Yes, Both diagonal are equal in length with √ 80 units.
We have to given that;
The coordinates of rectangle PQRS are P(1, 6), Q(1, 2), R(9, 2), and S(9, 6).
Hence, The length of diagonal are PR and QS.
Since, We know that;
The distance between two points (x₁ , y₁) and (x₂, y₂) is,
⇒ d = √ (x₂ - x₁)² + (y₂ - y₁)²
Hence, Length of PR is,
PR = √ (x₂ - x₁)² + (y₂ - y₁)²
PR = √ (9 - 1)² + (2 - 6)²
PR = √ 64 + 16
PR = √ 80
And, Lenght of QS is,
QS = √ (x₂ - x₁)² + (y₂ - y₁)²
QS = √ (9 - 1)² + (2 - 6)²
QS = √ 64 + 16
QS = √ 80
Thus, Both diagonal are equal in length with √ 80 units.
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3) Use the figure to answer the
following question.
These prisms are made from the same size unit cubes.
Which rectangular prism has greater volume?
Some of the cubes might be hidden behind other cubes. Try to visualize all of the cubes.
Choose 1 answer:
*The 2 prisms have equal volume.
*Option A above
*Option B above
*Option C above
The blue rectangular prism have a greater volume of 36 cubic units which makes the option C correct.
Volume of a rectangular prismThe volume of a rectangular prism is calculated by multiplication of its three dimensions which are the length, width, and height . That is Length × Width × Height in the same units.
volume of red rectangular prism = 4 units × 3 units × 2 units
volume of red rectangular prism = 24 cubic units
volume of blue rectangular prism = 4 units × 3 units × 3 units
volume of blue rectangular prism = 36 cubic units
Therefore, the blue rectangular prism have a greater volume of 36 cubic units
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9. If a resident who has only completed high school is chosen at random, what is the probability that they are under age 50? Round your answer to the nearest thousandth.
10. If a resident who is aged 20-29 is chosen at random, what is the probability that they have completed only high school or just some college? Round your answer to the nearest thousandth.
To answer these questions, I would need more information about the population being referred to. Specifically, I would need to know the number of residents who have only completed high school and are under age 50, as well as the total number of residents who have only completed high school. I would also need to know the number of residents aged 20-29 who have completed only high school or just some college, as well as the total number of residents aged 20-29.
Do you have this information available?
A sample is taken from all teen drivers at a high school. They are given a
survey that includes the question, "Do you ever engage in the illegal activity of
texting while driving?" What is this an example of?
OA. Nonselection bias
OB. Nonresponse bias
C. Selection bias
OD. Response bias
The given scenario, where a sample of teen drivers at a high school is surveyed about their engagement in the illegal activity of texting while driving, is an example of Selection bias. Option C
How to determine what type of exampleSelection bias occurs when the process of selecting participants for a study or survey is not random or representative of the entire population.
In this case, the sample consists only of teen drivers at a high school, which may not accurately represent all teen drivers in the broader population. The sample is limited to a specific group, which can introduce bias and affect the generalizability of the results to the wider population of teen drivers.
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Factor completely 2x² - 18x + 36.
O 2(x − 6)(x − 3)
O 2(x − 6)(x + 3)
O2(x − 3)(x + 6)
O2(x + 3)(x + 6)
Answer: 2(x − 6)(x − 3) is the answer
Step-by-step explanation:
Eric is working on the problem:
Hank's Auto Wash recently acquired an automatic car-washing machine that is
expected to generate $45,000 in revenue per year, t years from now, for the next 6
years. If the income is reinvested in a business earning interest at the rate of 8% per
year, compounded continuously, find the Accumulated Total Value of this income
stream at the end of 6 years.
Which of the following is NOT a good method for solving the problem?
The correct option number that is NOT a good method for solving the problem is: Option C: 20.48.[c-0.08.6-c0] (45000. ((0.08)(6)=0.08. t)at 45000-(00:48) Il 6 -0.08- 1) at -562500- 20.48.[c-0.08.6-c0]
The problem requires finding the Accumulated Total Value of the income stream generated by Hank's Auto Wash over six years, assuming the income is reinvested at an interest rate of 8% per year, compounded continuously. To solve the problem, we need to use the formula for continuous compounding:
A = P[tex]e^{(rt)[/tex]
Where A is the accumulated total value, P is the initial principal (in this case, the annual revenue of $45,000), e is the mathematical constant e (approximately 2.71828), r is the interest rate (0.08), and t is the time period (6 years).
Plugging in the values, we get:
A = 45000[tex]e^{(0.086)[/tex]
A = 45000[tex]e^{0.48[/tex]
A = 450001.6186
A = $72,838.50
Therefore, the accumulated total value of the income stream at the end of 6 years is $72,838.50.
The method that is NOT a good method for solving the problem is "45000.20.48.[c-0.08.6-c0]." This is not a valid formula for calculating the accumulated total value of an income stream under continuous compounding.
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PLEASE HURRY
The histograms display the frequency of temperatures in two different locations in a 30-day period.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 14. A shaded bar stops at 10 above 60 to 69, at 9 above 70 to 79, at 5 above 80 to 89, at 4 above 90 to 99, and at 2 above 100 to 109. There is no shaded bar above 110 to 119. The graph is titled Temps in Sunny Town.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 14. There is no shaded bar above 60 to 69. A shaded bar stops at 4 above 70 to 79, at 4 above 80 to 89, at 6 above 90 to 99, at 6 above 100 to 109 and at 10 above 110 to 119. The graph is titled Temps in Beach Town.
When comparing the data, which measure of center should be used to determine which location typically has the cooler temperature?
Median, because Sunny Town is symmetric
Mean, because Sunny Town is skewed
Median, because Beach Town is skewed
Mean, because Beach Town is symmetric
Answer:
Median, because Sunny Town is symmetric.
Identify the solution(s) of z^2-4=0
answer
(z+2)(z-2)
steps
its a rule
a²-b²= (a+b) (a-b)
vedantu
At Mr. Heritage and Mr. Fraser's old school they are working on making a new sandbox for the kindergarten kids to play in. One design is a 3 m x 3 m x 30 cm. A second design is 3.25 m x 3.25 m x 25 cm. For each design, calculate the area of materials needed to build it (think about the shape, AND what it will look like-sketching it is a good idea AND make the problem real- what would a sandbox LOOK like...), and the volume of sand it will hold. Which design would you recommend?
Find 2 solutions
Factoring in the dimensions , Design 1 would be the best recommendation because it requires less material and can hold a slightly larger volume of sand in comparison to Design 2.
How do we calculate?For Design 1:
Dimensions: 3 m x 3 m x 30 cm
We find the total area:
Two faces measures 3 m x 3 m = 9 m² each for the bottom and top
Two faces measures 3 m x 30 cm = 0.9 m² each for back and front
Two faces measures 3 m x 30 cm = 0.9 m² each
Therefore the total area of materials needed for Design 1 is found as
= 9 m² + 9 m² + 0.9 m² + 0.9 m² + 0.9 m² + 0.9 m² = 21.6 m²
Design 2:
Dimensions: 3.25 m x 3.25 m x 25 cm
In the same way, we find the area of materials needed for Design 2:
Total area of materials needed for Design 2 = 10.5625 m² + 10.5625 m² + 0.8125 m² + 0.8125 m² + 0.8125 m² + 0.8125 m² = 24.375 m²
Design 1 volume is :
Volume = Length x Width x Height
Volume of sand for Design 1 = 3 m x 3 m x 0.3 m = 2.7 m³
Design 2 volume is :
Volume of sand for Design 2 = 3.25 m x 3.25 m x 0.25 m = 2.40625 m³
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Dependent and Independent Variables
Can you think of a relationship between two quantities in your life? How could you apply your knowledge of dependent and independent variables to the scenario?
Answer:
Dependent and Independent could be used like a ride on a bike, or even traveling to a friend's house. The dependent variable depends on the independent variable, so let's say I biked at a speed of 7 min per hour and I traveled 42 miles. The independent variable is minutes, because distance depends on time.
Step-by-step explanation:
Sort the square roots into rational or irrational
225
/300
/120
√81
/576
/36
12
A441
/50
/324
/200
Rational square roots: √225, √81, √576, √36, √441, √324
Irrational square roots: √300, √120, √12, √50, √200
Let's determine whether each square root is rational or irrational:
√225 = 15. This is a rational number since it can be expressed as a fraction of two integers (15 = 15/1).
√300 ≈ 17.32050808. This is an irrational number because it cannot be expressed as a fraction of two integers and it has non-repeating, non-terminating decimal digits.
√120 ≈ 10.95445115. This is also an irrational number for the same reasons as above.
√81 = 9. This is a rational number since it can be expressed as a fraction of two integers (9 = 9/1).
√576 = 24. This is a rational number since it can be expressed as a fraction of two integers (24 = 24/1).
√36 = 6. This is a rational number since it can be expressed as a fraction of two integers (6 = 6/1).
√12 ≈ 3.464101615. This is an irrational number because it cannot be expressed as a fraction of two integers and it has non-repeating, non-terminating decimal digits.
√441 = 21. This is a rational number since it can be expressed as a fraction of two integers (21 = 21/1).
√50 ≈ 7.071067812. This is an irrational number for the same reasons as above.
√324 = 18. This is a rational number since it can be expressed as a fraction of two integers (18 = 18/1).
√200 ≈ 14.14213562. This is an irrational number because it cannot be expressed as a fraction of two integers and it has non-repeating, non-terminating decimal digits.
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In the figure, A MNP-AXYZ. Find the value of x.
X
P
+F
M
18
N
Z
27
G 12
The solution is: the values of x and y is 32° and 51° respectively.
Using the triangle theorem, the values of x and y is 32° and 51° respectively
From △MNP
∠M + ∠N + ∠P = 180° (Sum of interior angles in a triangle)
N = 180 - (142 + 24)
N = 180 - 168
N = 14°
Equate the expression :
2x - 50 = 14
2x = 14 + 50
2x = 64
x = 64 / 2
x = 32°
From ; 2x - y = 13 _____(1)
Substitute x = 32 into the expression ;
2(32) - y = 13
64 - y = 13
64 - 13 = y
51° = y
Therefore, the values of x and y is 32° and 51° respectively.
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complete question:
Find the value of x and y. Triangle MNP = triangle TUS
3. Find the distance from point A
B(-2, 1) D (0.0) A (2.4) C(2,-1)
The distance between point A (2, 4) and point B (-2, 1) is equal to 5 units.
How to determine the distance between the coordinates for each points?In Mathematics and Geometry, the distance between two (2) end points that are on a coordinate plane can be calculated by using the following mathematical equation:
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Where:
x and y represent the data points (coordinates) on a cartesian coordinate.
By substituting the given end points into the distance formula, we have the following;
Distance = √[(-2 - 2)² + (1 - 4)²]
Distance = √[(-4)² + (-3)²]
Distance = √[16 + 9]
Distance = √25
Distance = 5 units.
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Complete Question:
3. Find the distance from point A to B.
A (2, 4) B (-2, 1) C(2, -1) D (0, 0)
Pedro look out a 4-year loan for $32,500 to help pay his college tuition. He has to pay 4% simple interest on the loan. How much interest will Pedro have to pay?
The interest Pedro will have to pay is $5200
Calculating how much interest will Pedro have to pay?From the question, we have the following parameters that can be used in our computation:
Principal = $32.500
Rate = 4% simple interest
Time = 4 years
The formula of simple iinterest is
I = Principal * Rate * Time
substitute the known values in the above equation, so, we have the following representation
I = 32500 * 4% * 4
Evaluate
I = 5200
Hence, Pedro have to pay $5200 as interest
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4x/3 +x/6=6 can u pls help
Answer:
Step-by-step explanation:
4x/3 + x/6 =6
get a common denominator first
8x/6 + x/6 =6
then add
9x/6 = 6
multiply by six
9x = 36
divide by 9
x= 4
Please help hurry! will give brainliest
Answer: 15/38 or 0.39473684210526315789473684210526
Step-by-step explanation:
Sorry if I'm wrong but I hope this helps! :)
What is the name of the following triangle?
Answer: Obtuse triangle? The line marked with O and E is more than 90 degrees
Step-by-step explanation:
Is the figure shown in the coordinate plane a parallelogram? Why or why not? Use the given coordinates to justify your answer.
The given image is a parallelogram, because the two lines are Parallel to each other implying that they will never cross each other
What is the coordinate plane?Based on the question above, the coordinates of the figure are:
O = (0,0)
P = (a, b)
S = (a + c, b)
T = (c,0)
Note that the vertices O and T and they can be seen on the same horizontal level, due to the fact that they have the same y-coordinate and can be used also for vertices P and S
The length of the sides by distance formula will be:
PS = c
OT = c
So this implies that the opposite sides are parallel and congruent. Therefore, the image is a parallelogram
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How many edges on a cylinder?
A cylinder has two types of edges: the curved edges and the top and bottom edges.
A cylinder is a three-dimensional geometric shape that consists of two circular bases and a curved surface connecting the bases. The circular bases have a certain number of edges, depending on the number of sides each base has.
Since a circle has no straight edges, the circular bases of a cylinder do not contribute any edges.
The curved surface of a cylinder has no straight edges either, as it consists of a smooth, continuous surface.
Therefore, the curved surface does not contribute any edges to the cylinder.
The only remaining edges are the top and bottom edges of the cylinder. Each base of the cylinder has a single edge that runs along the circumference of the circular base.
Hence, the cylinder has two edges from its top and bottom bases.
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you are paid 16.50/hr. you work 40 hr/week and 4 weeks/month. Your deductions are FICA (7.65%) and Federal Tax withholding (10%). The following table shows your monthly expenses.
1. What is your gross income per month?
After considering all the given data we come to the conclusion that the gross income of the given individual is = $2640.
The individual's gross income per month can be evaluated as follows
Gross Income = Hourly rate × Hours worked per week × Weeks per month
Staging the values given in the problem statement:
Gross Income = 16.50 × 40 × 4 = $2640
The FICA tax is a mixture of Social Security and Medicare taxes, here it involves the total 15.3% of earnings. The individual is responsible for half of the total bill (7.65%), which involves a 6.2% Social Security tax and 1.45% Medicare tax on the individual's earnings.
The Federal Tax withholding is 10% of the individual's gross income per month.
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Answer the question by comparing the equation,
f
(
x
)
=
2
cos
(
2
π
6
(
x
+
4
)
)
+
3
to the equation,
f
(
x
)
=
acos
(
2
π
b
(
x
+
c
)
)
+
d
.
What is the period of the function?
The calculated value of the period of the function is 6
Calculating the period of the function?From the question, we have the following parameters that can be used in our computation:
The equation, f(x) = 2cos(2π/6(x + 4)) +3
A sinusoidal function is represented as
f(x) = acos(2π/b(x + c)) + d
Where the period is B
When the equations are compared, we have
2π/b = 2π/6
This gives
b = 6
Hence, the period of the function is 6
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Complete question
Answer the question by comparing the equation,f(x)=2cos(2π6(x+4))+3 to the equation,f(x)=acos(2πb(x+c))+d.What is the period of the function?
Which ordered pair is a solution to the system of linear equations? x + 4y = 3 y = −4x − 3 (1, 1) (1, −1) (−1, 1) (−1, −1)
Answer:
(-1,1)
Step-by-step explanation:
Solve for the first variable in one of the equations, then substitute the result into the other equation.
equation form:
x=-1, y=1
have a great day and thx for your inquiry :)
By substituting each of the provided options into the given system of linear equations, it is revealed that the ordered pair (-1, 1) is a valid solution for both the equations.
The correct answer is (-1, 1)
In mathematics, a system of linear equations consists of multiple linear equations with the same variables. These equations describe various relationships among these variables, typically representing lines in a multi-dimensional space. Solving such systems involves finding values for the variables that satisfy all equations simultaneously. Methods like substitution, elimination, or matrix algebra can be used to solve these systems. These systems are fundamental in fields like physics, engineering, economics, and computer science for modeling and solving real-world problems involving multiple interconnected variables.
We can solve this problem by substituting values from the given options into the equations and checking for which option both equations are valid. The system of linear equations is: x + 4y = 3 and y = -4x - 3.
Option (1, 1): For x = 1 and y = 1, our system becomes 1 + 4*1 = 5 and y = -4*1 - 3 = -7. Both do not hold true.Option (1, -1): For x = 1 and y = -1, our system becomes 1 + 4*-1 = -3 and y = -4*1 - 3 = -7. Both do not hold true.Option (-1, 1): For x = -1 and y = 1, our system becomes -1 + 4*1 = 3 (correct) and y = -4*-1 - 3 = 1 (correct). Thus, option (-1, 1) is a solution to the system of equations.Option (-1, -1): For x = -1 and y = -1, our system becomes -1 + 4*-1 = -5 and y = -4*-1 - 3 = 1. Both do not hold true.Therefore, the ordered pair that is a solution to the system of linear equations is (-1, 1).
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Because you loved Professor Salaam’s class so much, you go to the market and decide to trade your car for 2 magical doubling beans. After 1 day, you notice that your 2 magical beans have turned into 4 magical beans. After 2 days you look and there are 8 magical beans. On the third day you notice there are now 16 beans. Since you are a brilliant mathematician, you decide to estimate how many beans you will have after 15 days.
Part A
How many beans will you have?
Part B
If each magical bean is worth $0.50, and your car was worth $65,000, did your trade make sense (after 15 days)?
(b)
A
YES
B
NO
C
MAYBE?
D
Not enough information
(c)
Part C
Estimate how many days you would need to have doubled your beans for the trade to make sense.
Part A: After 15 days will have 32,768 magical beans.
Part B: As the value of the magical beans is less than the value of the car the trade does not make sense at least not from a financial perspective. B NO.
Part C: We would need at least 17 days for the number of magical beans to exceed the value of the car. C MAYBE?.
Based on the given information can observe that the number of beans doubles every day.
So, after 15 days will have 2¹⁵ = 32,768 magical beans.
The value of the 32,768 magical beans would be:
32,768 beans × $0.50/bean
= $16,384
Part C:
Let us assume that after 'n' days, the number of beans would be equal to or greater than the value of the car.
Value of the car in terms of magical beans = $65,000/$0.5 per bean
= 130,000 beans
Now, we can set up an equation based on the doubling of beans:
2ⁿ >= 130,000
Taking the logarithm base 2 on both sides, we get:
n × log2(2) >= log2(130,000)
n >= log2(130,000)
n >= 16.98
We would need at least 17 days for the number of magical beans to exceed the value of the car.
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I need an answer ASAP!!!
And also possibly an explanation on how to solve, I really don't understand this.
Please help, thanks!
Answer:
D=2, 3, 5, 6, 7, 8, 9,
Step-by-step explanation:
btw can i js get 1 brainly?
{2,3,5,6,7,8,9}
The union of two sets A and B is defined as the set of all the elements that lie in set A and set B or both the elements in A and B altogether.
Which of the following could be the measures of the three angles of a triangle?
(1) 40°, 90°, 60°
(3) 120°, 30°, 20°
(2) 50°, 100°, 30°
(4) 70°, 70°, 60°
Answer:
Step-by-step explanation:
The sum of three angles in a triangle is equal to 180°.
(1) 40°, 90°, 60°
40 + 90 + 60 = 190. Therefore, it could not be the measures of the three angles if a triangle.
(3) 120°, 30°, 20°
120 + 30 + 20 = 170. Therefore, it could not be the measures of the three angles if a triangle.
(2) 50°, 100°, 30°
50 + 100 + 30 = 180. Therefore, it could be the measures of the three angles if a triangle.
(4) 70°, 70°, 60°
70 + 70 + 60 = 200. Therefore, it could not be the measures of the three angles if a triangle.
Determine the measures of the marked angles in the figure shown.
The measures of the marked angles in the figure are:
x = 0.8°
6x + 8° = 12.8°
x + 12° = 12.8°
How do we calculate?We have that:
x + 12° and 6x + 8°.
We equate the expression: 6x + 8° = x + 12°
We then solve for x:
6x - x = 12° - 8°
5x = 4°
We then divide both sides by 5:
x = 4° / 5
x = 0.8°
We get the measure of the marked angle for
6x + 8°:
6(0.8°) + 8° = 4.8° + 8° = 12.8°
We also get the measure of the marked angle as:
x + 12°:
0.8° + 12° = 12.8°
In conclusion, an angle is formed when two straight lines or rays meet at a common endpoint.
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find the area of the figure 8m, 5m 5m, 15m, 18m A= [?] m^2
Answer:
302 m²
Step-by-step explanation:
You want the area of the figure composed of a triangle and rectangle.
AreaThe formulas for the areas of the parts are given in the problem statement.
TriangleThe base length of the triangle is (18 m - 5m - 5 m) = 8 m. Then its area is ...
A = 1/2bh
A = 1/2(8 m)(8 m) = 32 m²
RectangleThe area of the rectangle is ...
A = LW
A = (18 m)(15 m) = 270 m²
FigureThe area of the figure is the sum of the areas of its parts:
A = (triangle area) + (rectangle area)
A = 32 m² +270 m² = 302 m²
The area of the figure is 302 m².
<95141404393>
Please help!!
Enter the correct answer in the box.
Function g is the result of these transformations on the parent sine function:
• vertical stretch by a factor of 3
• horizontal shift left
units
• vertical shift down 4 units
Substitute the values of A, C, and D to complete the equation modeling function g.
Answer:
By substituting the values of A, C, and D the equation modelling the function is;g(x) = 3·sin(x - π/2) - 4
Step-by-step explanation:
From the given information, we have;The vertical stretch of the sine function = 3 × The parent function∴ A = 3Given that the horizontal shift left = π/2 units, (from an online source with similar question)The vertical shift down = 4 unitsThe given function, g is g(x) = A·sin(x + C) + DWhere;A = The amplitude = The maximum displacement from the rest or equilibrium position = 3C = The horizontal shift = -π/2 (The negative sign is for the shifting to the left)D = The vertical shift = -4 (The negative sign is for a shift in the downward direction)Therefore, the equation modelling the function is;g(x) = 3·sin(x - π/2) - 4
A veterinarian visits an aninal shelter with 147 dogs. 42 are randomly selected for a study. Of tjose selected 14 have a disease. What is the best estimate for the number of dogs that suffer from tge disease? 49, 41,52 or 38?
Answer:
The answer is 49
Step-by-step explanation:
We can use proportions to estimate the number of dogs in the entire population that have the disease, based on the sample of dogs with the disease.
We know that 42 dogs were selected for the study, and 14 of them had the disease. This means that the proportion of dogs in the sample with the disease is:
14/42 = 0.3333
We can use this proportion to estimate the number of dogs in the entire population that have the disease, by multiplying it by the total number of dogs:
0.3333 * 147 = 49
Therefore, the best estimate for the number of dogs that suffer from the disease is 49.
This sentence includes a participial phrase. True or false.
The picture frame held a picture of our family on vacation.
True
False
The sentence given in the question does not include a participial phrase. Hence, correct option is False
The sentence "The picture frame held a picture of our family on vacation" does not include a participial phrase.
A participial phrase is a phrase that acts as an adjective. In this sentence, the phrase "on vacation" is an adjective phrase that describes the noun "family." However, it is not a participial phrase because it is not formed from a verb.
A participle is a verb form that can be used as an adjective. In this sentence, the verb "hold" is not used as an adjective.
Therefore, the phrase "on vacation" is not a participial phrase.
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