The speed of the river's current is 0.4 miles per hour.
To determine the speed of the river's current, we can set up a system of equations based on the information given.
Let's denote the speed of the river's current as v miles per hour.
During the downstream leg of the triathlon, the participant swims with the current, so their effective speed is the sum of their swimming speed and the current's speed:
Effective speed downstream = 2 + v miles per hour
During the upstream leg, the participant swims against the current, so their effective speed is the difference between their swimming speed and the current's speed:
Effective speed upstream = 2 - v miles per hour
We are given that the total swim time is 1.25 hours. Since the participant swims the same distance both downstream and upstream, we can set up the following equation based on the time and distance relationship:
Time downstream + Time upstream = Total swim time
(1.2 miles) / (Effective speed downstream) + (1.2 miles) / (Effective speed upstream) = 1.25 hours
Substituting the expressions for the effective speeds, we have:
(1.2 miles) / (2 + v) + (1.2 miles) / (2 - v) = 1.25
To solve this equation, we can clear the denominators by multiplying both sides by (2 + v)(2 - v):
(1.2 miles)(2 - v) + (1.2 miles)(2 + v) = 1.25(2 + v)(2 - v)
Simplifying the equation:
2.4 - 1.2v + 2.4 + 1.2v = 1.25(4 - [tex]v^2[/tex])
4.8 = 5 - 1.25[tex]v^2[/tex]
Rearranging terms:
1.25[tex]v^2[/tex] = 5 - 4.8
1.25[tex]v^2[/tex] = 0.2
Dividing both sides by 1.25:
[tex]v^2[/tex] = 0.2 / 1.25
[tex]v^2[/tex] = 0.16
Taking the square root of both sides:
v = ± √0.16
Since the speed of the river's current cannot be negative, we take the positive square root:
v = 0.4
Therefore, the speed of the river's current is 0.4 miles per hour.
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Suppose . has 4 critical points. List them in increasing lexographic order. By that we mean that (x, y) comes before (z, w) if or if and . Also, determine whether the critical point a local maximum, a local minimim, or a saddle point.
The points are (0,0) Minimum and (1/6, 1/18) is the saddle point.
What is the saddle point?
A saddle point, also known as a minimax point, is a place on the surface of a function's graph where the slopes in orthogonal directions are all zero but the function does not have a local extremum.To solve the question we have:
f(x,y) = xy(1-2x-6y)
Therefore, f(x,y) = xy-2x²y-6xy²
Finding the partial derivative of the above gives:
fₓ = y - 4xy-6y²
= x - 2x²-12xy
Therefore, when the above equations are set to 0 we get:
y - 4xy-6y² = 0.......(1)
x - 2x²-12xy = 0......(2)
Dividing equations (1) and (2) by y and x respectively give:
1 - 4x - 6y = 0
1 - 2x - 12y = 0
Solving gives:
x = 0.167 = 1/6
y = 0.056 = 1/18
When we place x in equation (1) we have:
y - 4(1/6)y-6y² = 0
y = 0 or y = 1/18
Similarly, x = 0 or 1/6
Therefore, the four critical points are:
(0,0) (1/6,1/18)
When x = 0 and y = 0
f(x,y) = 0 Hence this is a minimum
When x = 1/6 and y = 1/18
f (x,y) = 1/324 Which is a saddle point.
Therefore, the points are (0,0) Minimum, and (1/6, 1/18) is the saddle point.
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The question you are looking for is here:
(1 point) The function f(x,y)=xy(1−2x−6y) has 4 critical points. List them and select the type of critical point. Points should be entered as ordered pairs and listed in increasing lexicographic order. By that, we mean that (x,y) comes before (z,w) if x
Find the lateral surface area of the
following prism:
5 cm
5 cm
apothem = 3.44 cm
cm
5 cm
10 cm
5 cm
LSA = [?] cm2
The laterals surface area of the given hexagonal prism is: 250 cm².
How to Find the Lateral Surface Area of Hexagonal Prism?Lateral surface area = 5ah, where:
a = edge length of the baseh = height of the prism.Given the following:
a = 5 cm
h = 10 cm
Lateral surface area of the hexagonal prism = 5ah = 5(5)(10)
Lateral surface area of the hexagonal prism = 250 cm²
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PLEASE HELP
If BC DA, then which segment is the shortest side?
The length of the shortest side is DC
How to determine the shortest side?As a general rule in triangle;
The smallest angle in a triangle is opposite the shortest side.
Similarly, the largest angle in a triangle is opposite the largest side.
From the given figure of triangles, the smallest angle is angle CBD with a measure of 47 degrees.
The side opposite this angle is side length DC
Hence, the length of the shortest side is DC
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Find the perimeter of the triangle whose coordinates are A (2, 2), B (3, 3), and C (4, 2)
The perimeter of the triangle whose coordinates are A (2, 2), B (3, 3), and C (4, 2) is 4.828
Finding the perimeter of a triangle with vertices?We can determine the perimeter of a triangle with vertices by utilizing the distance formula.
Given that, we have the vertices (x₁,y₁), (x₂, y₂), (x₃, y₃). Then the length of each sides can be expressed as follows:
SIde AB = [tex]\mathbf{\sqrt{(x_1 -x_2)^2 +(y_1 -y_2)^2}}[/tex]
Side AC = [tex]\mathbf{\sqrt{(x_1 -x_3)^2 +(y_1 -y_3)^2}}[/tex]
Side BC = [tex]\mathbf{\sqrt{(x_2 -x_3)^2 +(y_2 -y_3)^2}}[/tex]
Replacing the values of the coordinates into the given formula above the perimeter of the triangle is 4.828
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Can someone help me with this problem pleaseee having a lot of trouble doing this!!!
1003 more square feet of wallpaper for the living room than the family room when family room is with dimensions (l = 3x, b = 3x, h = x), living room is with dimensions (l = 5x, b = 3x, h = x) and doors are with dimension (b =3, h = 7) {where x = 8}. This can be obtained by forming equations for the given figures.
What is the expression of square feet of wallpaper for family room?Given that,
dimensions (l = 3x, b = 3x, h = x) and there is one door (b =3, h = 7)
expression of square feet of wallpaper for family room,
⇒ area of four walls - area of one door= [(3x)(x)+(3x)(x)+(3x)(x)+(3x)(x)] - [3×7]
=[3x²+3x²+3x²+3x²] - 21
=12x² - 21 square feet
What is the expression of square feet of wallpaper for living room?
Given that,
height and width are same as of the family room but length is 5 times more than height [length = 5(height) ⇒ l = 5x]
dimensions (l = 5x, b = 3x, h = x) and there is two doors (b =3, h = 7)
expression of square feet of wallpaper for family room,
area of four walls - area of two doors= [(3x)(x)+(5x)(x)+(3x)(x)+(5x)(x)] - 2[3×7]
=[3x²+5x²+3x²+5x²] - 2(21)
=16x² - 42 square feet
What is the total amount of wallpaper needed?
total amount of wallpaper needed
⇒wallpaper for family room + wallpaper for living room = 12x²-21 + 16x²-42
=28x²-63 square feet
How much more square feet the living room will require more than family room when x = 8?Family room ⇒ 12x²-21 = 12(8²)-21 = 768-21=747 square feet Living room ⇒ 16x²-42 = 16(8²)-42 = 1792-42 = 1750 square feet
Area of wallpaper of living room - area of wallpaper of family room
= 1750 - 747
= 1003 square feet
Hence 1003 more square feet of wallpaper for the living room than the family room when family room is with dimensions (l = 3x, b = 3x, h = x), living room is with dimensions (l = 5x, b = 3x, h = x) and doors are with dimension (b =3, h = 7) {where x = 8}.
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A certain quadratic function has the factors
3,
(x+2)，
and
(x - 5)
. What are the zeros of this function?
a. x=2 and x=-5
b. x=2, x=5, and x=-3
c. x=-2 and x=5
d. x=-2, x=5, and x=3
[tex]f(x) = 3(x + 2)(x - 5)[/tex]
[tex]solving \: f(x) = 0 \\ 3(x + 2)(x - 5) = 0 \\ (x + 2)(x - 5) = \frac{0}{3} \\ (x + 2)(x - 5) = 0 \\ x + 2 = 0 \: \: \: \: \: \: \: \: \: \: x - 5 = 0 \\ x = - 2 \: \: \: \: \: \: \: \: \: \: x = + 5[/tex]
Option CA rectangular paperboard measuring 20 invhes long and 15 inches wide has a semicircle cut out of it, as shown below. What is the perimeter of the paperboard that remains after the semicircle is removed? (Use the value 3.14 for pie, and do not round your answer. Be sure to include the correct unit in your answer.)
The perimeter of the rectangle is 70 Inches square
How to determine the perimeterThe formula for perimeter of a rectangle is given as;
Perimeter = 2 ( l + w)
length = 20 inches
width = 15 inches
Perimeter = 2 ( 20 + 15 )
Perimeter = 2 ( 35)
Perimeter = 70 Inches square
Thus, the perimeter of the rectangle is 70 Inches square
Note that it is a general knowledge on the given question.
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One of the criticisms of the Social Readjustment Rating Scale is that it does NOT take into account:
What is one major limitation of the Social Readjustment Rating Scale?
The Social Readjustment Rating Scale has severe limitations, despite being a helpful tool for the research of life transition and disease. The current measure cannot be used to assess the impact of various life changes (such as positive or negative ones) on the development of sickness.Learn more about Social Readjustment Rating Scale brainly.com/question/13044228
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What is the total surface area of a regular square based pyramid which has a slant height of 10 units and base side lengths of 6 units?
360 square inches
420 square inches
216 square inches
200 square inches.
168 square inches.
The total surface area of a regular square pyramid having slant height of 10units and base length of 6 units is 168 square inches which is fifth option.
Given that slant height is 10 units and base lengths of 6 units.
We are required to calculate total surface area of regular square pyramid.
We know that total surface area of regular square based pyramid is equal to [tex]s^{2} +s\sqrt{s^{2} +4h^{2} }[/tex] in which s is side of base length and h is slant height of regular square pyramid.
Total surface area=[tex]6^{2} +6\sqrt{6^{2} +4*10^{2} }[/tex]
=36+6[tex]\sqrt{36+400}[/tex]
=36+6[tex]\sqrt{436}[/tex]
=36+6*20.88
=36+125.28
=161.28
Nearest option is 168 square inches.
Hence the total surface are of regular square based pyramid is option 5 which is 168 square inches.
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find area and perimeter show your work
Answer:
A= 16
P=16
Step-by-step explanation:
A=h^bxb/ 2
P= side+base+side
Find the equation of a line perpendicular to 2x+4y=8 which cross the y intercept
Answer: [tex]y=2x+2[/tex]
Step-by-step explanation:
[tex]2x+4y=8\\\\x+2y=4\\\\2y=-x+4\\\\y=-\frac{1}{2}x+2[/tex]
So, the slope of the given line is -1/2, meaning the slope of the line we want to find is 2.
Since the y-intercept is the given line is (0,2), the equation is [tex]y=2x+2[/tex]
PLEASE HELP URGENT!!!
From-
~xXIndieKidXx~
Answer:
C. 9
Step-by-step explanation:
The cubed root of 729 is the number that is multiplied 3 times to get 729. In this case, it's 9.
9*9*9 = 81*9
81*9 = 729
A metallurgist has one alloy containing 39% copper and another containing 65% copper. How many pounds of each alloy must he use to make 48 pounds of a third alloy containing 62% copper? (Round to two decimal places if necessary.)
The metallurgist must use 5.538 pounds of an alloy with 39 % copper and 42.462 pounds of an alloy with 62 % copper.
How to calculate proportions of components associated to an alloy
Herein we must create a new alloy by using correct quantities of two alloys with distinct copper concentrations. All required information can be found by concept of weighted averages:
(62/100) · (48 lb) = (39/100) · x + (65/100) · (48 - x)
62 · 48 = 39 · x + 65 · 48 - 65 · x
3 · 48 = 26 · x
x = 5.538 lb
The metallurgist must use 5.538 pounds of an alloy with 39 % copper and 42.462 pounds of an alloy with 62 % copper.
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Whales evolved in the early Cambrian and include transitional species such as Kutchicetus and Rodhocetus.
False, Whales evolved in the early Cambrian and include transitional species such as Kutchicetus and Rodhocetus.
What animals evolved during Cambrian period?
Animals include, from left: Dinomischus, Ottoia, Halucinoginia, Wiwaxia, Trilobites, Archeocyathans, Microdictyon, Canadia, and Pikia. Two larger Anomolocarus are seen in the distant background.When did animals evolve in the Cambrian?
The Cambrian explosion happened more than 500 million years ago. It was when most of the major animal groups started to appear in the fossil record, a time of rapid expansion of different forms of life on Earth.What long lived group of arthropods went extinct at the end of the Permian?
The trilobites, a group of extinct arthropods, as well as the closely related eurypterids, first appeared in the Permian. The Paleozoic Era saw the extinction of rugose and tabulate corals.Learn more about Cambrian animals evolved.
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The complete question is -
True or false . Whales evolved in the early Cambrian and include transitional species such as Kutchicetus and Rodhocetus.
Question 6 of 20
What is the common difference between consecutive terms in the following
arithmetic sequence?
51, 47, 43, 39, ...
OA. 3
B. -3
O C. -4
D. 4
Common difference formula
[tex]\boxed{\sf d=t_2-t_1}[/tex]
So
Here
[tex]\\ \tt{:}\longrightarrow d=47-51[/tex]
[tex]\\ \tt{:}\longrightarrow d=-4[/tex]
Option C
Answer:
C. -4
Step-by-step explanation:
Given sequence: 51, 47, 43, 39, ...
To find the common difference (d) between consecutive terms in an arithmetic sequence, subtract the previous term from the next term:
[tex]\implies \sf d=47-51=-4[/tex]
[tex]\implies \sf d=43-47=-4[/tex]
[tex]\implies \sf d=39-43=-4[/tex]
Therefore, the common difference for the given arithmetic sequence is -4.
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A super sundae ice cream cone has a radius of 0. 5 in and a depth of 4 in. A wonderful waffle cone has a radius 0. 9 in and a depth of 3 in. Which cone holds more ice cream?
The wonderful waffle cone holds more ice cream than super sundae cone.
In this question,
The ice cream cone is the shape of hemisphere at the top and cone shape at the bottom.
Volume of ice cream cone = volume of hemisphere + volume of cone
Volume of ice cream cone = [tex]\frac{2}{3}\pi r^{3} +\frac{1}{3} \pi r^{2} h[/tex]
Volume of super sundae cone:
Radius of hemisphere = height of hemisphere = 0.5 in
Depth of the ice cream cone = 4 in
Volume of super sundae cone = [tex]\frac{2}{3}\pi (0.5)^{3} +\frac{1}{3} \pi (0.5)^{2} (4)[/tex]
⇒ [tex]\frac{2}{3}(3.14)(0.125) +\frac{1}{3} (3.14)(0.25)(4)[/tex]
⇒ 0.2616+1.0466
⇒ 1.3082 ≈ 1.31 cubic in.
Volume of wonderful waffle cone:
Radius of hemisphere = height of hemisphere = 0.9 in
Depth of the ice cream cone = 3 in
Volume of wonderful waffle cone = [tex]\frac{2}{3}\pi (0.9)^{3} +\frac{1}{3} \pi (0.9)^{2} (3)[/tex]
⇒ [tex]\frac{2}{3}(3.14)(0.729) +\frac{1}{3} (3.14)(0.81)(3)[/tex]
⇒ 1.526+2.5434
⇒ 4.0694 ≈ 4.07 cubic in.
Thus volume of wonderful waffle cone > volume of super sundae cone.
Hence we can conclude that the wonderful waffle cone holds more ice cream than super sundae cone.
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What is the radius for a circle whose equation is x² + y² = 16?
OA. 4
OB. 16
C. 8
OD. 256
Answer:The radius is √16.
Step-by-step explanation:
Prove by induction:
5| (21^n+9)
It's kind of self-evident. Any power of 21 will have a 1 in the units place, and adding 9 to it makes it 0 and hence the number is divisible by 5.
To prove the claim by induction, first establish the base case. I assume [tex]n\in\Bbb N[/tex], so for [tex]n=1[/tex] we have
[tex]21^1 + 9 = 21 + 9 = 30[/tex]
and of course 30 = 5×6 is divisible by 5.
Assume the claim is true for [tex]n=k[/tex], that [tex]5 \mid 21^k + 9[/tex]. This means that for some integer [tex]\ell[/tex], we can write
[tex]21^k + 9 = 5\ell[/tex]
Now the induction step: when [tex]n=k+1[/tex], we have
[tex]21^{k+1} + 9 = \bigg(21\times(21^k + 9) - 9\times21\bigg) + 9 \\\\ ~~~~~~~~~~~~~~ = 21\times5\ell - 9\times20 \\\\ ~~~~~~~~~~~~~~= 5\times(21\ell - 9\times4)[/tex]
which is divisible by 5. QED
A scale model of a rectangular building lot measures 7 feet by 5 feet. If the actual house will be built using a scale factor of 12, what is the area of the actual building lot?
The area of the actual building lot is 5040 square ft
Scale factorsThis factors are used to enlarge or diminish the given figure. Given the scale model of a rectangular building lot measures 7 feet by 5 feet. If the actual house will be built using a scale factor of 12, the new length and width is expressed as:
Length = 12 * 7 = 84ft
Width = 5*12=60 ft
Determine the area
Area = 84 * 60
Area = 5040 square feet
Hence the area of the actual building lot is 5040 square ft
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I NEED THE ANSWER TO D please provide
Answer:
y = 2/5x -4
Step-by-step explanation:
Point-Slope Form formula
y - y1 = m (x - x1)
slope = m = 2/5
(-5, -6)
y - -6 = 2/5 (x - -5)
y + 6 = 2/5x + 2
y = 2/5x - 4
patrickJMT
i need help please! I think I know the answer but for some reason my brain's telling me that it's wrong so if someone could explain how to get the answer so I can check that would be great.
Considering the slopes of the segments, the correct option is:
D. No, because the triangle ABC doesn't have a pair of perpendicular sides.
When are lines parallel, perpendicular or neither?The slope, given by change in y divided by change in x, determines if the lines are parallel, perpendicular, or neither, as follows:
If they are equal, the lines are parallel.If their multiplication is of -1, they are perpendicular.Otherwise, they are neither.Here, we have to find if there are perpendicular segments, that is, if two slopes multiplied have a value of -1, then:
mAB = (-7 - 9)/(11 - 1) = -8/5.mAC = (3 - 9)/(-9 - 1) = 3/5.mBC = (3 - (-7))/(-9 - 11) = -1/2.No sides are perpendicular, hence option D is correct.
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What is the domain of f(x) = 5x – 7?
{x | x > –7}
{x | x < –7}
{x | x > 0}
{x | x is a real number}
Answer:
{x:x is a real number}
Since any value can replace x to give an integer.
{x:x is a real number}
Find the surface area of the prism. Round to the nearest tenth if necessary.
The surface area of the prism according to the segment labels is; 480mm².
What is the surface area of the prism?The prism given in the task content is five-faced and hence, its surface area can be evaluated as follows;
Surface area = 2(0.5×15×8)+(15×9)+(8×9) + (17×9).
Hence, the surface area of the prism upon evaluation is; 480mm².
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The graph shows a system of inequalities.
The graph shows a dashed upward opening parabola with a vertex at 0 comma 0 that passes through negative 3 comma 9 and 3 comma 9, with shading inside the parabola. It also shows a graph of a downward opening parabola with a vertex at 4 comma 22 that passes through 0 comma 6 and 8 comma 6, with shading inside the parabola.
Which point is a solution to the system?
(–1, 6)
(0, 22)
(2, 9)
(8, 2)
The number of tickets sold on Friday were 66 children tickets and 97 adult tickets.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The equation of the parabola passing through (0, 0), (-3, 9) and (3, 9) is y = x²
The equation of the parabola with vertex at (4, 22) passing through (0, 6), (8, 6) and (3, 9) is y < -x² + 8x + 6
The solution to the system of equation is the darker region and it contains the point (-1, 6)
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Answer:
(2,9)
Step-by-step explanation:
Got it on FlVS
At a coffee shop, the manager recorded the number of customers who visited the store at the end of each hour. The graph shows the recordings for a 24-hour period. The function describing this graph is a transformation of the parent sine function, y=sin(x)
Which value is closest to the amplitude of the transformed function?
O 83 customers
O 27 customers
O 54 customers
O 30 customers
Answer:
Step-by-step explanation:
The amplitude of a sine function is equal to one-half the distance between the maximum and minimum values of the function.
In this case, the maximum value is approximately 84 customers, and the minimum value is approximately 30 customers
Therefore, the value that is closest to the amplitude of the transformed function is 27 customers.
There is a total of 32 cubic centimeters of a liquid in two beakers. one of these beakers contains 15 cubic centimeters of the liquid. how much liquid does the other beaker contain? a. 13 cc b. 15 cc c. 16 cc d. 17 cc
The correct option is (d).
The other beaker contains 17 cc (cubic centimetres) of the liquid.
What is cubic centimetres of liquid mean?The volume of a cube with dimensions of 1 cm ×1 cm× 1 cm is equal to one cubic centimetre (or cubic centimetre in US English) (SI unit symbol: cm³; non-SI abbreviations: cc and ccm). A millilitre's volume is equal to one cubic centimetre.
According to the question,
The total liquid is 32 in cubic centimetres which is stored in the two beakers.
In the first beaker the liquid stored is 15 cubic centimetres.
The second beaker will contain the liquid = total liquid stored in both beakers - liquid stored in the first beaker.
Liquid in second beaker = 32 - 15
= 17
Therefore, the liquid stored in the second beaker is 17 cc (cubic centimetres).
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Round 18.57631 to three decimal places.
❄ Hi there,
let us revise the rounding rules and then, get down to rounding the number.
[tex]\sf{Rounding \ Rules:}[/tex]
If the number you need to round is followed by a number from 0 to 4, you round down.If the number you need to round is followed by a number that's 5 or more, you round up.Now we can start the rounding process.
Reading the problem & the directions, we notice that we need to round to 3 decimal places (3 numbers after the decimal point).
Looking at the fourth number, we notice that it's less than 5.
∴ we need to round down ↡
↬[tex]\sf{18.57631 \ rounded \ to \ 3 \ DP \ = \bf{18.576}}[/tex]
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
❄
Find the sum. express the answer in scientific notation. (1.54 times 10 superscript 6 baseline) (6.15 times 10 superscript 6 baseline) 7.69 times 10 superscript 6 9.471 times 10 superscript 6 7.69 times 10 superscript 12 9.471 times 10 superscript 12
The sum of the numbers is 7.69 * 10^6
How to evaluate the sum?The expression is given as:
(1.54 times 10 superscript 6 baseline) (6.15 times 10 superscript 6 baseline)
Rewrite properly
(1.54 * 10^6) + (6.15 * 10^6)
Factor out 10^6
(1.54 + 6.15) * 10^6
Evaluate the sum
7.69 * 10^6
Hence, the sum of the numbers is 7.69 * 10^6
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Answer:
a
Step-by-step explanation:
Find the sum. Express the answer in scientific notation.
(1.54 times 10 Superscript 6 Baseline) + (6.15 times 10 Superscript 6 Baseline)
7.69 times 10 Superscript 6
9.471 times 10 Superscript 6
7.69 times 10 Superscript 12
9.471 times 10 Superscript 12
A rectangular swimming pool with a length of 18m and width of 8m is surrounded by a concrete patio. The patio is a uniform 3m width around the entire pool. What is the area of the patio
The area of the patio is 192 [tex]m^{2}[/tex]
What is area?An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure. The square unit, which is frequently expressed as square inches, square feet, etc., is the accepted unit of area.
The word "area" refers to a free space. A shape's length and width are used to compute its area.
Length of swimming pool=18 m
Width of swimming pool=8 m
Area of swimming pool= 18*8 = 144[tex]m^{2}[/tex]
Width of patio=3m
Total length of swimming pool=18+2(3)=24 m
Total width of swimming pool=8+2(3)=14 m
Total area=24*14=336 [tex]m^{2}[/tex]
Area of patio= total area - Area of swimming pool
=336-144
=192 [tex]m^{2}[/tex]
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Tyler's playlist has 36 songs. Noah’s playlist has one quarter as many songs as Tyler's playlist. How many songs are on Noah’s playlist?
Answer: 9
Step-by-step explanation:
Answer:
9 songs
Step-by-step explanation:
a quarter is basically a fourth of a number so you need to just divide the number by four