The directions of motion for this calculation are:
i) Right, right, left
ii) Undetermined
The first operation is subtraction of y from x, which moves to the right on the number line. The second operation is addition of the opposite of z, which is subtraction of z from the result of the first operation. This also moves to the right on the number line. The final operation is addition of the opposite of z, which is subtraction of z from the result of the second operation. This moves to the left on the number line. Therefore, the directions of motion are right, right, left.
Since we don't know the values of x, y, and z, we cannot determine the sign of the final answer. Therefore, the answer is undetermined.
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What is the probability of selecting a 2 and then
a number divisible by 4 ?
a.
5/66
b.
1/20
C.
1/24
D.
1/22
Answer: C. 1/24 and that's is your answer to your question
HELP MARKING BRAINLEIST IF RIGHT ASAP
Step-by-step explanation:
you don't know Pythagoras ?
c² = a² + b²
c is the Hypotenuse (the side opposite of the 90° angle), a and b are the legs.
please remember this for life !
so, in our case :
c² = 6² + 4² = 36 + 16 = 52
c = sqrt(52) = sqrt(4×13) = 2×sqrt(13) =
= 7.211102551... ≈ 7.2 miles
If the height is h, the leaf scar is l, how can you model the pattern using an equation?
i need explanation please
The mathematical model that pattern using an equation to represents the height is h, the leaf scar is l is given by x = c × l × √n × cos(n × φ) , and y = c × l × √n × sin(n × φ) + h.
The pattern of leaf scars on a tree trunk is often modeled using a mathematical function called a phyllotaxis spiral.
This spiral can be represented by the polar equation,
r = c × √n
where r is the radius of the spiral,
n is the index of the leaf scar,
c is a constant that determines the tightness of the spiral,
and the angle of rotation is equal to,
θ = n × φ
where φ is the golden angle, which is approximately 137.5°.
To incorporate the height h and leaf scar size l into the model,
Make the following modifications,
Add a vertical displacement factor h to the polar equation, which shifts the spiral upward by h units.
Multiply the radius by a factor that is proportional to the size of the leaf scar l.
The modified polar equation for the phyllotaxis spiral would be,
r = c × l × √n
θ = n × φ
where r is the radius of the spiral,
n is the index of the leaf scar,
c is a constant that determines the tightness of the spiral,
l is the size of the leaf scar,
and φ is the golden angle.
To convert this polar equation to a Cartesian equation that relates x and y coordinates,
x = r × cos(θ)
y = r × sin(θ) + h
Substituting the expressions for r and θ from above, we get,
x = c × l × √n × cos(n × φ)
y = c × l × √n × sin(n × φ) + h
Therefore, mathematical equation that models the phyllotaxis spiral of leaf scars on a tree trunk, taking into account the height h and the size of the leaf scar l is
x = c × l × √n × cos(n × φ)
y = c × l × √n × sin(n × φ) + h
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Natalie saves money in her piggy bank. Maria saves money in a savings account at a bank.
Which statement about the savings plans is true?
Responses
Natalie uses a safer way to save money because she can protect her piggy bank.
Maria's way of saving money allows her to earn interest and make her money grow.
Maria will have less money because she must pay sales tax on her money.
Natalie's method of saving is better because Maria must pay interest on her money.
In a case whereby Natalie saves money in her piggy bank. Maria saves money in a savings account at a bank the statement about the savings plans that is true is B.Maria's way of saving money allows her to earn interest and make her money grow.
What is savings account ?An efficient approach to keep your money safe and earning interest is in a savings account. You can keep your savings in a liquid state with a savings account, which allows you to access your money anytime you need to, while also creating some breathing room between your savings and your daily spending requirements.
Because of their safety, liquidity, and potential for collecting interest, savings accounts are a suitable way to put money set aside for future use. These accounts are perfect for saving for short-term objectives like a trip or home repair or for your emergency fund.
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[tex]x=log125/log25[/tex]
Answer:
[tex]x = \frac{ log(125) }{ log(25) } = \frac{ log( {5}^{3} ) }{ log( {5}^{2} ) } = \frac{3 log(5) }{2 log(5) } = \frac{3}{2} = 1 \frac{1}{2} [/tex]
If a+b=3 and ab=4 find the value of a3+b3
Answer:
-9
Step-by-step explanation:
Recall the following relationships about the sum of cubes and a square binomial:
[tex]a^3+b^3=(a+b)(a^2-ab+b^2)[/tex]
[tex](a+b)^2=a^2+2ab+b^2[/tex]
The second factor on the right hand side of equation 1 looks similar to the right hand side of equation 2, but differs slightly.
Carefully choosing to subtract 3ab from both sides of the equation 2, and Combining like terms yields...
[tex](a+b)^2-3ab=a^2-ab+b^2[/tex]
This now matches the second factor on the right hand side of the first equation. So, with substitution, the first equation becomes:
[tex]a^3+b^3=(a+b)(a^2-ab+b^2)[/tex]
[tex]a^3+b^3=(a+b)((a+b)^2-3ab)[/tex]
Note that all of the parts on the right hand side of the equation are given in the question:
a+b=3 and ab=4
With some substitution and simplification
[tex]a^3+b^3=(a+b)((a+b)^2-3ab)[/tex]
[tex]=(3)((3)^2-3(4))[/tex]
[tex]=(3)(9-3(4))[/tex]
[tex]=(3)(9-12)[/tex]
[tex]=(3)(-3)[/tex]
[tex]=-9[/tex]
2 questions that I am stuck on.
8. x=(a+b)/c.
The given equation is,
(b-cx)/a+(a-cx)/b+2=0
⇒b/a-cx/a+a/b-cx/b+2=0
Taking the variables to LHS and constants to RHS,
-cx/a-cx/b=-b/a-a/b-2
or, cx/a+cx/b=b/a+a/b+2
or, cx(1/a+1/b)=b/a+a/b+2
Multiplying both sides of the above equation by ab,
or, cx(a+b)/ab=(a²+b²+2ab)/ab
⇒cx(a+b)=(a²+b²+2ab)
or, cx(a+b)=(a+b)²
∴ x=(a+b)²/c(a+b)=(a+b)/c
Hence x=(a+b)/c.
9. x= -ab(c-a+b)
The given equation is,
a/(x+a)+b/(x-b)=(a+b)/(x+c)
Multiplying the LHS and RHS of the equation by (x+a)(x-b)(x+c),
a(x-b)(x+c)+b(x+a)(x+c)=(a+b)(x+a)(x-b)
⇒a(x²-bx+cx-bc)+b(x²+ax+cx+ac)=(a+b)(x²+ax-bx-ab)
The above equation has terms with variables x²,x and constant terms.
Keeping the like terms together,
x²(a+b-a-b)+x(-ab+ac+ab+bc-a²+b²)= abc-abc-a²b-ab²
⇒ x²(0)+x(ac+bc-a²+b²)= -a²b-ab²
⇒ x = (-a²b-ab²)/(ac+bc-a²+b²)
= -ab(a+b)/[c(a+b)-(a+b)(a-b)]
= -ab(a+b)/(a+b)(c-a+b)
= -ab/(c-a+b)
Hence, x= -ab/(c-a+b)
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The solutions for questions 8 and 9 are:
8. b = (ac - 2ab)/(2-a)
9. x = [-b ± sqrt((a+b)^2 + 4b(a+c))]/(2b)
How did we get the values?To solve the equation:
(b-cx)/a+(a-cx)/b+2=0
Simplify the equation by finding a common denominator.
Multiply the first term by b/b and the second term by a/a, then add them together:
(b^2 - bcx + a^2 - acx)/(ab) + 2 = 0
collect like terms:
(b^2 + a^2)/(ab) - cx(a+b)/(ab) + 2 = 0
Multiply both sides by ab to eliminate the denominator:
b^2 + a^2 - cx(a+b) + 2ab = 0
Simplify:
cx = (a^2 + b^2 + 2ab)/(a+b)
cx = (a+b)^2/(a+b)
cx = a+b
Substitute cx with a+b:
(b-c(a+b))/a + (a-c(a+b))/b + 2 = 0
Simplify:
(2b - ac - bc)/(ab) = -2
Multiply both sides by ab:
2b - ac - bc = -2ab
Solve for b:
b = (ac - 2ab)/(2-a)
9. To solve the equation:
a/(x+a) + b/(x-b) = (a+b)/(x+c)
We can start by finding a common denominator on the left side:
(a(x-b) + b(x+a))/((x+a)(x-b)) = (a+b)/(x+c)
Simplify:
(ax - ab + bx + ab)/((x+a)(x-b)) = (a+b)/(x+c)
collect like terms:
(ax + bx)/((x+a)(x-b)) = (a+b)/(x+c)
Factor out x:
x(a+b)/((x+a)(x-b)) = (a+b)/(x+c)
Cross-multiply:
(a+b)(x+c) = x(a+b)(x-b)
Expand and simplify:
ax + bx + ac + bc = ax^2 - bx^2
Rearrange and simplify:
bx^2 + (a+b)x - (a+c)b = 0
Use the quadratic formula to solve for x:
x = [-b ± sqrt((a+b)^2 + 4b(a+c))]/(2b)
Note that this equation has a restriction on x, namely that x cannot be equal to a or b, since that would make some of the denominators zero.
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Once Farid spends 15 minutes on a single level in his favorite video game, he loses a life. He has already spent 10 minutes on the level he's playing now.
Let x represent how many more minutes Farid can play on that level without losing a life. Which inequality describes the problem?
A. 10 + x > 15
B. 10 + x < 15
Solve the inequality. Then, complete the sentence to describe the solution.
Farid can play less than _______ more minutes on that level without losing a life
The correct inequality to describe the problem is A. 10 + x > 15, which means that the total time Farid spends on the level (10 + x) must be greater than 15 minutes in order for him to lose a life.
To solve the inequality, we can start by isolating x on one side of the inequality:
10 + x > 15
Subtracting 10 from both sides, we get:
x > 5
This means that Farid can play for up to 5 more minutes on the level without losing a life, since spending a total of 10 + 5 = 15 minutes on the level would cause him to lose a life.
Therefore, the solution to the inequality is "Farid can play less than 5 more minutes on that level without losing a life."
Overall, the correct option is A. 10 + x > 15.
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Use Newton's method to approximate a root of the equation5sin(x)=xas follows. Letx1=1 be the initial approximation. The second approximationx2 is and the third approximationx3 is
The second approximation x2 is approximately 1.112141637097, and the third approximation x3 is approximately 1.130884826739.
Newton's method to approximate a root of the equation 5sin(x) = x.
We are given the initial approximation x1 = 1. To find the second approximation x2 and the third approximation x3, we need to follow these steps:
Step 1: Write down the given function and its derivative. f(x) = 5sin(x) - x f'(x) = 5cos(x) - 1
Step 2: Apply Newton's method formula to find the next approximation. x_{n+1} = x_n - f(x_n) / f'(x_n)
Step 3: Calculate the second approximation x2 using x1 = 1. x2 = x1 - f(x1) / f'(x1) x2 = 1 - (5sin(1) - 1) / (5cos(1) - 1) x2 ≈ 1.112141637097
Step 4: Calculate the third approximation x3 using x2. x3 = x2 - f(x2) / f'(x2) x3 ≈ 1.112141637097 - (5sin(1.112141637097) - 1.112141637097) / (5cos(1.112141637097) - 1) x3 ≈ 1.130884826739
So, the second approximation x2 is approximately 1.112141637097, and the third approximation x3 is approximately 1.130884826739.
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Please help me with this ASAP!
Answer:
19
Step-by-step explanation:
Answer:
d
Step-by-step explanation:
Larijah is creating a circular board game with a spinner with four regions that players use to determine what happens on their turns. she wants to meet these requirements: - exactly a quarter of the circle should contain the ""lose a turn"" region. - ""move one space"" should be three times the angle as ""move two spaces"". - ""move two spaces"" should be twice the angle as ""trade places with any opponent"". what is the measure of the ""trade places with any opponent"" region?
The measure of the trade places with any opponent region is 30°
Let the measure of the trade places with any opponent = x
Move two space is twice the angle as trade places with any opponent
Move two space = 2x
Move one space is three times the angle as moving two spaces
Move one space = 3(2x)
Move one space = 6x
Lose your turn is a quarter
Lose your turn = 90°
The sum of a complete angle = 360°
90 + x + 2x + 6x = 360°
9x = 360 - 90
9x = 270
x = 30
The measure of the trade places with any opponent region is 30°
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In a recent poll six hundred adults were asked a series of questions about the state of the economy and their children's future. One question was, "do you expect your children to have a better life than you have had, a worse life, or a life about the same as yours?" Suppose the responses showed 245 better, 311 worse, and 44 about the same. Use the sign test and ???? = 0. 05 to determine whether there is a difference between the number of adults who feel their children will have a better life compared to a worse life. State the null and alternative hypotheses. (Let p = the proportion of adults who feel their children will have a better life. ) H0: p ≠ 0. 50
Null Hypothesis (H0): The proportion of adults who feel their children will have a better life is equal to 0.5.
Alternative Hypothesis (HA): The proportion of adults who feel their children will have a better life is not equal to 0.5.
How to explain the hypothesisThe sign test is a non-parametric statistical test used to test the hypothesis that the median of a population is equal to a specified value.
The critical value is 1.96.
The absolute value of the test statistic is greater than 1.96. Therefore, we reject the null hypothesis and conclude that there is a significant difference between the number of adults who feel their children will have a better life compared to a worse life.
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Barry is selling baseball cards. he sold 2 for $8.00 and 4 for $14.00. what will barry charge for 7 baseball cards if he keeps selling cards at the same rate?
Barry will charge $24.50 for 7 baseball cards if he keeps selling cards at the same rate.
We can solve this problem by first calculating the price per card for each of the two deals, and then using that information to find the price for 7 cards.
Let x be the price of one baseball card, in dollars. From the information given, we know that:
2 cards cost $8.00, so 1 card costs $4.00: 2x = 8.00 => x = 4.00
4 cards cost $14.00, so 1 card costs $3.50: 4x = 14.00 => x = 3.50
So we see that the price per card is different for the two deals. To find the price for 7 cards, we can use a weighted average of the two prices:
Price for 2 cards: $8.00
Price for 4 cards: $14.00
Total price for 6 cards: $22.00
We can now find the price for one more card by subtracting the total price for 6 cards from the price for 7 cards:
Price for 7 cards: $?
Price for 6 cards: $22.00
Price for 1 card: $?
Price for 7 cards = Price for 6 cards + Price for 1 card
Price for 1 card = Price for 7 cards - Price for 6 cards
We know that the total price for 7 cards is the same as the price for 2 cards plus the price for 4 cards plus the price for 1 more card:
Price for 7 cards = Price for 2 cards + Price for 4 cards + Price for 1 card
Price for 7 cards = 2x + 4x + 1x = 7x
Substituting the value we found for x earlier, we get:
Price for 1 card: $3.50
Price for 7 cards: $24.50
Therefore, Barry will charge $24.50 for 7 baseball cards if he keeps selling cards at the same rate.
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The value of a stock in 1940 is $1. 25. Its value grows
by 7% each year after 1940.
A. ) Write an equation representing the value of the
stock, V(t), in dollars, t years after 1940.
The equation representing the value of the stock, V(t), in dollars, t years after 1940 is V(t) = $1.25 * [tex]1.07^t[/tex].
Let V(0) be the value of the stock in 1940, which is given as $1.25. Then, the value of the stock after t years (t > 0) can be found by multiplying the initial value with the growth factor of 1.07 raised to the power of the number of years of growth. Thus, the equation representing the value of the stock, V(t), in dollars, t years after 1940 is:
V(t) = V(0) * [tex](1 + 0.07)^t[/tex]
Substituting the given value of V(0) = $1.25, we get:
V(t) = $1.25 * [tex](1 + 0.07)^t[/tex]
Simplifying this expression, we get:
V(t) = $1.25 * [tex]1.07^t[/tex]
Therefore, the equation representing the value of the stock, V(t), in dollars, t years after 1940 is V(t) = $1.25 * [tex]1.07^t[/tex].
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(a) Find a counterexample which shows that WAT is not true if we replace the closed interval [a,b] with the open interval (a,b).(b) What happens if we replace [a,b] with the closed set [a,\infty). Does the theorem hold?
(a) WAT is not true for the open interval (0,1) with function f(x) = 1/x.
(b) WAT holds for the closed set [a,∞) with any continuous function f(x).
(a) The Weierstrass Approximation Theorem (WAT) is not true if we replace the closed interval [a,b] with the open interval (a,b). A counterexample is the function f(x) = 1/x on the open interval (0,1). This function is continuous on (0,1) but it is not uniformly continuous, so it cannot be uniformly approximated by a polynomial.
(b) The Weierstrass Approximation Theorem holds if we replace [a,b] with the closed set [a,∞). That is, if f(x) is a continuous function on [a,∞), then for any ε > 0, there exists a polynomial p(x) such that |f(x) - p(x)| < ε for all x in [a,∞). The proof is similar to the proof of the original theorem using the Bernstein polynomials.
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Which expression is the best estimate of the product of startfraction 7 over 8 endfraction and 8 and startfraction 1 over 10 endfraction?.
The best estimate of the product is b) 1 times 10.
The expression (7/8)8(1/10) can be simplified by canceling out the factor of 8 in the numerator and denominator. This yields the expression 7/10. Therefore, the best estimate of this expression would be 1 times 10, since 7/10 is closest to 1 when rounded to the nearest whole number, and 10 is the closest whole number to the denominator of 7/10.
Thus, the answer is option b, 1 times 10. It is important to note that when estimating products or other mathematical expressions, it is important to consider the context and choose an estimate that is reasonable and makes sense in the given situation.
Correct Question :
Which expression is the best estimate of the product of (7/8)8(1/10)?
a) 0 times 8
b) 1 times 10
c) 7 times 8
d) 1 times 8
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C C
A student believes that a certain number cube is unfair and is more likely to land with a six facing up. The student rolls
the number cube 45 times and the cube lands with a six facing up 12 times. Assuming the conditions for inference
have been met, what is the 99% confidence interval for the true proportion of times the number cube would land with a
six facing up?
0. 27 2. 58
0. 221-0. 27)
45
0. 7342. 33
0. 731-0. 73)
45
0. 27 2. 33
0. 271 -0. 20)
45
0. 73 +2. 58
0. 73(10. 73)
45
Mix
Save and Exit
we can say with 99% confidence that the true proportion of times the number cube would land with a six facing up is between 0.05 and 0.49.
Find out the confidence interval for the true proportion of time?To find the 99% confidence interval for the true proportion of times the number cube would land with a six facing up, we can use the formula:
CI = p ± zsqrt(p(1-p)/n)
where:
CI is the confidence interval
p is the sample proportion (number of times the cube landed with a six facing up divided by the total number of rolls)
z is the z-score corresponding to the desired confidence level (99% in this case)
n is the sample size (45 in this case)
First, let's calculate the sample proportion:
p = 12/45 = 0.27
Next, we need to find the z-score corresponding to a 99% confidence level. Using a standard normal distribution table or calculator, we find that the z-score is 2.58.
Now we can plug in the values and calculate the confidence interval:
CI = 0.27 ± 2.58sqrt(0.27(1-0.27)/45)
CI = 0.27 ± 0.22
CI = (0.05, 0.49)
The number cube would land with a six facing up between 0.05 and 0.49.
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One can of pumpkin pie mix will make a pie ofdiameter 8 in. if 2 cans 9f pie mix are used to make a larger pie of the same thickness, find the diameter use square root of 2 equals 1. 414
The diameter of the larger pie is 8 x sqrt(2) inches.
How to find the diameter?The area of a circle is proportional to the square of its diameter. If the diameter of a pie made with one can of pumpkin pie mix is 8 inches, then its area is (4 inches)^2 x pi = 16 pi square inches.
If two cans of pie mix are used to make a larger pie of the same thickness, the total area of the pie will be twice that of the smaller pie.
So, the area of the larger pie is 2 x 16 pi = 32 pi square inches.
To find the diameter of the larger pie, we need to solve for d in the equation:
Area of circle = (d/2)^2 x pi
32 pi = (d/2)^2 x pi
32 = (d/2)^2
Taking the square root of both sides, we get:
sqrt(32) = d/2 x sqrt(2)
d/2 = sqrt(32)/sqrt(2)
d/2 = 4 x sqrt(2)
d = 8 x sqrt(2)
Therefore, the diameter of the larger pie is 8 x sqrt(2) inches.
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PLEASE HELP 30 POINTS
Formula for the volume of a cylinder = pi x r^2 x h
---r = radius
---h = height
This problem gives us the diameter. To find the radius from a given diameter, all we need to do is divide the diameter by 2.
radius = 3
height = 22
volume = 3.14 x 3^2 x 22
volume = 3.14 x 9 x 22
volume = 621.72
volume (rounded) = 622
Answer: 622 m^3
Hope this helps!
Each phrase in the table describes two variables which are strongly correlated. select all phrases that imply correlation without causation.
the number of stuffed animals produced at a factory and the number of newborn babies
the number of hits by a baseball team in a game and the number of runs they score
the number of people at a store and the number of coupons given out
the amount of snow plows on the street and the amount of snowfall
the number of videos rented and the number of new films in theaters
the number of pets in a neighborhood and the amount of grass fields nearby
The phrases that imply correlation without causation are:
The number of stuffed animals produced at a factory and the number of newborn babies.The number of hits by a baseball team in a game and the number of runs they score.The phrases that imply correlation without causation.The number of people at a store and the number of coupons given out.The number of videos rented and the number of new films in theaters.The number of pets in a neighborhood and the amount of grass fields nearby.These correlations do not imply a causal relationship, meaning that an increase or decrease in one variable does not directly cause a corresponding change in the other variable.
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Complete the eqaution of the line through (-8, -2) and (-4, 6)
Answer:
y = 2x + 14
Step-by-step explanation:
y = mx + b to write the equation, we need 2 things: the slope and the y-intercept
y = ___x + ____
Slope:
Change in y over the change in x. We find the change by subtracting. The y values are 6 and -2. The x values are -4 and -8
[tex]\frac{6- (-2)}{-4 -(-8)}[/tex] = [tex]\frac{6+2}{-4+8}[/tex] = [tex]\frac{8}4}[/tex] = 2
The slope is 2.
y-intercept:
Use either of the points given and the slope 2 to find the y-intercept. I am going to use the points(-4,6). I will use -4 for x and 6 for y given from the point
y = mx + b
6 = 2(-4) + b
6 = -8 + b Add 8 to both sides
14 = b
The y-intercept is 14.
y = 2x + 14
Helping in the name of Jesus.
Solve for x trigonometry
Answer:
x ≈ 36.87°
Step-by-step explanation:
using the sine ratio in the right triangle
sin x = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{3}{5}[/tex] , then
x = [tex]sin^{-1}[/tex] ( [tex]\frac{3}{5}[/tex] ) ≈ 36.87° ( to the nearest hundredth )
16 workers will build a house; they can do so in 144 days. if all workers work a the same rate, how many more workers would be needed to build the same house in 96 days
To build a house in 96 days, more workers are required such that the total number of workers becomes 24.
Let W be the number of workers required to build the house in 96 days. Using the work formula, we can write:
(16 workers) x (144 days) = (W workers) x (96 days)
Simplifying the equation, we get:
W = (16 workers x 144 days) / 96 days = 24 workers
Therefore, to build the house in 96 days, 24 workers are required, which is 8 more workers than the original 16. This is because, to complete the work in a shorter time, more workers are needed to contribute their efforts to the work.
The total work done by all the workers remains constant, so if we decrease the time taken to complete the work, we need to increase the number of workers to maintain the same work rate.
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If the points a,b and c have the coordinates a(5,2) , b(2,-3) and c(-8,3) show that the triangle abc is a right angled triangle
Points a,b and c satisfied the Pythagoras theorem. Thus, the triangle abc is a right angled triangle.
Define about the right angled triangle:Every triangle has inner angles that add up to 180 degrees. A right angle and a right triangle are both formed when one of their internal angles is 90 degrees.
The internal 90° angle of right triangles is denoted by a little square in the vertex. The complimentary angles of the other two sides of a right triangle sum up to 90 degrees.The triangle's legs, which are typically denoted by the letters a and b, are the sides that face the complimentary angles.Given coordinates :
a(5,2) , b(2,-3) and c(-8,3).
Find the distance between the points using the distance formula:
d = √[(x2 - x1)² + (y2 - y1)²]
ab = √[(2 - 5)² + (- 3 - 2)²]
ab = √[(-3)² + (- 5)²]
ab = √[9 + 25]
ab = √34
ab² = 34
bc = √[(2 + 8)² + (- 3 - 3)²]
bc = √[(10)² + (- 6)²]
bc = √[100 + 36]
bc = √136
bc² = 136
ac = √[(-8 - 5)² + (3 - 2)²]
ac = √[(-13)² + (1)²]
ac = √[169 + 1]
ac = √170
ac² = 170
Now,
(ac)² = (bc)² + (ab)²
170 = 136 + 24
170 = 170
This, points a,b and c satisfied the Pythagoras theorem. Thus, the triangle abc is a right angled triangle.
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What is your net pay after FICA has been taken out if you make $47,000?
Remember that FICA is 7.65%
Answer:
3595.5
Step-by-step explanation:
Consider the following. u = 71 + 9j, v = 8i+2j (a) Find the projection of u onto v. (b) Find the vector component of u orthogonal to v.
A. proj_v(u) = (586 / 68) * (8i + 2j) = (293 / 34) * (8i + 2j) ≈ 8.62i + 2.15j
B. u_orthogonal = (71 + 9j) - (8.62i + 2.15j) ≈ 62.38i + 6.85j
(a) To find the projection of vector u onto vector v, we use the formula:
proj_v(u) = (u·v / ||v||^2) * v
where u = 71 + 9j, v = 8i + 2j, "·" represents the dot product, and ||v|| represents the magnitude of v.
First, let's find the dot product u·v:
u·v = (71)(8) + (9)(2) = 568 + 18 = 586
Next, we find the magnitude of v:
||v|| = √((8)^2 + (2)^2) = √(64 + 4) = √68
Now, we find ||v||^2:
||v||^2 = 68
Finally, we can find the projection of u onto v:
proj_v(u) = (586 / 68) * (8i + 2j) = (293 / 34) * (8i + 2j) ≈ 8.62i + 2.15j
(b) To find the vector component of u orthogonal to v, we subtract the projection of u onto v from u:
u_orthogonal = u - proj_v(u)
u_orthogonal = (71 + 9j) - (8.62i + 2.15j) ≈ 62.38i + 6.85j
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so if i went to park at 4:30 and it took me 24 minutes , when did i leave home
I must have left home at 4:54 PM in order to arrive at the park at 4:30 PM after 24 minutes of travel time.
When was the time I left home?Given the parameters in the question: if i went to park at 4:30 and it took me 24 minutes
Arrival time = 4 : 30PM
Travel time = 24 minutes
I can determine when i left home by simply subtracting the travel time from the time I arrived.
Hence,
Add the travel time to the time you arrived at the park.
4:30 PM (arrival time) + 24 minutes (travel time) = 4:54 PM
Therefore, I must have left home at 4:54 PM.
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The table shows nutrients information for three beverages.
a: which has the most calories per fluid ounce?
b: which has the least sodium per fluid ounce?
bevarage/ serving size/ calorie/ sodium
whole milk/ 1 c/ 146/ 98mg
orange juice/ 1 pt/ 210/ 10mg
apple juice/ 24 fl oz./ 351/ 21mg
Answer:
a) apple juice
b) whole milk
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Write an expression for the arc length of the rose r = cos 3θ. SET UP ONLY. Do not simplify.
L = ∫√(cos^2(3θ) + 9sin^2(3θ)) dθ.
This expression represents the arc length of the rose curve r = cos(3θ).
To understand how to set up an expression for the arc length of the rose curve r = cos(3θ), we first need to understand the concept of arc length in polar coordinates.
In Cartesian coordinates, the distance between two points can be calculated using the Pythagorean theorem. However, in polar coordinates, the distance between two points is given by the arc length formula, which involves integrating a function.
Consider a curve defined by the polar equation r = f(θ). To find the arc length of the curve between two angles θ1 and θ2, we divide the interval [θ1, θ2] into small pieces, and approximate the length of each piece as the hypotenuse of a right triangle.
The base of the triangle is a small change in θ, and the height is a small change in r. By taking the limit as the length of the intervals goes to zero, we can integrate to find the exact length of the curve.
The arc length formula for polar coordinates is given by:
L = ∫√(r^2 + (dr/dθ)^2) dθ.
This formula calculates the length of the curve r = f(θ) between θ1 and θ2. The expression inside the square root is the Pythagorean theorem for polar coordinates, and dr/dθ is the derivative of r with respect to θ.
Now, let's use this formula to find the arc length of the rose curve r = cos(3θ).
First, we need to find the derivative of r with respect to θ, which is given by:
dr/dθ = -3sin(3θ).
Now, we can plug in r and dr/dθ into the arc length formula:
L = ∫√((cos(3θ))^2 + (-3sin(3θ))^2) dθ.
Simplifying the expression inside the square root, we get:
L = ∫√(cos^2(3θ) + 9sin^2(3θ)) dθ.
This expression represents the arc length of the rose curve r = cos(3θ). By evaluating this integral between the appropriate limits of integration, we can find the exact length of the curve.
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Todd had a piggy bank holding $384. He began taking out money each month. The table shows the amount remaining, in dollars, after each of the first four months
A piggy bank is a small container typically used by children to save money. In this scenario, Todd had a piggy bank holding $384 and began taking out money each month. The table provided shows the amount remaining in the piggy bank, in dollars, after each of the first four months. This information can be used to track Todd's spending and savings habits.
In the first month, Todd took out $60, leaving him with $324 in his piggy bank. In the second month, he took out an additional $48, leaving him with $276. By the third month, Todd had taken out a total of $105, leaving him with $279 in his piggy bank. Finally, in the fourth month, he took out $62, leaving him with $217.
By tracking his spending and savings over the course of these four months, Todd can assess his financial habits and make any necessary adjustments. It is important for individuals to develop good financial habits early on in life, and using a piggy bank can be a fun and effective way to do so.
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