centimeters longer than the width.
The area of a rectangle is found by multiplying the length times the width.
Which equation models this situation?
w + 8 = 48
w + 8w = 48
w(w+8)=48w(w+8)=48
8w = 48
Which graph represents the solution set for the inequality 16 ≥ -3x + 4 > -17?
Solve sin2x + 2sinx = 0 for 0 ≤ x < 2π. ...?
Use compensation to find product for 195x5
Solve by factoring.
g^2+4g-32=0
Answer: The solution is g = 4, -8.
Step-by-step explanation: We are given to solve the following algebraic equation.
[tex]g^2+4g-32=0.[/tex]
Since the above algebraic equation is quadratic, so it will have two solutions.
The solution by the method of factorization is as follows:
[tex]g^2+4g-32=0\\\\\Rightarrow g^2+8g-4g-32=0\\\\\Rightarrow g(g+8)-4(g+8)=0\\\\\Rightarrow (g-4)(g+8)=0\\\\\Rightarrow g-4=0,~~~g+8=0\\\\\Rightarrow g=4, -8.[/tex]
Thus, the required solution is g = 4, -8.
Round each number to the nearest hundredth. What is the best estimate for the sum of 12.547 + 83.919?
A wooden beam 24 feet long leans against a wall and makes an angle of 71° with the ground. How high up the wall does the beam reach to the nearest foot?
The beam reaches approximately 23 feet up the wall.
Given that, a wooden beam is 24 feet in length and makes an angle of 71° with the ground.
We need to determine how high does it touches the wall,
To find the height up the wall reached by the wooden beam, we can use trigonometry.
Let's denote the height as "h".
In a right triangle formed by the wooden beam, the height "h" represents the opposite side, and the length of the beam (24 feet) represents the hypotenuse.
The angle between the ground and the beam is given as 71°.
We can use the sine function to solve for "h" since sine is defined as the ratio of the opposite side to the hypotenuse in a right triangle.
sin(71°) = h / 24
To find "h," we rearrange the equation:
h = sin(71°) × 24
Calculating this, we get:
h ≈ 0.9511 × 24 ≈ 22.8264
Rounding to the nearest foot, the beam reaches approximately 23 feet up the wall.
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