Answer:
x = 1.64 in the size of the side of the square
Step-by-step explanation:
Let call x side of the square to be cut from cornes, then:
First side of rectangular base
L = 14 - 2*x
And the other side
d = 8 -2*x
Then Volume of the box
V(b) = L*d*x
V(x) = ( 14- 2*x ) * ( 8 -2*x)*x
V(x) = ( 112 - 28*x -16*x + 4*x² )*x ⇒ 4*x³ - 44*x² + 112*x
Taking derivatives on both sides of the equation we get:
V´(x) = 12*x² - 88*x +112
V´(x) = 0 ⇒ 12*x² - 88*x +112 = 0
A second degree equation, solvin it
3x² - 22*x + 28 = 0
x₁,₂ = [ 22 ± √484 - 336 ] / 6
x₁ = (22 + 12,17) /6 x₂ = ( 22 - 12.17 ) / 6
x₁ = 5.69 We dismiss this solution since it make side 8 - 2x a negative length
x₂ = 9.83/6
x₂ = 1.64
Then x = x₂ = 1.64 in
Answer:
1.64 in
Step-by-step explanation:
A local dinner theater sells adult tickets for $105 each and children’s tickets for $60 each. For a certain show, the theater sells 84 tickets for a total of $7155. How many of each type of ticket were sold?
write a system of equations that models this problem and then show all the steps to solve your system of equations using the linear combination.
Answer:
The answer to your question is he sold 47 adult tickets and 37 children tickets.
Step-by-step explanation:
Data
Adult ticket = a = $105
Children ticket = c = $60
Total number of tickets = 84
Total money earn = $7155
Equations
a + c = 84 ------------ (I)
105a + 60c = 7155 -------------(II)
Multiply equation I by -60
-60a - 60c = -5040
105a + 60c = 7155
Simplify
45a = 2115
a = 2115 / 45
a = 47 tickets
Substitute a in equation I
47 + c = 84
c = 84 - 47
c = 37 tickets
You can form linear equations from the given description then use that system to derive the solution.
The amount of each type of tickets sold are:
Children tickets sold = 37
Adult tickets sold = 47
How to form mathematical expression from the given description?You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.
Using the above methodology to get the system of equation modelling the given situationLet the amount of adult tickets sold be "a"
Let the amount of children tickets sold be "c"
Since the total amount of tickets sold is given as 84
Thus,
Total tickets = children tickets + adult tickets
84 = c + a
a + c = 84
since 1 adult ticket costs $105,
thus, "a" adult tickets cost [tex]105 \times a = 105a \text{\:\:(Written in short)}[/tex] (in dollars)
Similarly,
since 1 children ticket costs $60
"c" children tickets cost [tex]60c[/tex] (in dollars)
Since the price obtained by selling those tickets is $7155
thus,
total amount earned = amount earned by children tickets + amount earned by adult tickets
$7155 = $60c + $105a
Thus, we got the system of equations as:
[tex]a + c = 84\\105a + 60c = 7155[/tex]
Multiplying first equation with -105 to make a's coefficient equal and opposite to make the addition of them eliminate "a":
[tex]-105a -105c = -105 \times 84\\105a + 60c = 7155\\\\\text{Addding both equations}\\\\-45c = 7155 - 8820 = -1665\\\\c = \dfrac{1665}{45} = 37[/tex]
Putting this value in first equation, we get:
[tex]a + c = 84\\a + 37 = 84\\a = 84 - 37 = 47[/tex]
Thus,
The amount of each type of tickets sold are:
Children tickets sold = 37
Adult tickets sold = 47
Learn more about system of linear equations here:
https://brainly.com/question/13722693
Last month 15 homes were sold in Town X. The average (arithmetic mean) sale price of the homes was $150,000 and the median sale price was $130,000. Which of the following statements must be true?I. At least one of the homes was sold for more than $165,000.II. At least one of the homes was sold for more than $130,0000 and less than $150,000.III. At least one of the homes was sold for less than $130,000.A. I onlyB. II onlyC. III onlyD. I and IIE. I and III
Answer:
A. 1 only.
Step-by-step explanation:
Sam has a total of 40 dvds, movies and tv shows. The number of movies is 4 less then 3 times the number of tv shows. Write and solove a system of equations to find the number of movies and tv shows.
Answer:Sam has 29 movies.
Sam has 11 TV shows.
Step-by-step explanation:
Let x represent the number of movies that Sam has.
Let y represent the number of TV shows that Sam has.
Sam has a total of 40 dvds, movies and tv shows. This means that
x + y = 40 - - - - - - - - - - -1
The number of movies is 4 less then 3 times the number of tv shows. This means that
x = 3y - 4 - - - - - - - - - - -2
Substituting equation 2 into equation 1, it becomes
3y - 4 + y = 40
4y - 4 = 40
4y = 40 + 4 = 44
y = 44/4 = 11
x = 3y - 4 = 3 × 11 - 4
x = 33 - 4
x = 29
By creating a system of equations from the given problem, m + t = 40 and m = 3t - 4, and solving it through substitution, it was determined that Sam has 29 movies and 11 TV shows in his DVD collection.
Explanation:To solve the given problem, we need to use a system of linear equations. The two variables we need to find are the number of movies (m) and the number of TV shows (t).
According to the problem, the total number of DVDs, which includes both movies and TV shows, is 40. This can be written as an equation: m + t = 40. Additionally, we are told that the number of movies is 4 less than three times the number of TV shows. This gives us a second equation: m = 3t - 4.
Now we have the following system of equations:
m + t = 40m = 3t - 4We can solve this system by substitution. First, substitute the second equation into the first equation:
(3t - 4) + t = 404t - 4 = 404t = 44t = 11Now that we have found the number of TV shows (t), we can calculate the number of movies (m):
m = 3t - 4m = 3(11) - 4m = 33 - 4m = 29Therefore, Sam has 29 movies and 11 TV shows in his collection of 40 DVDs.
In an experiment, it is important that independent and dependent variables are given _____, which specify procedures for manipulating the independent variable and measuring the dependent variable.
Answer:
a relationship ( model equation)
Step-by-step explanation:
the relationship specifies how the dependent variable relies on the independent variable.This helps in manipulating of the variable to see its effect/outcome.The relationship can be mathematical or logical ; it can also be a set of algorithm (program) which can be worked on using the independent variables as inputs. Usually the independent variables influence the dependent variables.
Taylor purchased one pack of cookies and gave away 5 cookies to her friends. If she had 1 cookie left, what is p, the number of cookies in each package?
Answer:
The number of cookies in each package = 6
Step-by-step explanation:
Given:
Taylor purchased a pack of cookies.
Number of cookies Taylor gave to her friends = 5
Number of cookies she had left = 1
To find the number of cookies 'p' in each package.
Solution:
[tex]p\rightarrow[/tex] Number of cookies in each package.
If Taylor gave away 5 cookies to her friends, then the number of cookies left in the package can be represented as:
⇒ [tex]p-5[/tex]
Number of cookies she had left = 1
So, the equation to solve for [tex]p[/tex] can be given as:
[tex]p-5=1[/tex]
Solving for [tex]p[/tex]
Adding 5 both sides.
[tex]p-5+5=1+5[/tex]
∴ [tex]p=6[/tex]
Thus, number of cookies in each package = 6.
Miss Alvarez has a piece of ribbon that is 2.65 feet long she cuts the ribbon into 5 equal pieces what is a good estimate of the length of each piece of ribbon
Final answer:
To find the length of each piece of ribbon, divide the total length of 2.65 feet by 5, resulting in 0.53 feet per piece, or approximately 6 inches after converting to a more convenient measurement.
Explanation:
The student's question involves the division of a length of ribbon into equal pieces. Miss Alvarez has a piece of ribbon that is 2.65 feet long and she cuts it into 5 equal pieces. To estimate the length of each piece, we would divide the total length of the ribbon by the number of pieces.
The calculation would be: 2.65 feet ÷ 5 pieces = 0.53 feet per piece. If we want a more convenient measure, we could convert feet to inches since there are 12 inches in a foot, resulting in approximately 6.36 inches per piece (0.53 feet × 12 inches/foot).
As an estimate and for ease of measurement, we might round this to the nearest whole number, suggesting that each piece of ribbon is approximately 6 inches in length.
Luke has 1/5 of a package of dried apricots. He divides the dried apricots equally into 4 small bags. Luke gives one of the bags to a friend and keeps the other three bags for himself. What fraction of the original package of dried apricots did Luke keep for himself?
Answer:
3/80
Step-by-step explanation:
If one fifth of apricots are split into 4 parts, each bag has 1/5 * 1/4 of the original apricots
1/5 * 1/4 = 1/20
Luke keeps 3/4 of those so that's
3/4 * 1/20 = 3/80
ANSWER THIS MATH QUESTION
Answer:
The slope of the line tangent to the function at x = 1 is 2.01 ≅2.Step-by-step explanation:
Using the formula of derivative, it can be easily shown that, [tex]\frac{d f(x)}{dx} = 2[/tex] where [tex]f(x) = x^{2}[/tex].
Here we need to show that as per the instructions in the given table.
Δy = f(x + Δx) - f(x) = f(1 + 0.01) - f(1) = [tex](1 + 0.01)^{2} - 1^{2} = 0.0201[/tex].
In the above equation, we have put x = 1 because we need to find the slope of the line tangent at x = 1.
Hence, dividing Δy by Δx, we get, [tex]\frac{0.0201}{0.01} = 2.01[/tex].
Let's examine this taking a smaller value.
If we take Δx = 0.001, then Δy = [tex]1.001^{2} - 1^{2} = 0.002001[/tex].
Thus, [tex]\frac{0.002001}{0.001} = 2.001[/tex].
The more smaller value of Δx is taken, the slope of the tangent will be approach towards the value of 2.
We can see here that the slope of the line tangent to the function at x = 1 is 2.001 ≅ 2.
How we arrived at the solution?We can use the formula of derivative: [tex]\frac{df(x)}{dx} = 2[/tex]
Looking at the instructions in the given table, we have:
Δy = f(x + Δx) - f(x) = f(1 + 0.01) - f(1) = (1 + 0.01)² - 1² = 0.0201
In the above written equation, x = 1 because we need to find the slope of the line tangent at x = 1.
Thus, Δy divided by Δx, we get, 0.0201/0.01 = 2.01
If we take Δx = 0.001, then Δy = 1.001² - 1² = 0.002001
So, we have: 0.002001/0.001 = 2.001
We can see here that the more smaller value of Δx is taken, the slope of the tangent will be approach towards the value of 2.
Learn more about tangent line on https://brainly.com/question/30162650
#SPJ6
A company makes steel rods shaped like cylinders. Each rod has a radius of 4 centimeters and a height of 30 centimeters. If the company used 94,953.6 of steel, how many rods did it make
Answer:
Company made 63 rods with the given amount of steel.
Step-by-step explanation:
Given:
Radius of each rod =4 cm
height of each rod = 30 cm
Number of steel company used = 94953.6
We need to find how many rods company can make.
Solution:
First we will find the Volume of each rod.
Since rod is in cylindrical shape.
So we will use Volume of cylinder.
Now Volume of cylinder is given by π times square of the radius times height.
framing in equation form we get;
Volume of each rod = [tex]\pi r^2h= \pi \times4^2\times 30 = 1507.96 \ cm^3[/tex]
So we can say that steel used to make each rod = 1507.96
Number of steel company used = 94953.6 (given)
To find the number of steel rod company made we will divide Number of steel company used by number of steel used to make each rod.
framing in equation form we get;
number of steel rod company made = [tex]\frac{94953.6}{1507.96}= 62.96\approx63[/tex]
Hence Company made 63 rods with the given amount of steel.
The number of rods made using given data is approximately 63 rods .
To find out how many steel rods a company made based on the total volume of steel used, we need to calculate the volume of one rod and then divide the total volume of steel by this.
The volume of a cylinder (which is the shape of the rods) is calculated using the formula V = πr²h, where V is the volume, r is the radius, and h is the height.
Given that each rod has a radius of 4 centimeters and a height of 30 centimeters, the volume of one rod can be found as follows:
V = π(4²)(30)
≈ 3.14(16)(30)
= 1,507.2 cm³
Given the total volume of steel used is 94,953.6 cm³, the number of rods made can be calculated by dividing the total volume of steel by the volume of one rod:
Number of rods = 94,953.6 cm³ / 1,507.2 cm³
≈ 63
Therefore, the company made approximately 63 steel rods.
1.Solve.
{y=2x−64x−2y=14
Use the substitution method.
2.Solve.
{y=x−63x+2y=8
Use the substitution method.
3.What is the y-coordinate of the solution for the system of equations?
{x−y=1227+3y=2x
Enter your answer in the box.
4.What is the y-coordinate of the solution of the system of equations?
{y=2x+14−4x−y=4
Enter your answer in the box.
Answer:
The answer to your question is below
Step-by-step explanation:
1.- y = 2x - 64
x - 2y = 14
Substitution
x - 2(2x - 64) = 14
Simplification
x - 4x + 128 = 14
x - 4x = 14 - 128
-3x = - 114
x = 114/3
x = 38
y = 2(38) - 64
y = 76 - 64
y = 12
Solution (38, 12)
2.- y = x - 6
3x + 2y = 8
Substitution
3x + 2(x - 6) = 8
Simplification
3x + 2x - 12 = 8
5x = 8 + 12
5x = 20
x = 20 / 5
x = 4
y = 4 - 6
y = -2
Solution (4 , -2)
3.- x - y = 12
27 + 3y = 2x
x = 12 + y
27 + 3y = 2(12 + y)
27 + 3y = 24 + 2y
3y - 2y = 24 - 27
y = -3
x = 12 - 3
x = 9
Solution y = -3
4.- y = 2x + 14
-4x - y = 4
-4x - (2x + 14) = 4
-4x - 2x - 14 = 4
-6x = 4 + 14
-6x = 18
x = 18/-6
x = -3
y = 2(-3) + 14
y = -6 + 14
y = 8
Solution y = 8
Answer:
There is no solution.
Step-by-step explanation:
The price of nails,n, is $1.29/lb, the price of washers, w, is $0.79/lb, and the price of bolts,b, is $2.39/lb.Write an expression to represent the total price of the supplies.
The expression to represent the total price of the supplies is 1.29n + 0.79w + 2.39b
Solution:
Let "n" be the number of nails
Let "w" be the number of washers
Let "b" be the number of bolts
Given that ,
Price of nail = $ 1.29 per lb
Price of washers = $ 0.79 per lb
Price of bolts = $ 2.39 per lb
To find: Expression to represent the total price of the supplies.
Total price = number of nails x Price of nail per lb + number of washers x Price of washers per lb + number of bolts x Price of bolts per lb
[tex]Total\ price = n \times 1.29 + w \times 0.79 + b \times 2.39\\\\Total\ price = 1.29n + 0.79w + 2.39b[/tex]
Thus the expression to represent the total price of the supplies is found
If there are 6 randomly selected digits in an automobile license tag, and each digit must be one of the 10 integers (0-9), then there are 106 possible license tags.A. TrueB. False
Answer: True.
Step-by-step explanation:
The total number of possible digits in the number system : 10 (from 0 to 9)
If there are 6 randomly selected digits in an automobile license tag, and each digit must be one of the 10 integers (0-9), then the choices for each digit in license tag = 10
Fundamental counting principle , the total number of ways to make 6-digits license tag where the choices for each digit in license tag is 10 will be :
[tex]10\times10\times10\times10\times10\times10=10^6[/tex]
Hence, there are [tex]10^6[/tex] possible license tags.
Therefore , the given statement is correct.
Final answer:
The statement is True because for each of the 6 digits in a license tag, there are 10 possible integers, giving us a total of 10^6 possible combinations.
Explanation:
The question relates to probability and combinatorics, which are branches of mathematics that deal with the likelihood of certain outcomes and the combination of different elements, respectively. If an automobile license tag consists of 6 randomly selected digits and each digit must be one of the 10 integers (0-9), then we must consider every digit independently.
Since there are 10 options for each digit, and there are 6 digits, we calculate the total number of possible license tags by multiplying the number of options for each digit. This is done by raising the number of options (10) to the power of the number of digits (6), which gives us: 10^6. Therefore, the statement is True as there are indeed 10^6 possible license tags.
Keith does work for his neighbors. When he earns $12 an hour. When he works indoors he earns $8 an hour. Last month he did 18 hours of work outdoors and 16 hours of work indoors. How much did keith earn last month
Answer: he earned $344 in all.
Step-by-step explanation:
When he does work outdoors he earns $12 an hour. This means that if he works outdoors for x hours, he would earn $12x
When he works indoors he earns $8 an hour. This means that if he works indoors for y hours, he would earn $8y.
Last month he worked 18 hours outdoors. This means that the total amount that he earned working outdoors is
12 × 18 = $216
He worked 16 hours indoors. This means that the total amount that he earned working indoors is
8 × 16 = $128
Total amount that he earned is
216 + 128 = $344
Rosita can wax her car in 2 hours or 120 minutes. When she works together with Helga, they can wax the car in 45 minutes. How long would it take Helga, working by herself, to wax the car?
Step-by-step explanation:
Let w be the work of waxing.
Rosita can wax her car in 2 hours or 120 minutes.
Time taken by Rosita = 120 minutes
[tex]\texttt{Rate of Rosita = }\frac{W}{120}[/tex]
Let time taken by Helga be t,
[tex]\texttt{Rate of Helga = }\frac{W}{t}[/tex]
When she works together with Helga, they can wax the car in 45 minutes.
We have
[tex]\frac{W}{\frac{W}{120}+\frac{W}{t}}=45\\\\120t=45(120+t)\\\\120t=5400+45t\\\\t=72minutes[/tex]
Time taken by Helga to wax the car is 72 minutes
Given the following triangle find side AC.
A. 11.89
B. 12.87
C. 13.98
D. 14.08
Answer:
The answer to your question is AC = 14
Step-by-step explanation:
To solve this problem, we must use trigonometric functions.
And we must look for a trigonometric function that relates the opposite side and the hypotenuse.
This trigonometric function is the sine
[tex]sin\alpha = \frac{opposite side}{hypotenuse}[/tex]
solve for Opposite side = AC
AC = hypotenuse x sin α
- Substitution
AC = 25 x sin 34
- Simplification
AC = 25 x 0.56
- Result
AC = 14
Joan spend half of her paycheck going to the movies. She washed the family car and earned 7 dollars. What is her weekly paycheck if she ended up with 18 dollars?
Answer:
her weekly allowance is $16
Step-by-step explanation:
Let x represent Joan's weekly paycheck.
Joan spent half of her paycheck going to the movies. This means that the total amount that she spent at the movies is x/2. The amount that she is left with would be
x - x/2 = x/2
She washed the family car and earned 7 dollars. This means that the total amount left with her is
x/2 + 7
if she ended with 18 dollars, it means that
x/2 + 7 = 18
x/2 = 18 - 7 = 11
x = 2 × 11 = $22
What is the common factor of the numerator and denominator in the expression (2x+3)(x−4)/(x−4)(x+4)?
Answer:
(2x-3)/(x+4)
Step-by-step explanation:
Answer:
(x - 4).
Step-by-step explanation:
(x - 4) is common to to top and bottom of the fraction.
The fraction simplifies to (2x+3)/(x+4).
Last week Stacy earned $24 for baby sitting for hours in her part time job at Burger city she work 12 hours and earned $78 how many total hours distese work last week?
Answer:
Last week she work [tex]3\frac{54}{78}\ hours[/tex].
Step-by-step explanation:
Given:
Last week Stacy earned $24 for baby sitting for hours in her part time job at Burger city she work 12 hours and earned $78.
Now, to find the total hours she work last week.
As, given she work 12 hours and earned $78.
So, to solve by using unitary method:
If she earned $78 in working 12 hours.
So, she earned $1 in working = [tex]\frac{12}{78}\ hour.[/tex]
Thus, she earned $24 in working = [tex]\frac{12}{78} \times 24[/tex]
[tex]=\frac{288}{78}[/tex]
[tex]=3\frac{54}{78}\ hours.[/tex]
Therefore, last week she work [tex]3\frac{54}{78}\ hours[/tex].
Jon's dog weighs ( v ) pounds. His cat weighs 21 pounds less than his dog. His bunny weighs 3 pounds less than his cat? What is the weight of Jon's pets?
Answer: the weight of Jon's pet is
(3v - 25) pounds
Step-by-step explanation:
The weight of Jon's dog is v pounds.
His cat weighs 21 pounds less than his dog. It means that the weight of his cat would be
(v - 21) pounds
His bunny weighs 3 pounds less than his cat. It means that the weight of his bunny would be
(v - 21) - 3 = (v - 24) pounds
Therefore, the weight of Jon's pets would be the sum of the weight of his dog, his cat and his bunny. It becomes
v + v - 21 + v - 24 = (3v - 25) pounds.
Final answer:
Jon's pets' total weight is calculated by adding the weight of the dog (v pounds), cat (v - 21 pounds), and bunny (v - 24 pounds), which results in 3v - 45 pounds.
Explanation:
To find the weight of Jon's pets, we start with the known weight of the dog and calculate the other animals' weights based on the given relationships. Jon's dog weighs ( v ) pounds. His cat weights 21 pounds less than his dog, so the cat weighs v - 21 pounds. The bunny weighs 3 pounds less than the cat, which means the bunny weighs (v - 21) - 3 pounds or v - 24 pounds.
Therefore, to find the total weight of Jon's pets, we add the weights of the dog, cat, and bunny together:
Dog's weight: v pounds
Cat's weight: v - 21 pounds
Bunny's weight: v - 24 pounds
The total weight is v + (v - 21) + (v - 24), which simplifies to 3v - 45 pounds.
Start with the logistic equation dx dt = kx(M − x). Suppose that we modify our harvesting. That is we will only harvest an amount proportional to current population. In other words we harvest hx per unit of time for some h > 0 (Similar to earlier example with h replaced with hx).
a) Construct the differential equation.
b) Show that if kM > h, then the equation is still logistic.
c) What happens when kM < h?
Answer:
a) [tex] \frac{dx}{dt}= kx (M-x) -hx[/tex]
[tex] \frac{dx}{dt}= kx (M -x- \frac{h}{k})[/tex]
b) [tex] M -\frac{h}{k}>0 [/tex]
Let's say that [tex] a=M -\frac{h}{k}>0[/tex]
If we multiply the woule equation by k we got:
[tex] kM -h >0[/tex]
So then we satisfy that the equation is also logistic since the parameter [tex] a>0[/tex]
c) If we assume that [tex] kM <h[/tex] then we have that [tex] a<0[/tex]
And then [tec] kx (a -x) <0[/tex] for any value of [tex] x>0[/tex]
And if that hhapens then the population will tend to 0 for any initial condition established/
Step-by-step explanation:
For this case we have the following logistic equation [tex] \frac{dx}{dt}= kx (M-x)[/tex]
Part a
We want to modify our harvesting for this case, so we harvest hx per unit of time for some [tex] h>0[/tex]
So then the model with harvesting who is proportional is given by:
[tex] \frac{dx}{dt}= kx (M-x) -hx[/tex]
And we can write like this:
[tex] \frac{dx}{dt}= kx (M -x- \frac{h}{k})[/tex]
Part b
For this case we assume that [tex] kM>h[/tex]and we need to show that the equation is still logistic. So we need that the sollowing quantity higher than 0
[tex] M -\frac{h}{k}>0 [/tex]
Let's say that [tex] a=M -\frac{h}{k}>0[/tex]
If we multiply the woule equation by k we got:
[tex] kM -h >0[/tex]
So then we satisfy that the equation is also logistic since the parameter [tex] a>0[/tex]
Part c
If we assume that [tex] kM <h[/tex] then we have that [tex] a<0[/tex]
And then [tec] kx (a -x) <0[/tex] for any value of [tex] x>0[/tex]
And if that hhapens then the population will tend to 0 for any initial condition established/
Triangle ABC is congruent to triangle PQR, angle B equals 3v+4, and angle Q equals 8v-6, find the measurements of angles B, and Q. please show step by step, thank you.
triangle RSt is similar to triangle xyz with rs= 3 inches and xy= 2 inches. Of the area of triangle RST is 27 in^2, determine and state the area of triangle XYZ in square inches.
Answer: The area of triangle ΔXYZ is 12 square inches.
Step-by-step explanation:
Since we have given that
RS = 3 inches
XY = 2 inches
Area of ΔRST = 27 in²
Since ΔRST is similar to ΔXYZ.
So, using the "Area similarity theorem":
[tex]\dfrac{\Delta RST}{\Delta XYZ}=\dfrac{RS^2}{XY^2}\\\\\dfrac{27}{\Delta XYZ}=\dfrac{3^2}{2^2}\\\\\dfrac{27}{\Delta XYZ}=\dfrac{9}{4}\\\\\Delta XYZ=3\times 4=12\ in^2[/tex]
Hence, the area of triangle ΔXYZ is 12 square inches.
The area of triangle XYZ is found by squaring the ratio of the corresponding sides of the similar triangles and multiplying it by the area of the larger triangle RST. With the side length ratio of 2:3, the area ratio is (2/3)², resulting in an area of 12 in² for triangle XYZ.
The student's question involves determining the area of a smaller similar triangle (XYZ) given the area of the larger similar triangle (RST) and the lengths of corresponding sides. To solve, we utilize the property that similar triangles' areas are proportional to the square of the ratio of their corresponding sides.
Given:
Length of RS in triangle RST = 3 inches
Length of XY in triangle XYZ = 2 inches
Area of triangle RST (A1) = 27 in²
We establish the ratio of their sides as 2 inches (XY) / 3 inches (RS), which simplifies to 2/3. The ratio of their areas would then be (2/3)² because the area of similar triangles scales with the square of the ratio of their corresponding linear dimensions. Hence, the Area of triangle XYZ (A2) will be A1 × (2/3)².
A2 = 27 in² × (2/3)2 = 27 × 4/9 = 12 in².
The area of triangle XYZ is 12 in².
What is 12 2/3 X 2 1/2
Answer:
31.67
Step-by-step explanation:
12 2/3 X 2 1/2
we begin by converting this into improper fractions,
= 38/3 * 5/2
= 95/3
= 31.67
Morten Andersen played in NFL for 25 years write and solve an equation to find how many points he averaged each year
Answer:
[tex] r =\frac{2437points}{25 years} =97.45 \frac{points}{year}[/tex]
So then we have that Morten Andersen scored on average 97.45 points per year in his career.
Step-by-step explanation:
Assuming the following table on the figure attached.
We see that the career points for Morten Andersen was 2437. That include all the points over alll the years the he played in the NFL.
Since the total years played by Morten Andersen was 25 we can write the following equation:
[tex] 25 r =2437[/tex]
Where [tex] r[/tex] represent the rate of points average per year.
If we solve for r from the last equation we can divide both sides of the equation and we got:
[tex] r =\frac{2437points}{25 years} =97.45 \frac{points}{year}[/tex]
So then we have that Morten Andersen scored on average 97.45 points per year in his career.
Hillary gets divorced in 2016 and is required to pay her ex-spouse $200 per month until her son reaches 18 years of age in 7 years and $120 per month thereafter. How much of her 2019 payments are deductible as alimony?
To know how much of Hillary's payments are deductible as alimony in 2019, we first need to figure out how old her son was when Hillary got divorced in 2016.
Given that Hillary has to pay until her son turns 18 and this occurs 7 years after the divorce, this means that her son was 18 - 7 = 11 years old in 2016.
Therefore, he will be turning 18 in 2025 (2016 + 9 years).
In 2019, which is 3 years after 2016, her son would be 11 + 3 = 14 years old. As her son has not yet reached 18 years old, Hillary is still making $200 payments per month in 2019.
Given there are 12 months in a year, the total amount of alimony payments that Hillary made in the year 2019 is 12 * $200 = $2400.
So, the amount of her 2019 payments that are deductible as alimony is $2400.
#SPJ3
The mean weight of the seven linebackers was 236 pounds. The first six linebackers weighed 215lb, 305lb, 265lb, 196lb, 221lb, and 236lb, respectevily. What was the weight of the seventh linebackers?
Answer:
The weight of the seventh linebacker is = 214 lb.
Step-by-step explanation:
Given:
Mean of 7 linebackers = 236 lb
The weights of first 6 linebackers are:
215 lb, 305 lb, 265 lb, 196 lb, 221 lb and 236 lb
To find the weight of seventh linebacker.
Solution:
Let the weight of the seventh linebacker be = [tex]x[/tex]
The mean of 7 line backers will be given as:
⇒ [tex]\frac{215+305+265+196+221+236+x}{7}[/tex]
The mean of the 7 linebackers is given = 236 lb
Thus, the equation to find [tex]x[/tex] will be :
[tex]\frac{215+305+265+196+221+236+x}{7}=236[/tex]
Simplifying.
[tex]\frac{1438+x}{7}=236[/tex]
Multiplying both sides by 7.
[tex]7.\frac{1438+x}{7}=236(7)[/tex]
[tex]1438+x=1652[/tex]
Subtracting both sides by 1438.
[tex]1438-1438+x=1652-1438[/tex]
∴ [tex]x=214[/tex]
Thus, the weight of the seventh linebacker is = 214 lb.
You swim at 3 km/hr with your body perpendicular to a stream with a current of 5 km/hr. your actual velocity is the vector sum of the stream's velocity and ytour swimming velocity. find your actual velocity?
Answer:
Step-by-step explanation:
You swim at 3 km/hr with your body perpendicular to a stream with a current of 5 km/hr.
If your actual velocity is the vector sum of the stream's velocity and your swimming velocity, it means that your actual velocity is the resultant velocity. Let R represent the resultant velocity. It means that
R² = 3² + 5² = 9 + 25
R² = 34
Taking square root of the left hand side and the right hand side of the equation, it becomes
R = √34 = 5.83 km/hr.
Final answer:
To find the swimmer's actual velocity in a stream where the swimmer's velocity is 3 km/hr and the stream's velocity is 5 km/hr, we use the Pythagorean theorem, resulting in an actual velocity of approximately 5.83 km/hr.
Explanation:
The question involves calculating the actual velocity of a swimmer moving in a stream. The swimmer swims at a rate of 3 km/hr perpendicular to the stream, while the stream itself has a current of 5 km/hr.
To find the swimmer's actual velocity when these two vectors are combined, we use the Pythagorean theorem, as the velocities are perpendicular to each other.
Let the swimmer's velocity be represented by Vswimmer = 3 km/hr and the stream's velocity by Vstream = 5 km/hr.
The actual velocity (Vactual) is the vector sum of these two velocities. Since they are at right angles to each other, Vactual can be calculated as [tex]\sqrt{((Vswimmer)^2 + (Vstream)^2)[/tex] .
Substituting the values gives Vactual =[tex]\sqrt{(3^2 + 5^2)} = \sqrt{(9 + 25)} = \sqrt{(34),[/tex] which approximately equals 5.83 km/hr.
Therefore, the actual velocity of the swimmer, taking into account the stream's current, is approximately 5.83 km/hr.
Jaimie paid $126 for 42 pretzels. He incorrectly calculates the rate per pretzel to be $84 per pretzel. Which statement identifies the error Jaimie most likely made in determining the rate per pretzel and describes the correct method for determining the rate per pretzel?
Answer:
see the explanation
Step-by-step explanation:
we know that
To determine the rate per pretzel or unit rate, divide the total paid by the number of pretzel
so
[tex]\frac{126}{42}=\$3\ per\ pretzel[/tex]
Jaimie's error
He subtracted 42 from $126 when he should have divided $126 by 42
A packaging company is going to make open-topped boxes, with square bases, that hold 140 cubic centimeters. What are the dimensions of the box that can be built with the least material? (Round your answers to the nearest hundredth.)
Answer:
x = 6.54 cm
h = 3.27 cm
Step-by-step explanation:
Volume of open top box
V = 140 cm³
Dimensions of the box
It is a base square box then area of the base of side x is
A(b) = x²
And we will call h the height of the box then
V = 140 ⇒ 140 = x²*h ⇒ h = 140/ x²
We have to calculate the area of the 4 sides
Area of one side is As = x*h ⇒ total area of 4 sides = 4 x* 140/x²
Ats = 560/x
Then Total area of the box is
A(t) = Area of the base + Total area of sides
A(x) = x² + 560/x
Taking derivatives on both sides of the equation we get:
A´(x) = 2x - 560/x²
A´(x) = 0 ⇒ 2x - 560/x² = 0 ⇒ 2x³ - 560 = 0
x³ = 280 ⇒ x = 6.54 cm
And h h = 140/ (6.54)² ⇒ h = 140/ 42.77 h = 3.27 cm
The systolic blood pressure of 18-year-old women is normally distributed with a mean of 120 mmHg and a standard deviation of 12 mmHg. What percentage of 18-year-old women have a systolic blood pressure between 96 mmHg and 144 mmHg?
Approximately 97.72% of 18-year-old women have a systolic blood pressure between 96 mmHg and 144 mmHg.
Explanation:To find the percentage of 18-year-old women with a systolic blood pressure between 96 mmHg and 144 mmHg, we need to calculate the z-scores for the given values using the formula z = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation.
For X = 96 mmHg, z = (96 - 120) / 12 = -2.
For X = 144 mmHg, z = (144 - 120) / 12 = 2.
Using a standard normal distribution table, we can find that approximately 0.9772 (97.72%) of the values fall within 2 standard deviations from the mean. Therefore, approximately 97.72% of 18-year-old women have a systolic blood pressure between 96 mmHg and 144 mmHg.
Learn more about Systolic blood pressure here:https://brainly.com/question/36602693
#SPJ3
Final answer:
Approximately 95% of 18-year-old women have a systolic blood pressure between 96 mmHg and 144 mmHg, as calculated using Z-scores and the standard normal distribution.
Explanation:
The question asks us to determine the percentage of 18-year-old women who have a systolic blood pressure between 96 mmHg and 144 mmHg, given that the systolic blood pressure is normally distributed with a mean of 120 mmHg and a standard deviation of 12 mmHg.
We will use the concept of Z-scores to find this probability. A Z-score represents the number of standard deviations a data point is from the mean. We can calculate the Z-scores for the systolic blood pressure values of 96 mmHg and 144 mmHg and then use the standard normal distribution table to find the percentages. The calculations are as follows:
Z-score for 96 mmHg = (96 - 120) / 12 = -2
Z-score for 144 mmHg = (144 - 120) / 12 = 2
Looking at the Z-score table, we find that the area between Z = -2 and Z = 2 covers approximately 95% of the data under the normal distribution curve. Therefore, about 95% of 18-year-old women will have a systolic blood pressure between 96 mmHg and 144 mmHg.