i. The position vector of X is 2b - a.
ii. The position vector of Y is (3b + c)/4.
iii. The ratio XY : Y Z is [tex]|(2b - a) - ((3b + c)/4)|/|((3b + c)/4) - (a + c)/2|[/tex]. Simplifying this expression will give us the final ratio.
i. To find the position vector x of point X, we can use the concept of vector addition. Since AB : BX = 2 : 1, we can express AB as a vector from A to B, which is given by (b - a). To find BX, we can use the fact that BX is twice as long as AB, so BX = 2 * (b - a). Adding this to the vector AB will give us the position vector of X: x = a + 2 * (b - a) = 2b - a.
ii. Similar to the previous part, we can express BC as a vector from B to C, which is given by (c - b). Since BY : YC = 1 : 3, we can find BY by dividing the vector BC into four equal parts and taking one part, so BY = (1/4) * (c - b). Adding this to the vector BY will give us the position vector of Y: y = b + (1/4) * (c - b) = (3b + c)/4.
iii. Z is the midpoint of AC, so we can find Z by taking the average of the vectors a and c: z = (a + c)/2. The ratio XY : YZ can be calculated by finding the lengths of the vectors XY and YZ and taking their ratio. Since XY = |x - y| and YZ = |y - z|, we have XY : YZ = |x - y|/|y - z|. Plugging in the values of x, y, and z we found earlier, we get XY : YZ =[tex]|(2b - a) - ((3b + c)/4)|/|((3b + c)/4) - (a + c)/2|[/tex].
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PLEASE HELP
Suppose that the functions fand g are defined for all real numbers x as follows.
f(x) = 5x
g(x)=4x-4
Write the expressions for (g.f)(x) and (g-f)(x) and evaluate (g+f)(2).
(g•f)(x) =
(g-f)(x) =
(g+r) (2)=
Graph the function f(x)= 3+2 in x and its inverse from model 1.
The graph of the function and its inverse is added as an attachment
Sketching the graph of the function and its inverseFrom the question, we have the following parameters that can be used in our computation:
f(x) = 3 + 2ln(x)
Express as an equation
So, we have
y = 3 + 2ln(x)
Swap x and y in the above equation
x = 3 + 2ln(y)
Next, we have
2ln(y) = x - 3
Divide by 2
ln(y) = (x - 3)/2
Take the exponent of both sides
[tex]y = e^{\frac{x - 3}{2}}[/tex]
Next, we plot the graphs
The graph of the functions is added as an attachment
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how can you write the expression with a rationalized denominator?
3 sqrt 2 / 3 sqrt 6
see photo attached for answers
The expression (3√2) / (3√6) with a rationalized denominator is 3√9 / 6. Option C is the correct answer.
To rationalize the denominator in the expression (3√2) / (3√6), we can multiply both the numerator and denominator by the conjugate of the denominator. The conjugate of √6 is -√6, so we multiply the expression by (-√6) / (-√6):
(3√2 / 3√6) * (-√6 / -√6)
This simplifies to:
-3√12 / (-3√36)
Further simplifying, we have:
-3√12 / (-3 * 6)
-3√12 / -18
Finally, we can cancel out the common factor of 3:
- 3√9 / - 6.
Simplifying further, we get:
3√9 / 6.
Option C is the correct answer.
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How would you describe the difference between the graphs of f (x) = 3x²
and g(x) = -2² ?
OA. g(x) is a reflection of f(x) over the line y = x.
B. g(x) is a reflection of f(x) over the line y = -1.
C. g(x) is a reflection of f(x) over the x-axis.
D. g(x) is a reflection of f(x) over the y-axis.
Comparing the characteristics of the two functions, we can conclude that the graph of g(x) = -2² is a reflection of the graph of f(x) = 3x² over the x-axis (option C).
The given functions are f(x) = 3x² and g(x) = -2².
To understand the difference between their graphs, let's examine the characteristics of each function individually:
Function f(x) = 3x²:
The coefficient of x² is positive (3), indicating an upward-opening parabola.
The graph of f(x) will be symmetric with respect to the y-axis, as any change in x will result in the same y-value due to the squaring of x.
The vertex of the parabola will be at the origin (0, 0) since there are no additional terms affecting the position of the graph.
Function g(x) = -2²:
The coefficient of x² is negative (-2), indicating a downward-opening parabola.
The negative sign will reflect the graph of f(x) across the x-axis, resulting in a vertical flip.
The vertex of the parabola will also be at the origin (0, 0) due to the absence of additional terms.
Comparing the characteristics of the two functions, we can conclude that the graph of g(x) = -2² is a reflection of the graph of f(x) = 3x² over the x-axis (option C). This means that g(x) is obtained by taking the graph of f(x) and flipping it vertically. The reflection occurs over the x-axis, causing the parabola to open downward instead of upward.
Therefore, the correct answer is option C: g(x) is a reflection of f(x) over the x-axis.
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At what points is the function y=sinx/3x continuous?
Answer: [tex](-\infty, 0) \cup (0, \infty)[/tex]
Step-by-step explanation:
The graph of [tex]\frac{\sin x}{x}[/tex] is continuous for all real [tex]x[/tex] except [tex]x=0[/tex], and multiplying this by [tex]1/3[/tex] does not change this.
GEOMETRY 100POINTSSS
Find x
Answer:
5.9
Step-by-step explanation:
sin Θ = opp/hyp
sin 36° = x/10
x = 10 × sin 36°
x = 5.88
Answer: 5.9
I just need help with the range domain is [-2,3)
Answer:
We don't need to worry about the displaystyle- {3} −3 anyway, because we dcided in the first step that displaystyle {x}ge- {2} x ≥ −2. So the domain for this case is displaystyle {x}ge- {2}, {x}ne {3} x≥ −2,x≠ 3, which we can write as displaystyle {left [- {2}, {3}right)}cup {left ({3},inftyright)} [−2,3)∪(3,∞).
Step-by-step explanation:
Similar Triangles
Determine whether the triangles are similar. If so, write a similarity statement. If not, what would be sufficient to
prove the triangles similar? Explain your reasoning.
I need help on number 1 and 2
The equivalent ratio of the corresponding sides and the triangle proportionality theorem indicates that the similar triangles are;
1. ΔAJK ~ ΔSWY according to the SAS similarity postulate
2. ΔLMN ~ ΔLPQ according to the AA similarity postulate
3. ΔPQN ~ ΔLMN
LM = 12, QP = 8
4. ΔLMK~ΔLNJ
NL = 21, ML = 14
What are similar triangles?
Similar triangles are triangles that have the same shape but may have different sizes.
1. The ratio of corresponding sides between the two triangles circumscribing the congruent included angle are;
24/16 = 3/2
18/12 = 3/2
The ratio of each of the two sides in the triangle ΔAJK to the corresponding sides in the triangle ΔSWY are equivalent and the included angle, therefore, the triangles ΔAJK and ΔSWY are similar according to the SAS similarity rule.
2. The ratio of the corresponding sides in each of the triangles are;
MN/LN = 8/10 = 4/5
PQ/LQ = 12/(10 + 5) = 12/15 = 4/5
The triangle proportionality theorem indicates that the side MN and PQ are parallel, therefore, the angles ∠LMN ≅ ∠LPQ and ∠LNM ≅ ∠LQP, which indicates that the triangles ΔLMN and ΔLPQ are similar according to the Angle-Angle AA similarity rule
3. The alternate interior angles theorem indicates;
Angles ∠PQN ≅ ∠LMN and ∠MLN ≅ ∠NPQ, therefore;
ΔPQN ~ ΔLMN by the AA similarity postulate
LM/QP = (x + 3)/(x - 1) = 18/12
12·x + 36 = 18·x - 18
18·x - 12·x = 36 + 18 = 54
6·x = 54
x = 54/6 = 9
LM = 9 + 3 = 12
QP = x - 1
QP = 9 - 1 = 8
4. The similar triangles are; ΔLMK and ΔLNJ
ΔLMK ~ ΔLNJ by AA similarity postulate
ML/NL = (6·x + 2)/(6·x + 2 + (x + 5)) = (6·x + 2)/((7·x + 7)
ML/NL = LK/LJ = (24 - 8)/24
(24 - 8)/24 = (6·x + 2)/((7·x + 7)
16/24 = (6·x + 2)/(7·x + 7)
16 × (7·x + 7) = 24 × (6·x + 2)
112·x + 112 = 144·x + 48
144·x - 112·x = 32·x = 112 - 48 = 64
x = 64/32 = 2
ML = 6 × 2 + 2 = 14
NL = 7 × 2 + 7 = 21
MN = 2 + 5 = 7
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The height h(x), of an object is given by the function h(x) = -16x + 176x + 65
where x is time in seconds and h(x) is height in feet. When does the object reach its maximum height? Round your answer to two decimal places.
To find an object's maximum height, we need to find the vertex of this quadratic equation.
Answer: 5.50 seconds
Terms to know:
Quadratic function: A quadratic function is a polynomial function of degree 2, which means the highest power of the variable in the equation is 2.
Vertex: The vertex of a quadratic function is the point on the graph where the function reaches its highest or lowest point. In the case of a quadratic function in the form f(x) = ax^2 + bx + c, the vertex is given by the coordinates (x, f(x)).
Step-by-step explanation:
The vertex of a quadratic equation can be represented as [tex](\frac{-b}{2a}, f(\frac{-b}{2a})[/tex]
Since we only are looking at the time it takes to reach maximum height we will only look at the x value.
[tex]x= \frac{-176}{2(-16)}[/tex]
[tex]x= 5.50[/tex]
A village P is 12 km from village Q. It takes 3 hours 20 minutes to travel from Q to P and back to Q by a boat. If the boat travels at a speed of 6 km/h from P to Q and (6 + x) km/h back to P, find the value of x.
Answer:
Hope this helps and have a nice day
Step-by-step explanation:
To find the value of x, we can use the formula:
Time = Distance / Speed
Let's calculate the time taken to travel from Q to P and back to Q.
From Q to P:
Distance = 12 km
Speed = 6 km/h
Time taken from Q to P = Distance / Speed = 12 km / 6 km/h = 2 hours
From P to Q:
Distance = 12 km
Speed = (6 + x) km/h
Time taken from P to Q = Distance / Speed = 12 km / (6 + x) km/h
Given that the total time taken for the round trip is 3 hours 20 minutes, we can convert it to hours:
Total time = 3 hours + (20 minutes / 60) hours = 3 + (1/3) hours = 10/3 hours
According to the problem, the total time is the sum of the time from Q to P and from P to Q:
Total time = Time taken from Q to P + Time taken from P to Q
Substituting the values:
10/3 hours = 2 hours + 12 km / (6 + x) km/h
Simplifying the equation:
10/3 = 2 + 12 / (6 + x)
Multiply both sides by (6 + x) to eliminate the denominator:
10(6 + x) = 2(6 + x) + 12
60 + 10x = 12 + 2x + 12
Collecting like terms:
8x = 24
Dividing both sides by 8:
x = 3
Therefore, the value of x is 3.
Answer:
x = 3
Step-by-step explanation:
speed = distance / time
time = distance / speed
Total time from P to Q to P:
T = 3h 20min
P to Q :
s = 6 km/h
d = 12 km
t = d/s
= 12/6
t = 2 h
time remaining t₁ = T - t
= 3h 20min - 2h
= 1 hr 20 min
= 60 + 20 min
= 80 min
t₁ = 80/60 hr
Q to P:
d₁ = 12km
t₁ = 80/60 hr
s₁ = d/t₁
[tex]= \frac{12}{\frac{80}{60} }\\ \\= \frac{12*60}{80}[/tex]
= 9
s₁ = 9 km/h
From question, s₁ = (6 + x)km/h
⇒ 6 + x = 9
⇒ x = 3
1cm on a picture of a swimming pool represents 1200cm of the actual swimming pool. The length of the pictured swimming pool is 4.5cm and the width is 3cm. What is the perimeter of the actual swimming pool? Express your answer in meters.
Answer:
180 meters
Step-by-step explanation:
To find the perimeter of the actual swimming pool, you need to first find the length and width of the actual swimming pool by multiplying the length and width of the pictured swimming pool by the scale factor of 1200 cm.
Length of actual swimming pool = 4.5 cm × 1200 cm = 5400 cmWidth of actual swimming pool = 3 cm × 1200 cm = 3600 cmPerimeter of actual swimming pool = (5400 cm + 3600 cm) × 2 = 18000 cm.Now that we know that the perimeter of the actual pool is 18000 centimeters, we need to convert that to meters! Keep in mind that:
100cm = 1mNow we can divide 18000 by 100:
18000 cm ÷ 100 = 180 m
Therefore, the perimeter of the actual swimming pool is 180 m.
14x^(2n+1)+7x^(n+3)-21^(n+2)
100 points will be awarded
Answer:
Step-by-step explanation:
The given expression is: 14x^(2n+1) + 7x^(n+3) - 21^(n+2)
Unfortunately, it seems there is a missing exponent for the term "21" in the expression. Please provide the correct exponent for 21, and I'll be happy to help you further simplify the expression.
James wants to have earned $6,180 amount of interest in 28 years. Currently he finds
that his annual interest rate is 6.12%. Calculate how much money James needs to invest
as his principal in order to achieve this goal.
Answer:
$3606.44
Step-by-step explanation:
The question asks us to calculate the principal amount that needs to be invested in order to earn an interest of $6180 in 28 years at an annual interest rate of 6.12%.
To do this, we need to use the formula for simple interest:
[tex]\boxed{I = \frac{P \times R \times T}{100}}[/tex],
where:
I = interest earned
P = principal invested
R = annual interest rate
T = time
By substituting the known values into the formula above and then solving for P, we can calculate the amount that James needs to invest:
[tex]6180 = \frac{P \times 6.12 \times 28}{100}[/tex]
⇒ [tex]6180 \times 100 = P \times 171.36[/tex] [Multiplying both sides by 100]
⇒ [tex]P = \frac{6180 \times 100}{171.36}[/tex] [Dividing both sides of the equation by 171.36]
⇒ [tex]P = \bf 3606.44[/tex]
Therefore, James needs to invest $3606.44.
Let N be the greatest number that will divide 1305,4665 and 6905 leaving the same remainder in each case. What is the sum of the digits in N.
Answer:
4
Step-by-step explanation:
You want the sum of digits of the largest number that divides 1305, 4665, and 6905 with the same remainder.
Largest divisorWe can look at 4665/1305 ≈ 3.57 and 6905/1305 ≈ 5.29 for a clue as to the divisor of interest. These quotients tell us that one possibility is the value that would give quotients of 4 and 6 after the remainder is subtracted from each of the numbers.
For 1305 and 4665, if r is the remainder, we require ...
4(1305 -r) = 4665 -r
5220 -4665 = 4r -r
555/3 = r = 185
If 185 is the remainder in this scenario, then 1305 -185 = 1120 is the divisor. Checking the remainder with 6905, we find ...
6905/1120 = 6 r 185
Sum of digitsThe sum of digits of this divisor is 1 + 1 + 2 + 0 = 4.
The sum of the digits in N is 4.
A company Charting its profits notices that the relationship between the number of units sold,x, and the profit,P, is a linear. If 170 units sold results in $20 profit and 220 units sold results in $2820 profit, write the profit function for this company.
P=
Find the marginal profit
$
Step-by-step explanation:
a linear relationship or function is described in general as
y = f(x) = ax + b
Because the variable term has the variable x only with the exponent 1, this makes this a straight line - hence the name "linear".
here f(x) is P(x) :
P(x) = ax + b
now we are using both given points (ordered pairs) to calculate a and b :
20 = a×170 + b
2820 = a×220 + b
to eliminate first one variable we subtract equation 1 from equation 2 :
2800 = a×50
a = 2800/50 = 280/5 = 56
now, we use that in any of the 2 original equations to get b :
20 = 56×170 + b
b = 20 - 56×170 = 20 - 9520 = -9500
so,
P(x) = 56x - 9500
the population of a certain state can be estimated by the equation p=80.7t+18,312.3, where p represents the population of the state in thousands of people t years since 2010
The estimated population of the state in the year 2022 is 19,280,700 people.
The given equation represents the population of a certain state as a function of time, where p is the population in thousands of people and t is the number of years since 2010.
The equation is given as p = 80.7t + 18,312.3.
To estimate the population of the state, we substitute the value of t into the equation. For example, if we want to estimate the population in the year 2022 (12 years since 2010), we substitute t = 12 into the equation:
p = 80.7(12) + 18,312.3
= 968.4 + 18,312.3
= 19,280.7.
The estimated population of the state in the year 2022 is 19,280,700 people.
We can estimate the population for any given year by substituting the corresponding value of t into the equation.
It's important to note that the population is given in thousands of people, so we multiply the final result by 1,000 to obtain the population in actual numbers.
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What else would need to be congruent to show that ABC=AXYZ by SAS?
A
B
OA. ZB=LY
B. BC = YZ
OC. C= LZ
OD. AC = XZ
с
X
Z
Given:
AB XY
BC=YZ
What is needed to be congruent to show that ABC=AXYZ is AC ≅ XZ. option D
How to determine the statementGiven that in ΔABC and ΔXYZ, ∠X ≅ ∠A and ∠Z ≅ ∠C.
We are to select the correct condition that we will need to show that the triangles ABC and XYZ are congruent to each other by ASA rule..
ASA Congruence Theorem: Two triangles are said to be congruent if two angles and the side lying between them of one triangle are congruent to the corresponding two angles and the side between them of the second triangle.
In ΔABC, side between ∠A and ∠C is AC,
in ΔXYZ, side between ∠X and ∠Z is XZ.
Therefore, for the triangles to be congruent by ASA rule, we must have AC ≅ XZ.
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what best describes the relationship between the computed mean of 52.4 and the actual mean of 52.7
The computed mean of 52.4 and the actual mean of 52.7 suggest a close relationship in terms of central tendency.
A computed mean is a statistical measure calculated by summing up a set of values and dividing by the number of observations. In this case, the computed mean of 52.4 implies that when the values are averaged, the result is 52.4.
The actual mean of 52.7 refers to the true average of the population or data set being analyzed. Since it is higher than the computed mean, it indicates that the sample used for computation might have slightly underestimated the true population mean.
However, the difference between the computed mean and the actual mean is relatively small, with only a 0.3 unit discrepancy.
Given the proximity of these two values, it suggests that the computed mean is a reasonably accurate estimate of the actual mean.
However, it's important to note that without additional information, such as the sample size or the variability of the data, it is difficult to draw definitive conclusions about the relationship between the computed mean and the actual mean.
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Given the function f(x) = 4 – 2x, find f(3r – 1).
Answer:
f(3r - 1) = -6r + 6
Step-by-step explanation:
To find f(3r - 1), we substitute 3r - 1 for x in the expression for f(x) and simplify:
f(x) = 4 - 2x
f(3r - 1) = 4 - 2(3r - 1)
= 4 - 6r + 2
= -6r + 6
So, f(3r - 1) = -6r + 6.
Dewan’s bank account balance is -$16.75. He deposits checks totaling $23.59. What is his new balance? -$1.08
Answer:
$6.84
Step-by-step explanation:
This is quite a simple question, simply add the new deposited amount into the original balance to get your answer.
Original balance: -$16.75Deposit: $23.59New balance: -$16.75 + $23.59 = $6.84what is (0.3)0 in binominal distribution
Answer:
When p, the probability of success, is zero in a binomial distribution, the probability of getting exactly k successes in n trials is also zero for all values of k except when k is zero (i.e., when there are no successes).
So, in the case of (0.3)^0, the result would be 1, because any number raised to the power of 0 is equal to 1. Therefore, the probability of getting zero successes in a binomial distribution when the probability of success is 0.3 is 1.
Diseases tend to spread according to the exponential growth model. In the early days of AIDS, the growth factor (i.e. common ratio; growth multiplier) was around 1.9. In 1983, about 1600 people in the U.S. died of AIDS. If the trend had continued unchecked, how many people would have died from AIDS in 2003?
which of the following are like radicals? Check all
of the boxes that apply.
3x√√xy
-12x√√xy
-2x√√xj
x-√4x2²
-x√x²y
2√xy
Answer:
the first 2
Step-by-step explanation:
let me know if it is wrong
The midpoint of AB is M(-4,2). If the coordinates of A are (-7,3), what are the
coordinates of B?
The midpoint of AB is M(-4,2). If the coordinates of A are (-7,3), and the coordinates of B is (-1, 1).
To find the coordinates of point B, we can use the midpoint formula, which states that the coordinates of the midpoint between two points (A and B) can be found by averaging the corresponding coordinates.
Let's denote the coordinates of point A as (x1, y1) and the coordinates of point B as (x2, y2). The midpoint M is given as (-4, 2).
Using the midpoint formula, we can set up the following equations:
(x1 + x2) / 2 = -4
(y1 + y2) / 2 = 2
Substituting the coordinates of point A (-7, 3), we have:
(-7 + x2) / 2 = -4
(3 + y2) / 2 = 2
Simplifying the equations:
-7 + x2 = -8
3 + y2 = 4
Solving for x2 and y2:
x2 = -8 + 7 = -1
y2 = 4 - 3 = 1
Therefore, the coordinates of point B are (-1, 1).
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50 PTS!!!!!!!!!!! I NEED HELP!!!!!
Answer this question based on the table above. Choose the right answer.
Is the statement true that between 1966 and 1976 the average number of miles flown per passenger increased by one-third. (Yes or no)
Answer:
No
Step-by-step explanation:
To determine if the average number of miles flown per passenger increased by one-third between 1966 and 1976, we need to compare the increase in miles flown during that period.
According to the given table:
In 1966, the average number of miles flown per passenger was 711 miles.In 1976, the average number of miles flown per passenger was 831 miles.To find the increase in miles flown, subtract the 1966 value from the 1976 value:
[tex]\begin{aligned}\sf Increase\; in\; miles\; flown &= \sf 831 \;miles - 711\; miles\\&= \sf 120\; miles\end{aligned}[/tex]
Therefore, the average number of miles flown per passenger between 1966 and 1976 increased by 120 miles.
To check if the increase is one-third of the initial value, we need to calculate one-third of the 1966 value:
[tex]\begin{aligned}\sf One\;third \;of \;711 \;miles &= \sf \dfrac{1}{3} \times 711\; miles\\\\ &= \sf \dfrac{711}{3} \; miles\\\\&=\sf 237\;miles\end{aligned}[/tex]
Since the increase in miles flown (120 miles) is not equal to one-third of the initial 1966 value (237 miles), the statement that the average number of miles flown per passenger increased by one-third between 1966 and 1976 is not true.
Dylan's mom told him that she would replace each one of his dimes with a quarter. If he uses all of his coins, determine if Dylan would then have enough money to buy a game priced at $20.98 if he must also pay an 8% sales tax.
Trent has an 8-foot tall tent in the shape of square based pyramid with a base length of 14 feet. If one bottle of waterproof spray covers 76 square feet, how many bottles will he need to waterproof his tent.
Trent will need approximately 2.86 bottles of waterproof spray to cover his tent.
To calculate the number of bottles of waterproof spray Trent will need to cover his tent, we first need to find the surface area of the tent.
The surface area of a square-based pyramid is given by the formula:
Surface Area = Base Area + (0.5 x Perimeter of Base x Slant Height)
The base of the pyramid is a square with a side length of 14 feet, so the base area is:
Base Area = (Side Length)^2 = 14^2 = 196 square feet
To find the slant height of the pyramid, we can use the Pythagorean theorem. The slant height is the hypotenuse of a right triangle formed by one side of the base, the height of the pyramid, and the slant height. The height of the pyramid is given as 8 feet, and half the length of the base is 7 feet.
Using the Pythagorean theorem:
[tex]Slant Height^2 = (Half Base Length)^2 + Height^2[/tex]
[tex]Slant Height^2 = 7^2 + 8^2Slant Height^2 = 49 + 64Slant Height^2 = 113Slant Height ≈ √113 ≈ 10.63 feet[/tex]
Now we can calculate the surface area of the tent:
Surface Area = 196 + (0.5 x 4 x 10.63)
Surface Area = 196 + (2 x 10.63)
Surface Area = 196 + 21.26
Surface Area ≈ 217.26 square feet
Since each bottle of waterproof spray covers 76 square feet, we can divide the total surface area of the tent by the coverage of each bottle to find the number of bottles needed:
Number of Bottles = Surface Area / Coverage per Bottle
Number of Bottles = 217.26 / 76
Number of Bottles ≈ 2.86
Therefore, Trent will need approximately 2.86 bottles of waterproof spray to cover his tent. Since we can't have a fraction of a bottle, he will need to round up to the nearest whole number. Therefore, Trent will need 3 bottles of waterproof spray to fully waterproof his tent.
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A rectangular pyramid is sliced. The slice passes through line segment AB and is parallel to the base.
Which two-dimensional figure represents the cross section?
A. A rectangle the same size as the base
B. A rectangle that is smaller than the base
C. A quadrilateral that is not a rectangle
D. A triangle with a height the same as the pyramid
Answer:
Step-by-step explanation:
The correct answer is A. A rectangle the same size as the base.
When a rectangular pyramid is sliced parallel to the base, the resulting cross-section is a rectangle that is the same size as the base. The parallel slicing ensures that the cross-section maintains the same dimensions as the base of the pyramid. Therefore, option A, a rectangle the same size as the base, represents the cross-section.
Find the limit (if the limit exists). Solve in two different ways.
The limit of the trigonometric expression is equal to 0.
How to determine the limit of a trigonometric expression
In this problem we find the case of a trigonometric expression, whose limit must be found. This can be done by means of algebra properties, trigonometric formula and known limits. First, write the entire expression below:
[tex]\lim_{\Delta x \to 0} \frac{\cos (\pi + \Delta x) + 1}{\Delta x}[/tex]
Second, use the trigonometric formula cos (π + Δx) = - cos Δx to simplify the resulting formula:
[tex]\lim_{\Delta x \to 0} \frac{1 - \cos \Delta x}{\Delta x}[/tex]
Third, use known limits to determine the result:
0
The limit of the trigonometric function [cos (π + Δx) + 1] / Δx evaluated at Δx → 0 is equal to 0.
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What is the z score for Brazil?
The z-score for Brazil is given as follows:
Z = 0.87.
What is the z-score formula?The z-score formula is defined as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
In which:
X is the measure.[tex]\mu[/tex] is the population mean.[tex]\sigma[/tex] is the population standard deviation.The parameters for this problem are given as follows:
[tex]X = 6.24, \mu = 4.8, \sigma = 1.66[/tex]
Hence the z-score for Brazil is given as follows:
Z = (6.24 - 4.8)/1.66
Z = 0.87.
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