The old age dependency ratio as a decimal is 0.190.
What is old age dependency ratio ?
The old age dependency ratio is a measure of the number of people who are considered "dependent" on those who are of working age.
Specifically, it is the ratio of the number of people aged 65 years and over to the number of people aged 15 to 64 years old.
Old Age Dependency Ratio = (Number of people over 65) / (Number of people aged 15-64)
Old Age Dependency Ratio = 40,809 / 214,965 = 0.1895
Therefore, Rounding this to the thousandths place the Old Age Dependency Ratio as a decimal is 0.190.
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Find the following. 2/5 of 240
Answer:
96
Step-by-step explanation:
2/5 of 240
2×240= 480
480÷5= 96
24 divide by 6 please just get an answer
Answer: 4
Step-by-step explanation:
Answer: 4
Step-by-step explanation:
24/6
= 4
A pizza has 8 slices. John wants to order enough pizzas so 14 people can have 3 slices each.
Answer:
C John should order 6 pizzas because if he orders 5 pizzas, he will be short 2 slices.
Step-by-step explanation:
14 people need 3 slices each. We need to multiply.
14*3 = 42
Each pizza has 8 slices so divide by 8
42 /8 = 5 remainder 2
We round up to make sure to have enough.
We need at least 6 pizzas to have enough. He is short 2 slices.
Answer:
C)
Step-by-step explanation:
John wants to order enough pizzas for 14 people to have 3 slices each. This means that he would need at least 42 slices of pizza:
[tex]14 * 3 = 42[/tex]
It is given that pizza has 8 slices. Divide 8 from 42:
[tex]\frac{42}{8} = 5.25[/tex]
Note that he cannot order .25 of a pizza, and so he will have to order 6.
C) John should order 6 pizzas because if he orders 5 pizza, he will be short 2 slices.
Note: The 2 slices is calculated by multiplying the total slices for a pizza (8) with .25:
[tex]8 * .25 = 2[/tex]
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Find the length of the midsegment of the trapezoid with the vertices 0,3 2,5 6,4 2,0
After answering the provided question, we can conclude that Therefore, coordinates the length of the midsegment of the trapezoid is [tex]\sqrt(13)[/tex]units.
what are coordinate ?In mathematics, a coordinate is a number or permutation of integers that indicates the location of a point or object in space. Coordinates are frequently used to define a point or object's position in a specific reference frame, such as the Euclidean or antarctic coordinate systems. In the Cartesian coordinate system, a point is located by its distance from the origin along the x-axis and its distance first from origin along the y-axis. These distances are represented by two numbers, its x-coordinate and the y-coordinate. The point's position in the plane is specified by the two coordinates.
To find the length of the midsegment of a trapezoid,
[tex]E = ( (x1 + x2)/2 , (y1 + y2)/2 )\\So, E = ( (0+2)/2 , (3+5)/2 ) = (1,4)\\F = ( (x3 + x4)/2 , (y3 + y4)/2 ) = ( (6+2)/2 , (4+0)/2 ) = (4,2)\\d = \sqrt( (x2 - x1)^2 + (y2 - y1)^2 )\\d =\sqrt( (4-1)^2 + (2-4)^2 ) = \sqrt(9+4) = \sqrt(13)\\[/tex]
Therefore, the length of the midsegment of the trapezoid is [tex]\sqrt(13)[/tex]units.
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Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match each hypotenuse length with the leg lengths that will create a right triangle.
unit √2 units
√5 units, √2 units
√2 units, √3 units
√5 units, 1 unit
Hypotenuse
√6 units
√5 units
√8 units
√3 units
√5 units, √3 units
Legs
The hypotenuse is √[(√2)² + (√3)²] = √(2+3) = √5 units.
What is the hypotenuse?The Iongest side of a right-angIed triangIe, or the side opposite the right angIe, is known as the hypotenuse in geometry. The Pythagorean theorem, which states that the square of the Iength of the hypotenuse equaIs the sum of the squares of the Iengths of the other two sides, can be used to determine the Iength of the hypotenuse.
The Iength of the Iegs are 1 unit, √2 units.
The hypotenuse is √[(1)² + (√2)²] = √(1+2) = √3 units.
The Iength of the Iegs are √5 units, √2 units.
The hypotenuse is √[(√5)² + (√2)²] = √(5+2) = √7 units.
The Iength of the Iegs are √5 units, √3 units.
The hypotenuse is √[(√5)² + (√3)²] = √(5+3) = √8 units.
The Iength of the Iegs are √5 units, 1 unit.
The hypotenuse is √[(√5)² + (1)²] = √(5+1) = √6 units.
The Iength of the Iegs are √2 units, √3 units.
The hypotenuse is √[(√2)² + (√3)²] = √(2+3) = √5 units.
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when joselyn went to the store she bought 2.7 kg of chocolate candy. what would joselyn do to find out how many grams she bought?
Using the conversion factor, Joselyn bought 2700 grams of chocolate candy
A conversion factor is a numerical ratio used to convert a measurement from one unit to another. It is a mathematical expression that is used to convert a quantity expressed in one unit of measure into an equivalent quantity expressed in another unit of measure.
To convert 2.7 kg to grams, Joselyn would use a conversion factor between kilograms and grams. The conversion factor is 1000 grams per 1 kilogram, which means there are 1000 grams in one kilogram.
So, to convert 2.7 kg to grams, Joselyn would multiply 2.7 kg by the conversion factor
2.7 kg x 1000 g/kg = 2700 g
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1.) Circle A has been transformed to Circle B. What is the translation rule for these circles?
A.) (x-2),(y+3)
B.) (x+2),(y+3)
C.) (x-1),(y+4)
D.) (x+4),(y+3)
*Please Show All Work***
2.) Circle A has been transformed to Circle B. What is the scale factor of Circle A to Circle B?
The translation rule for these circles is C): (x-1),(y+4), with a scale factor of 1/4. This means that when transforming Circle A to Circle B, each x-coordinate is decreased by 1 and each y-coordinate is increased by 4.
What is circle?Circle is a two-dimensional shape with no sides or corners. Its defining feature is its curved line, which forms a continuous loop. The circle has no beginning or end, which symbolizes eternity, completeness and unity. Circles are often used in various designs, logos and artwork, as well as in mathematics, science, engineering and architecture.
The translation rule for these circles is C): (x-1),(y+4). We can calculate the scale factor by determining the difference between the coordinates of the two circles.
The coordinates of Circle A are (x,y). The coordinates of Circle B are (x-1, y+4). Therefore, the difference between the two is (1,4).
The scale factor is the ratio of the differences. Therefore, the scale factor is 1/4.
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Therefore, the translation rule for these circles is C): (x-1),(y+4), and the scale factor is 1/4.
In conclusion, the translation rule for these circles is C): (x-1),(y+4), with a scale factor of 1/4. This means that when transforming Circle A to Circle B, each x-coordinate is decreased by 1 and each y-coordinate is increased by 4.
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hi do you no what is 5364 rouded to the nearest thousand.
5,364 → 5,000
Therefore, 5,364 rounded to the nearest thousand is 5,000
Answer:
5000
Step-by-step explanation:
See, the thousands digit is not really in play, if the hundreds place is 5+, you raise the thousand up and if it's 4 or less, you round it down
Have you heard of 'five or more, raise the score, four or less, let it rest'
And for ex: 3678 rounded to the nearest thousand is 4000
a water trough is long and a cross-section has the shape of an isosceles trapezoid that is wide at the bottom, wide at the top, and has height . if the trough is being filled with water at a rate of , how fast is the water level rising when the water is deep?
The water level is rising at a rate of 0.1 cm/min when the water is 50 cm deep
Let's begin by finding the volume of water in the trough when the water is 50 cm deep. We know that the trough has an isosceles trapezoid cross-section, so we can find the area of the cross-section using the formula for the area of a trapezoid
A = ((b1 + b2)/2) × h
where b1 and b2 are the lengths of the parallel sides of the trapezoid, and h is the height of the trapezoid.
In this case, b1 = 20 cm, b2 = 80 cm, and h = 60 cm. So the area of the cross-section is
A = ((20 + 80)/2) × 60
A = 3000 cm^2
To find the volume of water in the trough when the water is 50 cm deep, we need to multiply the cross-sectional area by the length of the trough and the depth of the water
V = A × L × d
V = 3000 cm^2 × 10 m × 0.5 m
V = 15000 L
Now that we know the volume of water in the trough, we can find how fast the water level is rising by taking the derivative of the volume with respect to time
dV/dt = 0.3 m^3/min
We need to convert this rate to units of L/min, so we can multiply by 1000 to convert m^3 to L
dV/dt = 0.3 m^3/min × 1000 L/m^3
dV/dt = 300 L/min
Finally, we can use the formula
dV/dt = A × dh/dt
to find how fast the water level is rising when the water is 50 cm deep. We know A = 3000 cm^2, and we want to find dh/dt when d = 50 cm. We can rearrange the formula to solve for dh/dt
dh/dt = dV/dt / A
dh/dt = 300 L/min / 3000 cm^2
dh/dt = 0.1 cm/min
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The given question is incomplete, the complete question is:
A water trough is 10 m long and has a cross-section in the shape of an isosceles trapezoid that is 20 cm wide at the bottom, 80 cm wide at the top, and has height 60 cm. If the trough is being filled with water at the rate of 0.3 m3/min how fast is the water level rising when the water is 50 cm deep?
Drag each problem to show if the unknown quantity in the problem is a part, a whole, or a percent
Answer:
you didnt post a pic to show us the options
Step-by-step explanation:
didnt show the options so we cant help
What is the difference when -6c+4 is subtracted from -8+7c
The difference when -6c + 4 is subtracted from -8 + 7c is -2c - 11. This can be simplified to -2c - 11, which is the answer.
To calculate the difference when -6c + 4 is subtracted from -8 + 7c, we must first expand the terms. The first term, -6c, can be broken down into -6 x c, which simplifies to -6c. The second term, 4, can remain as is. The third term, -8, can also remain as is. The fourth term, 7c, can be broken down into 7 x c, which simplifies to 7c.
We can then calculate the difference by performing the subtraction. We begin by subtracting the second term, 4, from the first term, -6c. We can do this by adding -4 to -6c, which results in -6c - 4. We then subtract the fourth term, 7c, from the third term, -8. We can do this by adding 8 to -7c, which results in -7c + 8.
We can then combine the two terms together. We do this by adding -6c - 4 to -7c + 8. This results in -13c + 4. We can simplify this to -2c - 11, which is the final answer.
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Will mark as brainiest
Answer:
(1 - 5x + y)(1 + 5x - y).
(9a - c + 3b)(9a + c - 3b).
(bc - b - c - 1)(bc + b + c - 1).
Step-by-step explanation:
1 - 25x^2 + 10xy - y^2
= 1 - (25x^2 - 10xy + y^2)
= 1 - (5x - y)^2
This is the difference of 2 squares, so the answer is
(1 - (5x - y))(1 + (5x - y))
= (1 - 5x + y)(1 + 5x - y).
81a^2 + 6bc - 9b^2 - c^2
= 81a^2 - (c^2 - 6bc + 9b^2)
= 81a^2 - (c - 3b)^2
= (9a - (c - 3b))(9a + (c - 3b))
= (9a - c + 3b)(9a + c - 3b)
b^2c^2 - 4bc - b^2 - c^2 + 1
= b^2c^2 - 4bc - b^2 - (c^2 - 1)
= (bc - b) - (c + 1))((bc + b) + (c - 1)
= (bc - b - c - 1)(bc + b + c - 1).
The circumference of a circle is 81.64 inches. What is the circle's radius? use 3.14 for pi
Answer:
13 cm
Step-by-step explanation:
c = Circumference=pid= 81.64 To find the radius of a circle you can just divide the diameter by 2.pi = 3.14d = diameter=c/3.14 Pi is always 3.14 or 22/7.d = 81.64/3.14d = 26r= radius= 26/2radius=13 cm
Answer: 13 inches
Step-by-step explanation:
The triangles shown are congruent. Fill in the blank to complete the congruence statement for the triangles shown:
uze =
Answer:
uze=nkw
Step-by-step explanation:
U has no stroke which follows N
Z has a stroke which follows K
E has two strokes which follows W
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
Simplify the expression.
4(-8x + 5) – (-33x – 26) =
Therefore, the simplified expression is: [tex]1x+46[/tex].
What is fraction?A fraction is a way of representing a part of a whole or a quantity that is not a whole number. It is expressed in the form of a numerator and a denominator separated by a line, called a fraction bar or a vinculum. The numerator is the top number in a fraction, and the denominator is the bottom number. The numerator represents the number of equal parts of a whole, and the denominator represents the total number of equal parts into which the whole is divided. For example, the fraction 3/4 represents three equal parts of a whole that is divided into four equal parts. Fractions can be used in many mathematical operations, such as addition, subtraction, multiplication, and division, and are an essential concept in mathematics.
Expanding the left-hand side, we get:
[tex]4(-8x + 5) - (-33x - 26)[/tex]
[tex]= -32x + 20 + 33x + 26[/tex]
Simplifying, we can combine like terms:
[tex]-32x + 33x + 20 + 26[/tex]
[tex]= 1x + 46[/tex]
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Professor Melendez has 10 students in her college algebra class. Their ages are shown below.
When the outliers are removed, what is the mean age of the remaining students? 19.27 19.18.18.18.7.19.2018
The mean age of the students in the class is 22.3.
The median age of the students is 19.
What is the median age of the remaining students?
There are two ourers in the data from Professor
Melender's class: 27 and 47
The median age of the remaining students in Professor Melendez's college algebra class is 18.5.
To find the median age of the remaining students in Professor Melendez's college algebra class, we need to first remove the outliers, which are the ages of 27 and 47. After removing these outliers, we are left with 8 ages: 19, 18, 18, 18, 7, 19, 20, and 18. To find the median age, we need to arrange the ages in order from least to greatest. The ordered list of ages is: 7, 18, 18, 18, 19, 19, 20. Since there are an even number of ages, we need to find the average of the middle two ages, which are 18 and 19. Thus, the median age of the remaining students is (18 + 19) / 2 = 18.5.
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Carlos earns $50 000 each year as a shop clerk and an extra $1200 each year for gardening on the weekend
A, calculate his annual gross salary
B, use his gross salary to find his income tax
C, what is his annual income, after tax
D what is his fortnightly net income, to the nearest cent after tax?
Part A: annual gross salary = $51,200. Part B: income tax= $46,080
Part C: annual income, after tax reduction = $46,080.
Part D: fortnightly net income $126.24 per day.
Explain about the annual gross salary:Before taxes, benefits, and other wage garnishments are taken out of an employee's paycheck, that amount is known as their gross pay. Net pay, often known as take-home pay, is the amount that is left after all withholdings have been taken into account.
Given data:
Earning from shop clerk - $50,000 per year.
Earning from gardening - $1,200 per year.
Part A: annual gross salary.
annual gross salary = $50,000 + $1,200
annual gross salary = $51,200
Part B: income tax.
income tax = 10% of gross income
income tax = 0.10 * 51,200
income tax = $5,120
Part C: annual income, after tax reduction:
Net income = Gross income - tax
Net income = 51,200 - 5,120
Net income = $46,080
Part D: fortnightly net income:
fortnightly net income = Total net income / 365 days
fortnightly net income = $46,080 / 365
fortnightly net income = $126.24 per day.
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Complete question:
Carlos earns $50 000 each year as a shop clerk and an extra $1200 each year for gardening on the weekend. Tax applied is 10% on gross income.
A, calculate his annual gross salary
B, use his gross salary to find his income tax
C, what is his annual income, after tax
D what is his fortnightly net income, to the nearest cent after tax?
Desmon and Garrett are running a marathon. Desmon raised $3,654 and Garrett raised $2,765. Jesse and Mikayla are running the same marathon. Jesse raised $4,876 and Mikayla raised $2,874. How much more money did Jesse and Mikayla raise than Garrett and Desmon?
Answer:$1,331
Step-by-step explanation: Add each pairs earnings then subtract and you'll get the answer.
The ratio of X to Y in a room is 6:5. If three boys leave the room, the ratio is 1:1. How many Y are in the room?
Answer:
15 Y (girls) in the room
Step-by-step explanation:
Given an initial ratio of boys : girls = 6 : 5 that becomes 1 : 1 when 3 boys leave the room, you want to know the number of girls in the room.
Ratio unitsThe initial difference in the number of ratio units is 6 -5 = 1. Removing 1 ratio unit from the "boys" side makes the ratio 5 : 5 = 1 : 1.
So, that 1 ratio unit corresponds to 3 boys. There are 5 ratio units of girls, so 3·5 = 15 girls.
There are 15 girls (Y) in the room.
__
Alternative solution
You could write an equation or two:
b/g = 6/5 . . . . . . initial ratio of boys/girls
(b-3)/g = 1/1 . . . . final ratio of boys/girls
Solving the first for b gives
b = 6/5g
Using that in the second gives ...
(6/5g -3) = g . . . . . . substitute for b, multiply by g
1/5g = 3 . . . . . . . . add 3-g
g = 15 . . . . . . . multiply by 5
Given triangle ABC with ordered pairs:
A - (1, -3)
B - (3, 0)
C - (4, -2)
Rotate ABC 180 degrees about the origin and then reflect it over the y-axis. Determine the points of A', B', and C'.
The points A', B', and C' are (1, 3), (3, 0) and (4, 2) respectively. The solution has been obtained by using the concept of transformation.
What is transformation?
On a coordinate plane, forms can be translated, rotated, and reflected thanks to transformations. Any line, any point, and any vector can be reflected, rotated, and translated.
We are given coordinates of triangle ABC as A (1, -3), B (3, 0) and C (4, -2).
Now, we need to rotate the triangle 180 degrees about the origin.
We know that the rotation rule for rotating 180 degrees about the origin is that (x, y) becomes (-x, -y).
So, we get the new coordinates as
A' (-1, 3)
B' (-3, 0)
C' (-4, 2)
Now, on reflecting it over the y - axis, we get
A' (1, 3)
B' (3, 0)
C' (4, 2)
Hence, the points A', B', and C' are (1, 3), (3, 0) and (4, 2) respectively.
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a researcher interested in the effects of sleep deprivation on reaction time randomly assigns participants to either a sleep deprivation group or a control group. after a night in the sleep laboratory, reaction times for all participants are obtained. what is the null hypothesis?
The null hypothesis would be, "sleep deprivation does not affect reaction time."
A null hypothesis is an assumption in which researchers claim that there is no relationship between two factors. The hypothesis is used to examine whether the research hypothesis is true or false. For instance, in this study, the researcher would hypothesize that sleep deprivation affects reaction time.
The null hypothesis would be, "sleep deprivation does not affect reaction time."
Hence, the null hypothesis for the researcher who is interested in the effects of sleep deprivation on reaction time, and who randomly assigns participants to either a sleep deprivation group or a control group is "Sleep deprivation does not affect reaction time."
This would be tested using statistical tests like t-test and ANOVA.
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Suppose the line segments that represent Wayne Street and George Street
are reflected in the y-axis. Draw the images. Are they parallel? Explain.
If the slopes are equal, the reflected line segments are parallel.
When a line segment is reflected in the y-axis, its image is formed by reflecting each point on the segment across the y-axis.
This means that the x-coordinate of each point is negated, while the y-coordinate remains the same.
To draw the images of Wayne Street and George Street, we need to know their coordinates.
Let's assume that Wayne Street runs from (2, 3) to (6, 5), while George Street runs from (-1, -2) to (-5, -4).
When we reflect Wayne Street in the y-axis, we negate the x-coordinates and keep the y-coordinates the same.
This gives us the image of Wayne Street, which runs from (-2, 3) to (-6, 5).
Similarly, when we reflect George Street in the y-axis, we get the image of George Street, which runs from (1, -2) to (5, -4).
We need to consider the slopes of the original segments and their images.
The slope of Wayne Street is (5-3)/(6-2) = 1/2, while the slope of George Street is (-4-(-2))/(-5-(-1)) = -1/2.
When we reflect a line segment in the y-axis, its slope is negated.
So,
The slope of the image of Wayne Street is -1/2, while the slope of the image of George Street is 1/2.
Therefore, the images of Wayne Street and George Street are not parallel, since their slopes are opposite.
In fact, they are perpendicular to each other, since the product of their slopes is (-1/2) x (1/2) = -1/4, which is equal to -1 (the negative reciprocal of each other).
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Complete the description of two methods that can be used to convert 62 inches to centimeters. Round
your answers to the nearest tenth, if necessary.
Part 1 out of 2
The first method is
1 in.
2.54 cm
11 12 13 14 15 16 17 18
17 18 19 20
? cm
1 in. × 62
2.54 cm x 62
11
62 in.
cm
In conclusion 62 inches is equal to 157.48 centimeters (rounded to the nearest tenth).
How to solve?
Part 1 of 2:
The first method to convert 62 inches to centimeters involves using the conversion factor of 1 inch equals 2.54 centimeters. We can set up a proportion to solve for the number of centimeters in 62 inches:
1 in. x cm
----- = -----
2.54 62 in.
To solve for x, we can cross-multiply and simplify:
1 × x = 2.54 × 62
x = 157.48
Therefore, 62 inches is equal to 157.48 centimeters (rounded to the nearest tenth).
So the first method gives us 157.5 cm as the answer.
Part 2 of 2:
The second method to convert 62 inches to centimeters involves multiplying 62 by the conversion factor of 2.54 centimeters per inch:
62 in. × 2.54 cm/in = 157.48 cm
Therefore, using this method, we also get 157.5 cm as the answer (rounded to the nearest tenth).
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Two identical square pyramids were joined at their bases to form the composite figure below. 2 square pyramids have a base of 24 centimeters by 24 centimeters. The triangular sides have a height of 5 centimeters. [Not drawn to scale] Which expression represents the total surface area, in square centimeters, of the figure? 8 (one-half (24) (5)) 8 (one-half (24) (13)) (24) (24) + 8 (one-half (24) (5)) (24) (24) + 8 (one-half (24) (13)) Mark this and return
Answer: The composite figure consists of two square pyramids, so we can find the total surface area by adding the surface area of each pyramid. The surface area of a square pyramid is given by:
S = B + (1/2)Pl
where B is the area of the base, P is the perimeter of the base, l is the slant height, and S is the total surface area.
For each pyramid, we have:
B = 24^2 = 576 cm^2
P = 4(24) = 96 cm
l = sqrt(24^2 + 5^2) = 25 cm
So the surface area of each pyramid is:
S = 576 + (1/2)(96)(25)
S = 576 + 1200
S = 1776 cm^2
Therefore, the total surface area of the composite figure is:
2S = 2(1776)
= 3532 cm^2
The expression that represents the total surface area, in square centimeters, of the figure is:
(24) (24) + 8 (one-half (24) (5)) + 8 (one-half (24) (13)) = 576 + 480 + 624 = 1680 cm^2
This expression only accounts for the surface area of the base and the triangular faces, but it does not include the surface area of the pyramid faces. So it is not correct.
The correct answer is:
8 (one-half (24) (5)) + 8 (one-half (24) (13)) = 480 + 624 = 1104 cm^2
which only represents the surface area of the triangular faces of both pyramids. To get the total surface area, we need to add the surface area of the base, which gives:
1104 + 2(576) = 2256 + 1104 = 3360 cm^2
Therefore, the total surface area of the composite figure is 3360 square centimeters.
Step-by-step explanation:
To get to 1, divide 116 by _____. From 1, multiply by ______ to get to 32. OR, in a single step, multiply 116 by _____ to get to 32.
Answer: To get to 1, divide 116 by __116___. From 1, multiply by ___32___ to get to 32. OR, in a single step, multiply 116 by __.3___ to get to 32.
Step-by-step explanation:
Write a matrix to represent the finite graph.
A,B,C,D,F
Based on the given graph, we can create a matrix to represent the graph as follows:
[tex]\left[\begin{array}{ccccc}A&B&C&D&F\\0&1&0&0&1\\1&0&1&1&0\\0&1&0&0&1\\0&1&0&0&0\\1&0&1&0&0\end{array}\right][/tex]
What is matrix?A matrix is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns. Matrices are commonly used in mathematics, physics, engineering, computer science, and many other fields to represent and manipulate data, equations, and systems of equations. A matrix can be represented using parentheses or brackets, with the entries separated by commas or spaces.
Here,
The rows and columns of the matrix represent the vertices of the graph, and the entries in the matrix represent the edges. If there is an edge between two vertices, the corresponding entry in the matrix is 1, otherwise it is 0. For example, there is an edge from vertex A to vertex B, so the entry in row A and column B is 1. Similarly, there is an edge from vertex B to vertex A, so the entry in row B and column A is also 1.
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from a certain distance, the angle of elevation to the top of a building is 17 degrees. at a point 50 meters closer to the building, the angle of elevation is 31 degrees. find the height of the building.
The height of the building is approximately 102.86 meters.
Given that from a certain distance, the angle of elevation to the top of a building is 17 degrees. At a point 50 meters closer to the building, the angle of elevation is 31 degrees. To find the height of the building.In the given figure, AB is a building and C and D are two different points at a certain distance from the building. So that, angle BCA = 17° and angle BDA = 31°.We have to find the height of the building AB.
Now, let's find the distance between the building and point C and D. Let, BC = x50 meters closer to the building, so BD = x + 50 metersWe know, tangent of an angle = Perpendicular / BaseFor the angle 17°, we have to find AC, so;tan(17°) = AB / ACAB = AC tan(17°) ---(1)For the angle 31°, we have to find AD, so;tan(31°) = AB / ADAB = AD tan(31°) ---(2)Now, find the difference between (1) and (2).AC tan(17°) - AD tan(31°) = 0AC / AD = tan(31°) / tan(17°) [Divide both sides by AD tan(17°)]AC / (AD + 50) = tan(31°) / tan(17°) ----(3)We know the value of (AC + AD) is the actual distance between the building and the point.
So,(AC + AD) = x + (x + 50) = 2x + 50 metersNow we can use the value of AC / (AD + 50) in equation (3) and solve for AB.AB = AC tan(17°) = (2x + 50) tan(17°) tan(31°) / (tan(31°) - tan(17°))Substitute the value of AB from equation (1), so;AC tan(17°) = (2x + 50) tan(17°) tan(31°) / (tan(31°) - tan(17°))AC = (2x + 50) tan(31°) / (tan(31°) - tan(17°))Now, let's use the value of AC in equation (1),AB = AC tan(17°) = (2x + 50) tan(17°) tan(31°) / (tan(31°) - tan(17°)) = 102.86 meters (approx.)So, the height of the building is AB = 102.86 meters (approx.)
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W= 85 / 5
W= 85 - 25
W - 85/ 5- 25
W= 85/ 25 - 5
Answer is 17, 60, -8, 4.25 in the given BODMAS
Brackets of Division, Multiplication, Addition, and Subtraction, or BODMAS, is an acronym. It is a method for resolving mathematical issues.
Brackets are resolved first in accordance with the BODMAS guidelines. Parentheses are also solved first in that case, then curly brackets, and finally square brackets.
It always produces the right outcomes when applied correctly. Uncertain questions that are poorly phrased may result in inaccurate answers.
Let's utilise BODMAS to answer a question:
W= 85 / 5
W = 17
W= 85 - 25
W = 60
W = 85/ 5- 25
W = -8
W= 85/ 25 - 5
W = 85/20
W = 4.25
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Which expression can be used to find the volume
of the rectangular prism in cubic centimeters?
Image shows a prism with a base area of 245 square cm and a height of 85 cm.
A.
85
+
245
B.
85
×
85
×
245
C.
85
+
(
85
×
245
)
D.
85
×
245
Answer: D. 85 ×245
is this help you give e hearts please
Answer:
D. 85 ×245
Question:
Which expression can be used to find the volume of the rectangular prism in cubic centimeters? The Image shows a prism with a base area of 245 square cm and a height of 85 cm.
Determine the coordinates of the image if triangle ABC is translated 6 units to the right.
A(-2, 1), B(6, 1), C(2, 5)
A(-2, 1), B(-6, 1), C'(-10, 5)
A'(-6, 7), B'(0,7), C'(-4, 11)
A'(-6, -5), B'(0, -5), C'(-4,-1)
Therefore option b is the right option: After translated it in 6units: we get
A'(-2, 1), B'(-6, 1), C'(-10, 5)
The picture's coordinates are:
A’(-2+6, 1) = (-4, 1)
B’(6+6, 1) = (12, 1)
C’(2+6, 5) = (8, 5)
Define coordinates of a triangle?
A location on the plane that is defined by an ordered pair of numbers is called a coordinate in a triangle (x,y). The y-coordinate and x-coordinate of a point indicate its vertical and horizontal positions, respectively.
Triangles can be described using a variety of coordinate systems in the Euclidean plane. Triangular coordinates is a name for one of these systems. It is a particular instance of barycentric coordinates for a triangle, and in that case it is sometimes referred to as a ternary plot or as areal coordinates
What exactly is barycentric cordinates?A barycentric coordinate system in geometry is a coordinate system where a point's location is determined by reference to a simplex (a triangle for points in a plane, a tetrahedron for points in three-dimensional space, etc.) . A point's barycentric coordinates can be thought of as the center of mass (or barycenter) of masses that are positioned at the vertices of a simplex. These masses can all be positive or negative, but only if the point is contained within the simplex.
Many branches of mathematics and physics, such as computer graphics, finite element analysis, and fluid dynamics, make use of barycentric coordinates.
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