A. On the sixth day, the plant grows to 64 times its original height.
B. On the nth day, the plant would [tex]2^n[/tex] time its original height.
A. From the given condition we can that the growth of the plant shows a geometric progression with a first term of 2 and a common ratio of 2.
On the first day, the plant grows to [tex]2^1[/tex] = 2 times its original height.
On the second day, the plant grows to [tex]2^2[/tex] = 4 times its original height.
Similarly, on the sixth day, the plant grows to [tex]2^6[/tex] = 64 times its original height.
B. The nth term of the progression can be calculated by multiplying the first term by the common ratio raised to the power of n-1.
In this case, the first term is 2 and the common ratio is 2. So the nth term is [tex]2 * 2^{n-1} = 2^n[/tex]
Hence, on the nth day, the plant grows to [tex]2^n[/tex] times its original height.
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Find the vector equation for the line of intersection of the planes x+4y-4z=-3 and x+z=5. r= < , ,0> +t <4, , >.
The vector equation for the line of intersection of the planes x+4y-4z=-3 and x + z = 5 is r = <5, -2, 0> + t <-1, 5/4, 1>
The equations of the planes are:
x + 4y - 4z = -3 ..............(1)
and x + z = 5 .............(2)
Subtract equation (2) from equation (1),
( x + 4y - 4z + 3) - (x + z - 5 ) = 0
4y - 5z + 8 = 0
we can rewrite is as,
4y = 5z - 8
y = 5/4 z - 8/4
y = 5/4 z - 2 ...............(3)
Here, we don't have enough equations to uniquely solve for either y or z. So, we set z = t, where t can be any real number.
The variable t is the free parameter for the parametrization of the line.
Substitute z = t in equation (3) we get,
y = 5/4 t - 2
From equation (2),
x = 5 - z
For z = t,
x = 5 - t
Thus, the parametrization of the line would be,
(x, y, z) = (5 - t, -2 + 5/4 t , t)
= <5, -2, 0> + t<-1, 5/4, 1>
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What i the 8th term in the arithmetic equence defined by the explicit formula an=6n−4?
Answer:
a₈ = 44
Step-by-step explanation:
to find a₈, substitute n = 8 into the explicit formula
a₈ = 6(8) - 4 = 48 - 4 = 44
since the mode is the most frequently occurring data value, . a. it can never be larger than the mean b. it is always larger than the median c. it is always larger than the mean d. more than one mode can exist
The distribution of the mean, median, and mode values will depend on how skewed the distribution is. As a result, mean or mode may be larger than or less than mode.
correct answer is D.
Different measures of the center in a set of numerical data include mean, median, and mode. They each attempt to condense a dataset into a single number that may be used to represent a "typical" data point.
The "mean" value is obtained by summing all the data points and dividing the result by the total number of data points.
The middle number, or median, is obtained by placing all data points in order and choosing the middle one (or, if there are two middle numbers, the mean of those two figures).
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Nikki gathered data about the length of time she spent listening to the radio and the number of commercials she heard. She organized the data in a scatter plot, where x represents the minutes spent listening and y represents the number of commercials. Then she used the graphing tool to find the equation of the line of best fit:
HELP!!
By using the equation of the line of best fit, the number of minutes Nikki would need to listen to the radio is equal to 63.275 minutes.
How to determine the number of minutes Nikki would need to listen to the radio?In order to determine the number of minutes Nikki would need to listen to the radio, we would have to substitute the value representing the number of commercials (y) into the linear equation and then evaluate as follows;
y = 0.338x − 1.387
When the value of y = 20 commercials, the number of minutes (x) in feet is given by;
20 = 0.338x − 1.387
By rearranging and collecting like terms, we have the following:
0.338x = 20 + 1.387
0.338x = 21.387
Number of minutes (x) = 21.387/0.338
Number of minutes (x) = 63.275 minutes.
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Complete Question:
Nikki gathered data about the length of time she spent listening to the radio and the number of commercials she heard. She organized the data in a scatter plot, where x represents the minutes spent listening and y represents the number of commercials. Then she used the graphing tool to find the equation of the line of best fit: y = 0.338x − 1.387. Based on the line of best fit, for approximately how many minutes will Nikki need to listen to the radio to hear 20 commercials?
Carmela's gross pay is $784.25. Her deductions total is $191.17. What percent of her gross pay is take-home pay?
The percent of Carmela's gross pay that is her take-home pay is 75%
How to calculate the percent of Carmela's gross pay that is her take-home pay?
Carmela's gross pay is $784.25
Her total deductions is $191.17
Therefore the percent of her gross pay can be calculated as follows
The first step is to subtract the deductions from the gross pay
784.25 - 191.17
= 593.08
The percent of the gross pay that is take-home pay is
593.08/784.24 × 100
= 0.75 × 100
= 75%
Hence 75% of her gross pay is take-home pay
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2. Amy has a room that is 6 feet by 10 feet. She bought tiles
that are 8 inches by 6 inches. How many tiles will she
need to cover the floor?
A unit can be used for measurement, and is commonly found in mathematics to describe length, size, etc.
Because we are dealing with different units here, we first would need to know how many inches are in one foot.
1 foot = 12 inches
Now that we know how many inches are in a foot, we can convert the length and width of the room from feet to inches.
6 feet = 72 inches
10 feet = 120 inches
Taking these numbers, we now need to figure out the area of the floor.
72 × 120 = 8640
Now, find the area of each tile.
6 × 8 = 48
Taking 8640, we can now divide that by 48 to get the number of tiles needed.
8640 ÷ 48 = 180
Therefore, 180 tiles are needed to cover the floor.
A student went on a two-day hike. • On day one, the student hiked 11 kilometers. On day two, the student hiked at a rate of 2 kilometers per hour for x hours. Which of the following graphs represents y, the total distance, in kilometers, the student hiked over both days after hiking for x hours on day two?
The slope is 2, which equals the distance travelled each hour. The total distance hiked at the start of the second day is represented by the y-intercept, which is 4, which is also the y-value. intercept's
Explain about the Slope?We locate the rise/run before calculating the slope. Since the line increases by 2 between each point, the rise is 2. It travels over 1 between the points, hence the run is 1. The slope is now 2/1, or 2.
Given that it is rise/run, this gives us miles/hours, which indicates the number of miles she treks per hour.
The line's crossing of the y-axis is known as the y-intercept. At four, this is.
The fact that the y-value at this time is 4 and the x-value at this point is 0 tells us that she has trekked 4 miles in the 0 hours since the start of the second day, which is the distance she has covered so far.
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Select the linear function that describes the relationship between the domain and range in the table below.
x f(x)
−1 5
0 3
1 1
The linear function that describes the relationship is y = -2x + 3
How to determine the linear functionFrom the question, we have the following parameters that can be used in our computation:
x f(x)
−1 5
0 3
1 1
A linear function is represented as
y = mx + c
Where
c = y when x = 0
This means thar
c = 3
So, we have
y = mx + 3
From the table, we can see that
As x increases by 1, y decrease by 2
This means that
m = -2
So, we have
y = -2x + 3
Hence, the equation is y = -2x + 3
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the sum of the cube of a number and the product of the number and twelve is equal to seven times the square of the number. find the number.
Answer:
4 or 3
Step-by-step explanation:
X³+12X=7X²
X³-7X²+12X=0
X(X²-7X+12)=0
SOLVING THE QUADRATIC EQUATION
you have X=3 or X=4
At the nearest wholesale store, 3 bags of cereal cost $21.75. Which equation represents the proportional relationship?
For integers a, b, and c, define a*b*c to mean ab-bc+ca then 1*-1*2 equals
Options;
A; -4
B; -2
C; 0
D; 2
E; 4
The operation of 1 * (-1) * 2 equals option D. 2.
What are Binary Operations?Binary operations are the operations which are performed on a specific set.
If the operation is defined on a set X, then binary operation can be defined as,
* : X * X → X.
Addition, subtraction, ... are some of the binary operations.
The given binary operation is defined as,
a * b * c = [tex]a^b-b^c+c^a[/tex]
We have to find the value of 1 * (-1) * 2.
By the definition,
1 * (-1) * 2 = [tex]1^{-1}-(-1)^{2}+2^1[/tex]
= 1 - 1 + 2
= 2
Hence the correct option is D.
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Jill and Jessica are bike riding at the park. Jill rides her bike around the two edges of the rectangular park while Jessica takes the short cut. How much farther does Jill ride than Jessica? Round to the nearest tenth.
Jill ride 43.39 meters farther than Jessica.
What is the Pythagorean theorem?
In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. The theorem can be used to determine how steep mountains or slopes are. To calculate the distance between an observer and a location on the ground when the observer is looking down from a tower or structure. It is mostly utilized in the construction industry.
Given, Jill and Jessica are bike riding at the park. Jill rides her bike around the two edges of the rectangular park while Jessica takes the shortcut
Given the length of the Rectangular park = 100m
The width of the park = 60m
Thus jill ride total = 60 + 100
Jill ride total = 160m
Jessica took a shortcut since she rides diagonally.
From the Pythagorean theorem:
hypotaneus² = base² + height²
Thus,
total distance Jessica covers = √(60² + 100²)
total distance Jessica covers = √3600 + 10000
total distance Jessica covers = √13600
total distance Jessica covers = 116.61
Difference between their distances = 160 - 116.61
Difference between their distances = 43.39
therefore, 43.39 m farther does Jill ride than Jessica.
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Complete question:
Identify the number of terms and then the resend themselves for each algebraic expression
The number of terms in the algebraic expressions are:
6y + 14 ⇒ 2 terms3x³ + 7x² + x - 5 ⇒ 4 termsHow to determine the number of terms in the algebraic expressionsFrom the question, we have the following parameters that can be used in our computation:
6y + 14 and 3x³ + 7x² + x - 5
Consider an expression given as
ax + b
The number of terms in the expression is 2 and the terms are ax and b
Using the above as a guide, we have the following:
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Complete question
Identify the number of terms and then the resend themselves for each algebraic expression
6y + 14 and 3x³ + 7x² + x - 5
The ratio of boys to girls in Mandy’s mathematics class is 3 to 12.
This ratio is the same in Mandy’s science class, in which there are 20 girls. How many boys are there in Mandy’s science class? Show your work
Number of boys in Mandy’s science class is 5.
Now, According to the question:
The ratio of boys to girls in Mandy’s mathematics class is 3 to 12.
This ratio is the same in Mandy’s science class,
There are 20 girls.
To find the how many boys are there in Mandy’s science class?
Based on the given condition:
Let the ratio be 3x and 12x
Now, According to the statement:
12x = 20
x = 20/12
x = 5/3
So, Number of boys = 3 × 5/3 = 5
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1. If mA = 3x° and
m
what is the value
of x?
Answer: I'm sorry, but the information provided is not enough to determine the value of x. The statement "mA = 3x°" does not provide enough context to understand what "mA" and "x" represent, and what the relationship between them is. Additionally, the statement "m" does not provide any information that can help determine the value of x. Can you please provide more information or context?
Step-by-step explanation:
Joshua goes to a store an buys an item that costs x dollars. He has a coupon for 5% off, and then a 6% tax is added to the discounted price. Write an expression in terms of x that represents the total amount that Joshua paid at the register
The expression representing the total amount paid by Joshua at the register is 1.007x dollars.
We have,
To represent the total amount that Joshua paid at the register, we need to account for the following steps:
- Applying the 5% discount to the original price x:
Discount = 5% of x = 0.05x
Calculating the price after the discount:
Price after discount = x - Discount = x - 0.05x = 0.95 x
Adding the 6% tax to the discounted price:
Tax = 6% of the discounted price = 0.06 x (0.95x)
The expression for the total amount that Joshua paid at the register:
Total amount paid
= Price after discount + Tax
= 0.95 x + 0.06 (0.95 * x)
Simplifying the expression:
Total amount paid = 0.95x + 0.057x
Total amount paid = 1.007x
Thus,
The expression representing the total amount paid by Joshua at the register is 1.007x dollars.
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Lucia and Danna both recently purchased fitness watches. The watches count the number of steps they walk in a day. At lunchtime, Lucia has 5445 steps and Danna has 4995 steps. Lucia averages 800 steps per hour and Danna averages 900 steps per hour.
A. Write and solve a system of linear equations that represent the total number of steps each person takes.
B. Interpret the meaning of the solution in terms of the problem situation.
The system of linear equations is y = 800x + 5445, and y = 900x + 4995. The solution is 4.50. This states that the number of steps taken by Danna and Lucia will be equal after 4.50 hours.
What is system of linear equation?The set of two or more linear equations containing the same variables is known as a system of linear equations in mathematics. In this case, linear equations are first-order equations, where the maximum power of the variable is 1. One, two, or three variables may be present in a linear equation.
Let us suppose the number of hours = x.
Let us suppose the total number of steps = y.
Given that, Lucia has 5445 steps and Lucia averages 800 steps per hour.
For Lucia the linear equation is:
y = 800x + 5445
For Danna, Danna has 4995 steps and Danna averages 900 steps per hour.
For Danna the linear equation is:
y = 900x + 4995
The system of linear equations is:
y = 800x + 5445 (equation 1)
y = 900x + 4995 (equation 2)
Substitute the value of y of equation 1 in equation 2:
800x + 5445 = 900x + 4995
5445 - 4995 = 900x - 800x
450 = 100x
x= 4.50
B. The solution of the linear equation is 4.50. This states that the number of steps taken by Danna and Lucia will be equal after 4.50 hours.
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What is the distance between AB and CD?
√5 is the minimum distance between the line AB and CD.
What are coordinates?A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.
Given Two lines AB and CD,
Since, The minimum distance between two lines is the distance between B and C As we can see in the graph
Since, coordinates of B and C are, (1, 2) and (3, 1)
From the formula of distance between two coordinates:
Distance = √((x₂ -x₁)² + (y₂ -y₁)²)
in our case,
Distance = √((3 - 1)² + (1-2)²)
Distance = √4 + 1)
Distance = √5
Therefore, the minimum distance between the line AB and CD is √5.
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Does the point (0, 0) satisfy the equation y = x?
Answer:
yes
Step-by-step explanation:
when y equals 0, x equals 0 also
y = x will produce a straight line passing through the point of origin (0,0)
A line includes the points (0, -8) and (3, 3).
Find the rate of change of the line. (1 point)
uy =
When the line passes through two points as shown, the slope is 11/3.
What is slope?The slope or gradient of a line in mathematics is a number that describes both the direction and the steepness of the line. The slope of a line indicates its steepness. Slope is calculated mathematically as "rise over run" (change in y divided by change in x). The slope is a numerical value that describes the steepness of a line and is typically calculated by dividing the vertical distance by the horizontal distance (rise over run) between two points.
Here,
m=3
m=(y2-y1)/(x2-x1)
3=(y+5)/(-3+(2))
-3=y+5
y=-8
The value of slope is 11/3 when the line is passing through 2 points as given.
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The area of a circle is 64π cm2, and the area of a sector of the circle is 32π cm2. What is the degree measure of that sector? (Just type the number of degrees. )
The degree measure of the sector is θ = 180°
We know that the area of a sector is nothing but the area inside the section of the circle created by two radii and an arc.
The formula for the area of a sector of the circle is:
area of a sector = [tex]\frac{\theta}{360} \times \pi \times r^2[/tex]
where θ is the central angle measure in degrees
And πr² is the area of the circle
Here, the area of a sector of the circle A = 32π cm²
and the area of a circle (πr²) = 64π cm²
Using above formula of the area of a sector of the circle,
[tex]A=\frac{\theta}{360} \times \pi \times r^2\\\\32\pi=\frac{\theta}{360} \times \pi \times r^2\\\\32\pi=\frac{\theta}{360} \times 64\times \pi\\\\\theta=\frac{360}{2}\\\\ \theta=180^{\circ}[/tex]
Therefore, the central angle associated to that sector is 180°
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Write two expressions that could be used to determine what 340 increased by 19% is
The new value = 340 + (19% × 340)
The actual change = The new value - 340
"Information available from the question"
340 increased by 19%
To write in mathematically:
The value of the percentage increase = 19% × 340
The new value = 340 + The value of the percentage increase
The new value = 340 + The value of the percentage increase
= 340 + (19% × 340)
= 340 + 19% × 340
= (1 + 19%) × 340
= (100% + 19%) × 340
= 119% × 340
= 119 ÷ 100 × 340
= 119 × 340 ÷ 100
= 40,460 ÷ 100
= 404.6
The actual change = The new value - 340
= 404.6 - 340
= 64.6
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What is the greatest common factor shared by 39 and 15
Answer:
3
Step-by-step explanation:
15 is divisible by 3, 3 × 5 = 15. Then of course 1 and 15 no other ones. 1,3,5,15
39 is divisible by 3, 3× 13 = 39, then 1 and 39. 1,3,13,39
The only common factors are 1 and 3, and since 3 is greater that is the greatest common factor.
Hope that helps! Let me know if you have any further questions.
The greatest common factor shared by numbers 39 and 15 is 3.
Given two numbers, 39 and 15.
The greatest common factor can be defined as the factor which is common to both 39 and 15 and is the greatest of all those common factors of 39 and 15.
First, list out the factors of 39 and 15.
Factors of 39 = 1, 3, 13, 39
Factors of 15 = 1, 3, 5, 15
The only factor which is common to both 39 and 15 is 3.
So, the greatest common factor of both is 3.
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In right triangle ABC, ZC is a right angle, m ZA = 52, AC = 10. 01, and AB = c.
sin 52° 0. 788
cos 52° 0. 616
tan 52° 1. 280
What is the measurement of AB?
If necessary, round your answer to two decimal places, like this: 42. 53
The length of side AB rounded to two decimal places is 16.25.
In a right angle triangle, the side on the base of the angle in question is divided by the hypotenuse. In this case, we can use the cosine ratio to find the length of AB.
We are provided with the following information,
C is the right angle, C= 90°
A= 52°
AC = 10. 01
sin 52° = 0. 788
cos 52° = 0. 616
tan 52° = 1. 280
Now,
since angle C is the right angle, AB is the hypotenuse.
Therefore, with respect to Angle A, AC will be the base and BC will be the perpendicular.
We know, cos x= base/hypotenuse
In this case, cos A = AC / AB
cos 52° = 10. 01/ AB
AB = 10. 01 / 0. 616
AB = 16.25
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What are the table of values for y=x^2+2x-3
By factoring the preceding quadratic equation and then inserting the values of "x," which are -3, -2, -1, 0, 1, 2, 3, 4, 5, the values of "y," which are 12, 5, 0, -3, -4, 3, 0, 5, 12, may be found.
How to find the Calculation?First, factorize the given quadratic equation before completing the table.
Now, the values of "x" according to the given table are:
x = -3, -2, -1, 0, 1, 2, 3, 4, 5
Add the expression x=-3 to the equation (1).
y = (-3-3)(-3+1)
y = 12
Add the expression x=-2 to the equation (1).
y = (-2-3)(-2+1)
y = 5
Put x=-1 as a value in the equation (1).
y = (-1-3)(-1+1)
y = 0
Put x=0 as the value in the equation (1).
y = (0-3)(0+1)
y = -3
Put x=1 as the value in the equation (1).
y = (1-3)(1+1)
y = -4
Put x=2 as a value in the equation (1).
y = (2-3)(2+1)
y = -3
Add the expression x=3 to the equation (1).
y = (3-3)(3+1)
y = 0
Add the expression x=4 to the equation (1).
y = (4-3)(4+1)
y = 5
Add the expression x=5 to the equation (1).
y = (5-3)(5+1) y = 12
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The function W
gives the temperature, in degrees Fahrenheit, of a pot of water on a stove t
minutes after the stove is turned on.
After 30 minutes, the pot is taken off the stove.
The graph of the function is shown.
Describe the range of the function.
The range would be; [75,212] and the greatest one is around 212.5. .5] a domain and a range.
What is the domain and range of the function?The domain of a function is defined as the set of all the possible input values that are valid for the given function.
The range of a function is defined as the set of all the possible output values that are valid for the given function.
Recall this by saying "DoLaR RiBiT," where "DoLaR" stands for "domain," "L" and "R" stand for "left to right," "R" stands for "range," and "B" and "T" stand for "bottom to top," and "R" stands for "range."
Since we can see that the function doesn't approach 250, in the graph, 250 is not inside the range.
Between the minimum and greatest value are the numbers that make up the range. The range would be; [75,212] because the lowest Y value is 75 and the greatest one is around 212.5. .5] a domain and a range.
The collection of values that can be substitute into a function's domain are called its parameters.
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If you invest $10,000 in a bank which one is a better investment? A) 9% compounded monthly b) 9. 3% compounded annually
If you invest $10000 in a bank , then the better investment plan is (a) 9% compounded monthly .
The amount to be invested in bank is = $10000 ;
the formula to calculate the final amount by compounding is given as :
A = P(1 + r/n)^(nt) ;
Where: (A) = final amount , (P) = initial amount ,
⇒ r is interest rate (in decimal form) , n is number of times the interest is compounded per year and
⇒ t is number of years investment is made
(a) the rate of interest is 9% compounded monthly ;
in this case n = 12 , because there are 12 months in 1 year ;
So , Amount = 10000(1 + 0.09/12)^(12×t)
Amount = 10000 × (1.0075)^(12×t)
Suppose t = 1 ;
we get , Amount = 10000 × (1.0075)¹² ≈ 10938 .
(b) the rate of interest is 9% compounded annually ;
in this case n = 1 , because compounded annually ;
So , Amount = 10000 × (1 + 0.09)^(1×t)
Amount = 10000 × (1.09)^t
Suppose t = 1 ; we get , Amount = 10000 × (1.09)¹ ≈ 10900 ;
On comparing both the interest value we observe that ,
the monthly compounding returns more value than compounding annually .
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HELP ASAP !! :80 POINTS
How long is the shortest route from Ellport to Union Falls using the roads shown?
If necessary, round your answer to the nearest tenth.
The shortest route from Ellport to Union Falls using road is 18 miles
What is an equation?An equation is an expression that shows the relationship between numbers and variables.
Pythagoras theorem is used to determine the measure of the sides of a right angled triangle. It is given by:
(hypotenuse side)² = (adjacent side)² + (opposite side)²
The distance from Larksville to Smithfield = 9 + 9 + 6 = 24 miles
The distance from Larksville to Union Falls = 19.5 + 6.5 = 26 miles
Let x represent the distance from Smithfield to Union falls, using Pythaoras:
26² = 24² + x²
x² = 100
x = 10 miles
the distance from Smithfield to Union falls is 10 miles.
Let y be the shortest route from Ellport to Union Falls, using Pythagoras:
y² = 10² + (9 + 6)²
y² = 10² + 15²
y² = 325
y = 18 miles
The distance from Ellport to Union Falls is 18 miles
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A right triangular prism has a triangular base with legs of 5 centimeters and 12 centimeters and a hypotenuse of 13 centimeters. What is the surface area in square centimeters if the height is 2 centimeters?
60
120
180
240
*answer is 180. How?
The surface area of the triangular prism is 120[tex]cm^2[/tex]
Now, According to the question:
A triangular prism is a polyhedron with a triangle for a base, thus it is a three-sided prism. Given that the triangle has three sides and a height of h, the surface area would be A = Ph + ab where P is the perimeter of the triangle.
We have :
A right triangular prism has a triangular base with legs of 5 centimeters and 12 centimeters and a hypotenuse of 13 centimeters.
Now,
Hypotenuse = 13
a = 5 cm
b = 12 cm
h = 2 cm
The perimeter of the triangle is the sum of all the sides or:
P = 13 + 5 + 12
P = 30 cm
To get the surface area, substitute the values in the formula below:
A = Ph + ab
A = (30)(2) + (5)(12)
A = 60 + 60
A = 120
Hence, The surface area of the triangular prism is 120[tex]cm^2[/tex]
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Some people took part in a game. The frequency shows information about their scores.ScoreFrequency - 758 - 10811 - 15916 - 201521 - 351636 - 5013Estimate the mean.Give your answer rounded to 2 decimal places.
The estimated mean score is given as follows:
19.12.
How to obtain the mean of a data-set?The mean of a data-set is obtained as the sum of all observations in the data-set divided by the number of observations.
For each score, we consider it to be the mean of each interval in the frequency table, hence the sum of all scores is given as follows:
4 x 19 + 9 x 14 + 13 x 15 + 18 x 28 + 28 x 10 + 43 x 13 = 1740.
The total number of scores is of:
19 + 14 + 15 + 20 + 10 + 13 = 91.
Hence the mean score is obtained as follows:
1740/91 = 19.12.
Missing InformationThe frequency distribution for this problem is given as follows:
1-7:19
8-10:14
11-15:15
16-20:20
21-35:10
36-50:13
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