The model for the BMI of a person is:
BMI = (152100/weight in pounds)/(height in inches)^2
The Body Mass Index (BMI) of a person can be calculated using the formula:
BMI = (weight in pounds)/(height in inches)^2
In this case, the BMI varies directly as a person's weight in pounds and inversely as the square of the person's height in inches. This means that as the weight increases, the BMI increases and as the height increases, the BMI decreases.
To find a model for the BMI of a person, we can use the formula:
BMI = k(weight in pounds)/(height in inches)^2
Where k is a constant of proportionality. To find the value of k, we can use the given information that a 6ft 6in tall person has a BMI of 25.
First, we need to convert the height from feet and inches to inches. 6ft 6in is equivalent to 78 inches. Then, we can plug in the values into the formula and solve for k:
25 = k(weight in pounds)/(78 inches)^2
25(78 inches)^2 = k(weight in pounds)
152100 = k(weight in pounds)
Therefore, the model for the BMI of a person is:
BMI = (152100/weight in pounds)/(height in inches)^2
This model can be used to calculate the BMI of a person given their weight in pounds and height in inches.
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In Exercises \( 1-8, W \) is a subset of \( R^{2} \) consisting of vectors of the form \[ \mathbf{x}=\left[\begin{array}{l} x_{1} \\ x_{2} \end{array}\right] \] In each case determine whether \( W \)
Yes
Yes, \( W \) is a subset of \( R^{2} \) since it consists of vectors of the form
\[ \mathbf{x}=\left[\begin{array}{l} x_{1} \\ x_{2} \end{array}\right] \]. Therefore, for Exercises \( 1-8 \), the answer is yes.
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Find the values of x and y
. Write your answer in
simplest form.
X
45°
X =
y =
y
16
&
Answer:
X: 45° Y:16°
Step-by-step explanation:
by help of teacher
extra points for help (dont guess please)
The exponential functions y=1.2ˣ shows exponential growth and y=0.71ˣ shows exponential decay.
What exactly are exponential functions?
Exponential functions are functions that involve a variable exponent. They are of the form f(x) = aˣ, where "a" is a positive constant base and "x" is the variable exponent.
Exponential functions exhibit rapid growth or decay, depending on the value of "a" and the sign of "x". For example, if "a" is greater than 1, the function grows rapidly as "x" increases, while if "a" is between 0 and 1, the function decays rapidly as "x" increases.
Now,
As stated above that for exponential function y=aˣ
when a>1 it shows exponential growth
and when a<1 it shows decay.
hence,
The exponential functions y=1.2ˣ shows exponential growth and y=0.71ˣ shows exponential decay.
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Find the minimum and maximum of P=4x+2y subject to 3x+5y>=20 3x+y<=16 -2x+y<=2 x>=0,y>=0
The minimum of P is 16 and the maximum of P is 24.
Calculating the value of P for these points, we get:
P(2,6) = 4*2 + 2*6 = 20
P(0,8) = 4*0 + 2*8 = 16
P(4,2) = 4*4 + 2*2 = 24
P(3,3) = 4*3 + 2*3 = 18
Therefore, the minimum of P is 16 and the maximum of P is 24.
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Please note that for 1 pound of bananas the cost is
$0.63/lb
(according to the US Bureau of Labor Statistics.) In 1939 , the cost of bananas was
14%
lower. Pam buys 5 pounds of bananas for children at the camp she works for. What would these bananas have cost in 1939?
The cost of 5 pounds of bananas in 1939 would have been $2.709.
According to the US Bureau of Labor Statistics, the cost of 1 pound of bananas is $0.63/lb. In 1939, the cost of bananas was 14% lower. Therefore, to find the cost of bananas in 1939, we need to calculate 14% of $0.63/lb and then subtract it from $0.63/lb.
Calculate 14% of $0.63/lb
0.14 * $0.63/lb = $0.0882/lb
Subtract $0.0882/lb from $0.63/lb to get the cost of bananas in 1939
$0.63/lb - $0.0882/lb = $0.5418/lb
Multiply the cost of bananas in 1939 by the number of pounds Pam buys
$0.5418/lb * 5 lb = $2.709
Therefore, the cost of 5 pounds of bananas in 1939 would have been $2.709.
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Three friends, Martin, Tyreese, and Braydon, are collecting donations to help in their community's clean-up initiative. Their total contribution goal is represented by the expression 7x2 − 4xy + 8. The friends have already collected the following amounts:
Martin: 5xy + 16
Tyreese: x2
Braydon: 4x2 − 7
Which expression represents the amount of money the friends still need to collect to meet their goal?
2x2 − 9xy − 1
2x2 + xy + 17
5x2 + 5xy + 9
12x2 + xy + 17
2x2 - 9xy - 1 is the expression for how much money the buddies still need to gather to reach their objective.
What exactly is a phrase?A mathematical expression is made up of a statement, at least two integers or variables, and one or more arithmetic operations. This mathematical procedure makes it possible to multiply, divide, add, or subtract quantities.
The total of what they have already raised towards the overall fundraising target.
The total contribution goal is given as: 7x² - 4xy + 8
The amount Martin has already collected is: 5xy + 16
The amount Tyreese has already collected is: x²
The amount Braydon has already collected is: 4x² - 7
Adding the amounts already collected:
= (5xy + 16) + x² + (4x² - 7)
= 5xy + x² + 4x² + 16 - 7
= 5xy + 5x² + 9
By deducting the total of the contributions from the overall contribution target:
= (7x² - 4xy + 8) - (5xy + 5x² + 9)
= 2x² - 9xy - 1
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Answer: A
Step-by-step explanation: i wish other people would just put the letter, but here ya go c:
Designing an Addition A 40-ft-wide house has a roof with a
6-12 pitch (the roof rises 6 ft for a run of 12 ft). The owner plans a 14-ft-wide addition that will have a 3-12 pitch to its roof. Find the lengths of AB and BC in the accompanying figure.
We can conclude that the measure of length AB is 23.46 ft and the measure of length BC is 9 ft.
What is sine formula in trigonometry?Sine formula is used to calculate the sine angle of a right-angled triangle which is the ratio of the opposite side and the hypotenuse.
Given is that a 40-ft-wide house has a roof with a 6-12 pitch (the roof
rises 6 ft for a run of 12 ft). The owner plans a 14-ft-wide addition that will
have a 3-12 pitch to its roof.
We can write the measure of length AB as -
AB = 6 + √(9 + 296)
AB = 6 + 17.46
AB = 23.46 ft
We can write the measure of length BC as -
BC = 6 + 1/4 x 12
BC = 6 + 3
BC = 9 ft
Therefore, we can conclude that the measure of length AB is 23.46 ft and the measure of length BC is 9 ft.
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NEED HELP DUE FRIDAY!!!!!!!!!!!
Find cos(A), sin(A), and tan(A) for triangle ABC.
Answer:
It’s a right triangle
Step-by-step explanation:
15 squared plus 8 squared equals 17 squared which 289=289
Calculate the interest earned when $46 230 is invested for 9 years at 7.8% p.a., with interest compounded twice a year.
Given:
What is the interest earned when $46,230 is invested for 9 years at 7.8% p.a?
To find:
The interest
Solution:
[tex]interest = \frac{p \times r \times t}{100} [/tex]let the interest be x. [tex]x = \frac{46230 \times 9 \times 7.8}{100} [/tex][tex]x = 32456.46[/tex]But the interest is compounded twice a year so, [tex]32456.46 \times 2 \times 9[/tex][tex] = 64912.92 \times 9[/tex][tex] = 584216.28[/tex]therefore, the final answer is 584,216.28point (s) possible Find the LCD (least common denominator ) of the set of fractions. Do not combine the fractions; only find the LCD. (7)/(20) and (9)/(40)
The answer are LCD (least common denominator) of the set of fractions (7)/(20) and (9)/(40) is 40.
Here is a step-by-step explanation on how to find the LCD:
1. Find the multiples of each denominator.
- Multiples of 20: 20, 40, 60, 80, 100, 120, 140, 160, 180, 200...
- Multiples of 40: 40, 80, 120, 160, 200, 240, 280, 320, 360, 400...
2. Compare the multiples of each denominator and find the smallest number that appears in both lists.
- The smallest number that appears in both lists is 40.
3. The smallest number that appears in both lists is the LCD.
- Therefore, the LCD of the set of fractions (7)/(20) and (9)/(40) is 40.
So the answer to the question "Find the LCD (least common denominator) of the set of fractions. Do not combine the fractions; only find the LCD. (7)/(20) and (9)/(40)" is 40.
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What is the solution to this equation?
9 ^x- 1 = 2
O A. 1
O B. 2
O C.
1/2
OD. -1/2
The solution to this equation 9ˣ - 1 = 2 is 1/2.
The correct option is A.
What is an equation?
Two algebraic expressions having same value and symbol '=' in between are called as an equation.
Given:
An equation:
9ˣ - 1 = 2
Simplifying,
9ˣ = 3
3²ˣ = 3
Comparing, we get,
2x = 1
x = 1/2
Therefore, the solution is x = 1/2.
Isn't it supposed to be one black triangle and one black square?
The value of the model expression when simplified is (d)
How to determine the expressionFrom the question, we have the following representation that can be used in our computation:
Black triangle = -xWhite triangle = xBlack square = -1White square = 1Using the above as a guide, we have the following:
The given expression is
3 * Black triangle + 2 * White triangle + 2 * Black square + 1 * White square
This gives
-3x + 2x - 2 + 1
Evaluate the like terms
-x - 1
This means
1 Black triangle and 1 Black square
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In Exercises 11-14|, use a matrix equation to solve the system of linear equations. \( 11\left\{\begin{array}{r}x+2 y=3 \\ 2 x+6 y=5\end{array}\right. \)
x = 4/3 and y = 2/3
To solve this system of linear equations using a matrix equation, we first need to construct a matrix by writing the coefficients of the variables and the constants from the equation in a rectangular array.
The matrix for the given equations will be:
Now, we can solve the system by multiplying the inverse of the matrix of coefficients with the matrix of constants. To find the inverse of the matrix, we can use the following equation:
where |A| is the determinant of the matrix, and adj(A) is the adjoint of the matrix.
We can use this equation to find the inverse of the matrix, which is:
We can then multiply this inverse by the matrix of constants to get the solution for the system:
Therefore, the solution for the system is x = 4/3 and y = 2/3.
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Find the constant of variation k for the direct variation.
f(x)
0
-1
-2
-3.5
x02
0
4
7
The value of the constant of variation for the direct variation is k = -1/2.
What is constant of variation?Variation depicts the relationship between two variables and how it changes. Often, a ratio is used to illustrate this connection. When we remark that a variation is continuous, we are referring to how consistently the ratio changes. Hence, whenever you read the phrase "constant of variation," just keep in mind that it refers to the stability of the relationship between the variables.
The direct variation is given by the following relations:
y = kx
Now, using the table substitute the value of y = f(x) and x:
y = kx
-2 = k(4)
k = -2/4
k = -1/2
Hence, the value of the constant of variation for the direct variation is k = -1/2.
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what is the ratio of 2:35
Answer:
2:35
Step-by-step explanation:
For each relationship described, type an equation using the variables y and z to create an identity. a. addition and subtraction: b. multiplication and division: (when y 0 or when z = 0)
Step-by-step explanation:
addition and subtraction:
y + z - z = y
b. multiplication and division:
When y ≠ 0:
yz / y = z
When z ≠ 0:
y / z * z = y
e) Solve: f(x) = g(x) for x = [-240°; 240°]
Answer:
218.88
Step-by-step explanation:
Ina makes cakes in a pan shaped like a rectangular prism. The base of the pan is an 8-inch by 12-inch rectangle, and the volume of the pan is 288 cubic inches. Find the surface area of a cheesecake baked in this pan
Answer:
312 square inches
Step-by-step explanation:
To find the surface area of a cake baked in a rectangular pan with an 8-inch by 12-inch base and a volume of 288 cubic inches, we need to find the dimensions of the pan. We can do this by dividing the volume by the area of the base, which gives us the height of the pan. Once we know the height, we can use the dimensions of the base and the height to find the surface area of the cake.
when flying on an air plane the weight limit for carry on luggage is 30 pounds there are approximately 453.6 grams in 1 pound which measurement is closet to the weight of the checked luggage in grams
Answer:
Step-by-step explanation:
30x453.6=13608 grams
Mrs.may mixed 4 gal of red paint with every 6 gal of blue paint in order to make purple paint. which ratio of gallons of red paint to gallons of blue pint will make the same shade of purple paint?
Answer: 20 gallons of red paint and 30 gallons blue paint
Step-by-step explanation:
Find the measure of pkt
Answer:
32°
Step-by-step explanation:
You want the measure of the smaller angle of the linear pair marked (3g+23) and (7g+127).
Linear pairThe angles of a linear pair total 180°, so we have ...
(3g +23) +(7g +127) = 180
10g = 30 . . . . . . . . . subtract 150
g = 3 . . . . . . . . . divide by 10
The smaller angle is ...
∠PKT = (3·3 +23)°
∠PKT = 32°
Use the commutative or associative property to simplify the expression. (1)/(13)(13y)
The simplified expression of (1)/(13)(13y) is 169y.
To simplify the expression (1)/(13)(13y) using the commutative or associative property, we can rearrange the terms and group them together.
Using the commutative property, we can rearrange the terms so that the two 13's are next to each other:
(1)(13)(13y) = (13)(13y)(1)
Now, using the associative property, we can group the two 13's together and simplify:
(13)(13y)(1) = (13*13)(y)(1) = (169)(y)(1)
Finally, we can simplify further by multiplying the 169 and 1 together:
(169)(y)(1) = (169y)(1) = 169y
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Joni says that a rectangular prism has two bases. How many possible pairs of bases does a rectangular prism really have? Explain
A rectangular prism actually has three pairs of bases. Each pair of bases is a set of two opposite and parallel faces on the rectangular prism.
The first pair of bases is the two opposite and parallel rectangles on the top and bottom of the prism. The second pair of bases is the two opposite and parallel rectangles on the front and back of the prism. The third pair of bases is the two opposite and parallel rectangles on the left and right sides of the prism.
Each pair of bases is congruent, meaning they have the same shape and size. This is because a rectangular prism is a type of polyhedron with six rectangular faces, and each pair of opposite faces is parallel and congruent to each other.
In conclusion, a rectangular prism has three pairs of bases, each consisting of two opposite and parallel rectangular faces.
I hope this helps! Let me know if you have any further questions.
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Use an appropriate infinite series method about x = 0 to find two solutions of the given differential equation. (Enter the first four nonzero terms for each linearly independent solution, if there are fewer than four nonzero terms then enter all terms. In each case, the first term has been provided for you. )
3xy" y+y=0
Y₁ = 1 -
12 = x2/3
The two linearly independent solutions are y₁(x) = 1 - (x²/3) + (x⁴/81) - (x⁶/2187) + … and y₂(x) = x - (x³/9) + (x⁵/405) - (x⁷/21870) + ...
We can use the power series method to find the two solutions of the given differential equation:
Let y = ∑anxn be a power series solution. Then, we have:
y' = ∑nanxn-1
y'' = ∑nan(n-1)xn-2
Substituting these into the differential equation and equating coefficients of like powers of x, we get:
3x∑nan(n-1)xn-1 + ∑anxn = 0
Simplifying, we obtain:
∑[3nan(n-1) + an-1]xn = 0
Since x ≠ 0, the coefficients of like powers of x must be zero. This gives us the recurrence relation:
an = -an-1/(3n(n-1)), n ≥ 1
Using this recurrence relation and the initial condition y(0) = 1, we can find the power series solution:
y₁(x) = 1 - (x²/3) + (x⁴/81) - (x⁶/2187) + ...
To find a second linearly independent solution, we can use the method of reduction of order. Let y₂(x) = v(x)y₁(x). Then, we have:
y₂' = v'y₁ + vy₁'
y₂'' = v''y₁ + 2v'y₁' + vy₁''
Substituting these into the differential equation and simplifying, we get:
v''y1x + (2v'y1' + vy1'')x + 3vy1 = 0
Since y₁(x) is a solution, we have:
y₁'' + (1/3x)y₁ = 0
Multiplying by y1 and integrating, we obtain:
(y₁')² + y₁²/3 = C
where C is a constant of integration. Using the initial condition y₂(0) = 0, we can find the second solution:
y₂(x) = x - (x³/9) + (x⁵/405) - (x⁷/21870) + ...
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Work the problem using the three-step method. Show your work.
The sum of three consecutive integers is 18. Find the integers.
WRITER
Answer:
5,6 and 7.
Step-by-step explanation:
I am not sure what the three step method is, but here is how I solved it.
Consecutive integers means integers in a row. For example, 5,6 7 are consecutive integers or -4,-3,-2 are consecutive integers.
Integers are all the whole numbers (0,1,2,3...) and their opposites (..., -3, -2, -1) 1/2 or -.23 are not integers.
Let x = the first number
Let x + 1 = the second number
Let x + 2 = the third number
x + (x + 1) + (x + 2) = 18 I do not need the parentheses, but I want you to see that the first number, plus the second number, plus the third number equals 18.
x + x + 1 + x + 2 = 18 Combine like terms
3x + 3 = 18 Subtract 3 from both sides of the equation
3x + 3 - 3 = 18 - 3
3x = 15 Divide both sides by 3
[tex]\frac{3x}{3}[/tex] = [tex]\frac{15}{3}[/tex]
x = 5
The first number is 5. The second number is 6 and the last number is 7.
Check:
5 + 6 + 7 = 18
18 =18 Checks.
Helping in the name of Jesus.
The surface area of a rectangular prism is 250 cm 2. If its height is 10 centimeters, and its width is 5 centimeters, what is its volume?
The volume of the rectangular prism whose surface area is 250 cm square is 250cubic centimeters.
The surface area of a rectanular prism is calculates by the formula
= 2( length*width + length*height + width*height ) square units
Let the length of the given prism be l centimeters.
Given, width is 5 centimeters and height is 10 centimeters of the rectangular prism.
The surface area of the rectangular prism is 250 cm square.
Thus by the above formula,
250 = 2 ( l*5 + l*10 +10*5)
⇒250 = 2 (15*l +50)
⇒ 250= 30*l + 100
⇒ 150 = 30*l
⇒l = 150/30 = 5 (centimeters)
Thus the volume of the given rectangular prism is calculated as
= ( length*width*height) cubic units
= (5*5*10) cubic centimeters
= 250 cubic centimeters
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How to express a two logarithm into a single logarithm
Answer:
There are different methods to express a two logarithm into a single logarithm, depending on the specific form of the logarithms involved. Here are some examples:
Logarithms with the same base:
If you have two logarithms with the same base, you can use the following logarithmic identity:
log_a(x) + log_a(y) = log_a(xy)
Using this identity, you can express a sum or difference of logarithms with the same base as a single logarithm:
Example 1: log_2(3) + log_2(5) = log_2(3*5) = log_2(15)
Example 2: log_5(7) - log_5(2) = log_5(7/2)
Logarithms with different bases:
If you have two logarithms with different bases, you can use the following change of base formula to express them with a common base:
log_a(x) = log_b(x) / log_b(a)
Using this formula, you can rewrite a logarithm with a base a as a logarithm with a base b:
Example 1: log_2(7) = log_10(7) / log_10(2)
Example 2: log_5(2) = log_2(2) / log_2(5)
Once you have expressed both logarithms with the same base, you can apply the logarithmic identity from method 1 to simplify them into a single logarithm.
On a certain day, the temperature of the pool was 76°F at 10 A.M. and 91°F at 1 P.M. If the temperature rose at a constant rate from 10 A.M. to 1P.M. on that day, what was the temperature at 11 A.M.? a. 79°F d. 89°F b. 81°F e. 90°F c. 86°F
The correct answer is b. 81°F.
On a certain day, the temperature of the pool rose at a constant rate from 76°F at 10 A.M. to 91°F at 1 P.M. To find the temperature at 11 A.M., we need to find the rate of change in temperature and then use it to calculate the temperature at 11 A.M.
The rate of change in temperature can be found by dividing the difference in temperature by the difference in time:
Rate of change = (91°F - 76°F) / (1 P.M. - 10 A.M.) = 15°F / 3 hours = 5°F per hour
Now, we can use this rate of change to find the temperature at 11 A.M.:
Temperature at 11 A.M. = 76°F + (5°F per hour)(1 hour) = 81°F
Therefore, the correct answer is b. 81°F.
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In the 2020 NFL season, Drew Brees completed 73.5% of his attempted passes, and Patrick Mahomes completed 68.8% of his attempted passes. Based on those statistics, which of the following statements is true?
A. Drew Brees must have attempted more passes
B.Patrick Mahomes must have completed more passes
C.Either quarterback could have completed more passes
D.. Drew Brees must have completed more passes
Statement C is true: Either quarterback could have completed more passes
What are basic attributes of a good conclusion?
Rephrase the thesis statement first, then explain what you mean and back it with information from the prompt to show what you mean. Describe how the evidence supports your claims in further detail.
We cannot determine which quarterback completed more passes based solely on their completion percentages.
For example, if Drew Brees attempted 100 passes and completed 73.5% of them, he would have completed 73.5 passes. If Patrick Mahomes attempted 200 passes and completed 68.8% of them, he would have completed 137.6 passes, which is more than Drew Brees.
On the other hand, if Drew Brees attempted 200 passes and completed 73.5% of them, he would have completed 147 passes, which is more than Patrick Mahomes' 137.6 completed passes in the above example.
Therefore, statement C is true: either quarterback could have completed more passes, depending on the number of passes attempted.
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Practice and Problem S Subtract using the vertical form. 1. (5g^(2)+6g-10)-(2g^(2)+2g+9)
(5g^(2)+6g-10)-(2g^(2)+2g+9) = 3g^(2) + 4g - 19
To subtract the two polynomials, we will use the vertical form. This means that we will line up the like terms and subtract them.
Step 1: Line up the like terms in the vertical form.
5g^(2) + 6g - 10
- (2g^(2) + 2g + 9)
Step 2: Distribute the negative sign to each term in the second polynomial.
5g^(2) + 6g - 10
- 2g^(2) - 2g - 9
Step 3: Subtract the like terms.
5g^(2) - 2g^(2) = 3g^(2)
6g - 2g = 4g
-10 - 9 = -19
Step 4: Write the final answer.
3g^(2) + 4g - 19
Therefore, the answer is 3g^(2) + 4g - 19.
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