[tex]{\qquad \qquad \huge \rm \underline { \underline{ Répondre}}}[/tex]
Standard equation of an ellipse is :
[tex]\qquad \rm\dashrightarrow \: \dfrac{ {(x - h)}^{2} }{ {a}^{2} } + \dfrac{ {(y - k)}^{2} }{ {b}^{2} } = 1[/tex]
If b is smaller than a, then it will be a horizontal ellipse, and if b is greater than a, it will be a vertical ellipse. and shifting depends upon coordinates of its centre.
Now, our given equation is :
[tex]\qquad \rm\dashrightarrow \: \dfrac{ {x}^{2} }{ 15 } + \dfrac{ {y }^{2} }{ {10} } = 1[/tex]
[tex]\qquad \rm\dashrightarrow \: \dfrac{ {x}^{2} }{ {(\sqrt{15})}^{2} } + \dfrac{ {y}^{2} }{ {(\sqrt{10}) {}^{2} } } = 1[/tex]
[ here, b = root 10 and a = root 15, hence a is greater than b here, which means : its a horizontal ellipse.
And since it is a horizontal ellipse with center at origin, it's major axis will lie on x - axis.
what is 1 oz in tbsp
There are 2 tablespoons in 1 fluid ounce. This conversion is often used in cooking and baking recipes, where ingredients are measured in ounces or tablespoons.
Fluid ounces and tablespoons are both units of volume used to measure liquids in cooking and baking recipes. One fluid ounce is equal to 29.5735 milliliters or approximately 2 tablespoons, which is equivalent to 6 teaspoons. Therefore, there are 2 tablespoons in 1 fluid ounce.
This conversion is important to know when following recipes that call for ingredients in fluid ounces or tablespoons. It allows for accurate measurement of ingredients, which is crucial for successful cooking and baking. Other common units of volume used in the kitchen include teaspoons, cups, and quarts, among others.
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There are 300,000 households in Clover City. A local television repair shop takes a random sample of 50 households and finds that the average number of televisions per household from the sample last year that needed to be repaired was 2.53 ± 0.71. Which of the following is an estimate of the total number of televisions that needed repairing last year in Clover City?
Try using Socratic and it may help
The perimeter of the rectangle below is 132 units. Find the value of Y.
4y
3y+3
The value of y is 9
What is perimeter?Perimeter is the distance around the edge of a shape. Learn how to find the perimeter by adding up the side lengths of various shapes.
Therefore, the perimeter of a rectangle can be expressed as:
P = 2(l+b)
l = 4y
b = 3y+3
132 = 2(4y+3y+3)
132 = 2( 7y+3)
132 = 14y +6
14y = 132 -6
14y = 126
divide both sides by 14
y = 126/14
y = 9
therefore the value of y is 9
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The value of y in the rectangle shown is: y = 7.
What is the Perimeter of a Rectangle?The perimeter of a rectangle = 2(length + width)
Given the following as shown in the image attached below:
Length of rectangle = 5y + 3
Width of rectangle = 4y
Perimeter = 132 units
Plug in the values:
132 = 2(5y + 3 + 4y)
Solve for y:
132 = 2(9y + 3)
132 = 18y + 6
132 - 6 = 18y
126 = 18y
126/18 = y
7 = y
y = 7
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what is 20 percent of 200?
Answer: 40
Step-by-step explanation:
20% = 0.2
0.2 x 200 = 40
the binomial probability distribution is a __________ probability distribution that describes probabilities for experiments in which there are two __________ outcomes.
The binomial probability distribution is a discrete probability distribution that describes the probabilities of two independent outcomes in an experiment. A Poisson probability distribution is a discrete distribution whereby the stochastic process x makes a difference the number of occasions that an event occurs in a given interval.
Is the result of such a laboratory activity a probability distribution?
A probability distribution consists of a table or an equation that associates each output of a random experiment with the likelihood of its event occurring. Consider the following simple experiment: we toss a coin twice. The experiment could result in the head count being equal in 2 different coin flips.
What are the two binomial distribution outcomes?
Binary Distribution
Each trial yields one of two outcomes: success or failure. The success probability, denoted by p, remains constant from trial to trial. The n trials are autonomous.
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Determine if the columns of the matrix form linearly independent set_ Justify your answer ~4 Select the correct choice below and fill in the answer box within your choice_ (Type an integer or simplified fraction for each matrix element ) If A is the given matrix then the augmented matrix presents the equation Ax = The reduced echelon form of this matrix indicates that Ax = 0 has more than one solution. Therefore the columns of _ form linearly independent set_ If A is the given matrix, then the augmented matrix represents the equation Ax = The reduced echelon form of this matrix indicates that Ax = 0 has only the trivial solution. Therefore, the columns of A form linearly independent set_ If A is the given matrix then the augmented matrix presents the equation Ax = The reduced echelon form of this matrix indicates that Ax = 0 has more than one solution. Therefore the columns of A do not form linearly independent set_ If A is the given matrix, then the augmented matrix represents the equation Ax =0. The reduced echelon form of this matrix indicates that Ax = 0 has only the trivial solution. Therefore the columns of _ do not form linearly independent set_
The correct choice is: If A is the given matrix then the augmented matrix presents the equation Ax = 0. The reduced echelon form of this matrix indicates that Ax = 0 has only the trivial solution. Therefore the columns of A do not form linearly independent set.
To determine if the columns of the matrix form a linearly independent set, we can perform row reduction on the matrix and examine the resulting reduced row echelon form.
The given matrix is:
[0 3 9]
[2 -7 -1]
[1 -4 -2]
[0 3 9]
[2 -7 -1]
[1 -4 -2]
R2 = R2 - 2R1
R3 = R3 - R1
[0 3 9]
[2 -7 -1]
[1 -4 -2]
R2 = R2 + 7/3 R3
[0 3 9]
[2 0 20/3]
[1 -4 -2]
R1 = R1 - 3/2 R2
R3 = R3 + 4R2
[0 3 0]
[2 0 20/3]
[1 0 2/3]
R1 = R1 / 3
R2 = R2 / 2
R3 = R3 / 3
[0 1 0]
[1 0 10/9]
[1 0 2/9]
The resulting reduced row echelon form shows that the third column is a linear combination of the first and second columns. Specifically, column 3 can be expressed as:
(2/9)*column 1 + (10/9)*column 2 = column 3
Since the third column can be expressed as a linear combination of the first and second columns, the columns of the matrix do not form a linearly independent set.
Therefore, the correct choice is:
If A is the given matrix then the augmented matrix presents the equation Ax = 0. The reduced echelon form of this matrix indicates that Ax = 0 has only the trivial solution. Therefore the columns of A do not form linearly independent set.
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where are the most densely populated areas of japan with over 1000 people per kilometer?
Furthermore, Tokyo Metropolis had the highest population density among Japan's prefectures, with 6,402.6 people per square kilometer. This one was nearly 18.9 times greater than that of the state median (338.2 persons per square kilometer). In 2020, Japan had 12 cities with an inhabitants of one thousand or maybe more.
What is the world's biggest and densetly populated Japanese island?
It is home to approximately 104 million people (2010), or more than 80% of the Japanese population. Honshu is the most highly populated island (429 people per km2) along with the most economically prosperous nation on the island.
Which two towns are situated in Japan's most densely populated areas?
Osaka, Kobe, and Kyoto make up Japan's most highly populated region, with each capital of a prefecture. This region is commonly referred to as the Kansai region.
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The diameter of a cylindrical water tank is 13 ft, and its height is 17 ft. What is the volume of the tank?
Use the value 3.14 for I, and round your answer to the nearest whole number.
Be sure to include the correct unit in your answer.
13 ft
17 ft
ft ft²
X
I need some help please
Answer: this is true
Step-by-step explanation:
How many terms will be in the expansion of (2x+3y) ∧ 6
The expansion of (2x+3y) ∧ 6 will contain 7 terms.
According to given condition :The expansion of [tex](2x+3y)^6[/tex] will contain 7 terms.
To see why, consider the binomial theorem, which tells us that the expansion of [tex](a + b) ^n[/tex] will have (n+1) terms, where the first term has coefficient 1 and the last term has coefficient 1.
In the case of [tex](2x+3y)^ 6[/tex], we can think of this as the expansion of [tex](2x + 3y) ^6 as (2x) ^ 6 + 6(2x) ^ 5(3y) + 15(2x) ^ 4(3y) ^ 2 + 20(2x) ^ 3(3y) ^3 + 15(2x) ^2(3y) ^ 4 + 6(2x)(3y) ^5 + (3y) ^6.[/tex]
As we can see, there are seven terms in this expansion, each with a different combination of powers of 2x and 3y. Therefore, the expansion of [tex](2x+3y)^ 6[/tex] will have 7 terms.
What is expression ?In mathematics, an expression is a combination of numbers, variables, and mathematical operations such as addition, subtraction, multiplication, division, exponentiation, or roots.
Expressions are used to represent numerical or algebraic quantities, and they can be as simple as a single number or variable, or as complex as a polynomial or rational function.
For example, the expression 2 + 3 represents the sum of 2 and 3, and the expression 3x - 7 represents the result of multiplying x by 3 and then subtracting 7.Expressions can be evaluated by following the order of operations, which tells us to perform operations in a specific order (parentheses, exponents, multiplication and division from left to right, and addition and subtraction from left to right).
Expressions can also be simplified or manipulated using algebraic rules and properties to make them easier to work with or to solve equations involving them.
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I NEED HELP W THIS QUESTION PLS BE FASTT
The area of the figure composed of the square and four semicircles is approximately 242.4 square units.
Describe Semicircle?A semicircle is a two-dimensional geometric shape that is half of a circle. It is formed by drawing a diameter of a circle and then drawing the arc that connects the two endpoints of the diameter. The diameter divides the circle into two equal parts, each of which is a semicircle.
A semicircle has several important properties, including:
It has one straight side, which is the diameter of the circle.
The other side is curved, and it is a half-circle.
The radius of the semicircle is equal to half the diameter of the circle.
The circumference of a semicircle is half the circumference of the circle.
The area of a semicircle is half the area of the circle.
Semicircles are used in many applications of geometry and trigonometry, including in the study of angles, arcs, and circles. They are also used in architecture and engineering to design buildings, bridges, and other structures that have semicircular features.
In addition to being a geometric shape, a semicircle can also refer to a half-circle that is used as a decorative element or design motif. Semicircles are often used in art, architecture, and graphic design to create visually interesting patterns and compositions.
To find the area of the figure composed of a square and four semicircles, we need to first find the area of the square and the area of the four semicircles. Then, we can subtract the area of the four semicircles from the area of the square to get the total area of the figure.
The area of the square is simply the side length squared, so in this case it is:
Area of square = (22)^2 = 484 square units
The diameter of each semicircle is equal to the side length of the square, so the radius is half of that or 11 units. Therefore, the area of each semicircle is:
Area of semicircle = (1/2) * π * r^2 = (1/2) * π * 11^2 = 60.4 square units
Since there are four semicircles, the total area of the four semicircles is:
Total area of semicircles = 4 * Area of semicircle = 4 * 60.4 = 241.6 square units
To get the area of the entire figure, we need to subtract the area of the four semicircles from the area of the square:
Area of figure = Area of square - Total area of semicircles
Area of figure = 484 - 241.6 = 242.4 square units
Rounding this to the nearest tenth gives:
Area of figure = 242.4 (rounded to the nearest tenth)
Therefore, the area of the figure composed of the square and four semicircles is approximately 242.4 square units.
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Will give 20 pts!
You kayak up a river at a rate of 168 feet every 2 minutes. You kayak 56 feet every 30 seconds on the way back down the river. How much farther do you kayak in 5 minutes on the way down the river than in 5 minutes on the way up the river?
You kayak 140 feet further in 5 minutes going downstream than you do in 5 minutes going upstream.
Relationship Between Speed, Time & Distance:Speed is determined by dividing the distance traveled by the time taken to travel it. It gives the distance traveled and the amount of time it took to travel that distance.
Speed is directly Proportional to Distance and Inversely proportional to Time. Hence,
Distance = Speed X Time.
Given: You paddle a kayak 168 feet up a river every two minutes.
Hence, 168/2 = 84 feet per minute.
Therefore you go up 84 feet in one minute.
You reach 84*5 = 420 feet in 5 minutes.
Given: As you paddle back down the river, you cover 56 feet every 30 seconds.
Speed is determined by distance traveled divided by time, therefore when traveling downward, 56/0.5 equals 112 feet per minute.
In one minute, you descend by 112 feet.
You descend 560 feet in 5 minutes, or 5*(112) feet.
As a result, you will move on 140 feet (560 - 420)=140 feet further .
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STUVWXYZ is a cuboid. M and N are the mid-points of
ST and WZ respectively.
Find angle
a SYW
b TNX
c ZMY
MN = 17.09 cm
NMV = 16.31°
A cuboid is a six-sided solid known as a hexahedron in geometry. Quadrilaterals make up its faces. Cuboid is short for "like a cube." A cuboid is similar to a cube in that a cuboid can become a cube by varying the lengths of the edges or the angles between the faces.
MV = 1/2 VS = 6cm (midpoint)
NV= 1/2YV = 5cm (midpoint)
MV = [tex]\sqrt{MV^2 + UV^2} = \sqrt{6^2 + 16^2} = 17.09cm[/tex]
MN = [tex]\sqrt{MU^2 + NU^2} = \sqrt{6^2 + 16^2 + 5^2} = 17.80cm[/tex]
tanNMV= 5/17.09
= 16.31°
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A survey asked a group of adults and youths if they prefer reading books printed on paper or electronic books.
Book Preference
Print Electronic Total
Youths 27 40 67
Adults 29 27 56
Total 56 67 123
What percent of the adults surveyed prefer reading electronic books? Round your answer to the nearest tenth of a percent.
Percentage
48.21% approximately 50%
We got the answer by dividing the number of adults that read electronic books by the total adults
27/56 = 0.4821
we then multiply by 100 to get the percentage of needed. this gives us a decimal
48.21
which when rounded off to the nearest tenth is 50%
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Find the area of a circle whose center is at (2, 2) and goes through the point (8, 2)
The area of the circle is 113.04 square units.
How to find the area of the circle?The area of a circle of radius R is given by:
A = π*R²
Where π = 3.14
Here we know that the center is at (2, 2) and the point (8, 2) is on the circle, then the radius is:
R = √( (2 - 2)² + (8 - 2)²)
R = 6
Then the area of the circle is:
A = 3.14*(6)² = 113.04 square units.
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Please help!!! I’m really confused and need help
Answer: I’m pretty sure it’s c
Step-by-step explanation:
how many milligrams are in milliliters
The density of water is 1 gram per milliliter, which means that 1 milliliter of water weighs 1000 milligrams (1 gram).
Milligrams (mg) and milliliters (ml) are two different units of measurement used for different purposes. Milligrams are used to measure mass or weight, while milliliters are used to measure volume or capacity.
The conversion between milligrams and milliliters depends on the density of the substance being measured. The density is a measure of the amount of mass per unit of volume.
In general, the conversion between milligrams and milliliters is not straightforward and requires knowing the density of the substance being measured. However, for liquids with a density of approximately 1 gram per milliliter, 1 milliliter is equivalent to 1000 milligrams.
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What is the conversion of 20 ml to tsp ?
There will be approx four teaspoons of US measurement system in 20 ml. That is the unit conversion of 20 mililitre is equals to four teaspoons.
A milliliter is a unit of volume equal to 1/1000 of a liter. It is the same as a cubic centimeter. A US teaspoon is a unit of volume in the cooking system that is equal to 1/3 of a tablespoon or 1/48 of a US cup. To calculate the value in milliliters to the corresponding value in teaspoons [US], multiply the amount in milliliters by 0.2028841362 (conversion factor). Here is the formula: Value in teaspoons [US]
= value in milliliters × 0.2028841362
Now we need to convert 20 ml to teaspoons. So using the above formula we can write the number of teaspoons in 20 ml is Value in teaspoons [US]
= value in milliliters × 0.2028841362
= 20 ml × 0.2028841362
= 4.057682724 ~ 4
Hence required value is 4 teaspoons.
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find the critical value that corresponds to the confidence level %.
The critical value, zα/2, that corresponds to a 87% confidence level is approximately 1.514.
The critical value, zα/2, is the z-score that cuts off an area of α/2 in the tails of the standard normal distribution. In other words, it represents the number of standard deviations away from the mean that corresponds to a particular level of confidence.
To find the critical value for a 87% confidence level, we first need to determine the area that is left in the tails of the distribution. Since the confidence level is 87%, the area in the middle of the distribution is (1 - 0.87) = 0.13. We then divide this area in half to get the area in each tail, which is 0.065.
Using a standard normal distribution table or a calculator, we can find that the z-score that cuts off an area of 0.065 in one tail is approximately 1.514. Therefore, the critical value, zα/2, is:
zα/2 = ±1.514
However, since we want to find the z-score that corresponds to the middle 87% of the distribution, we need to add the absolute value of this number to the mean of the distribution, which is 0. This gives us:
zα/2 = |1.514| = 1.514
Therefore, the critical value, zα/2, that corresponds to a 87% confidence level is approximately 1.514
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--The question is incomplete, answering to the question below--
"Find the critical value, zα/2 that corresponds to the given confidence level 87%"
What is a heart shaped mathematical curve?
A heart-shaped mathematical curve is a cardioid (picture is attached below).
In the mathematical branch of geometry, we can use certain equations, etc. to create a heart-shaped mathematical curve which is called a cardioid. Its name has been derived from the greek word kardiá which literally translates to heart.
It can be described as a plane curve that is drawn by a point on the perimeter of a circle and this circle is rolling around a fixed circle that has a similar radius. It is also described as an epicycloid having a single cusp. The equation (a+x)^(a-x) can be used to make a cardioid.
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Using the special right triangle shortcuts, what is the length of the hypotenuse of a 45-45-90 triangle with a leg length of 8?
The length of the hypotenuse is 8√2 units.
What is Pythagoras theorem?According to the Pythagoras theorem, we can write -
the square of the hypotenuse is equal to the sum of the squares of the other two sides.Mathematically, we can write -(hypotenuse)² = (base)² + (perpendicular)²
(h)² = (b)² + (p)²
Given is a 45 - 45 - 90 triangle with a leg length of 8.
Equal Opp. Angles Theorem -
The angles opposite to equal sides are equal and vice - versa is also true. So, we can conclude that both leg length and height length are equal. Mathematically, we can say : (base) = (perpendicular) = 8 unitsWe can write using the Pythagoras theorem as -
x² = 8² + 8²
x² = 64 + 64
x² = 128
x = √(2 x 2 x 2 x 2 x 2 x 2 x 2)
x = √(2² x 2² x 2² x 2 )
x = 8√2
Therefore, the length of the hypotenuse is 8√2 units.
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what is chi square distribution table
A chi-square distribution table is a table that lists critical values for the chi-square distribution.
The chi-square distribution is a probability distribution that is used in statistical hypothesis testing to test whether a set of observed data is consistent with a specified theoretical distribution.
The table is used to find the probability that the chi-square statistic computed from the data is greater than or equal to a given critical value. The critical values depend on the degrees of freedom (df), which are determined by the number of categories in the data.
The chi-square distribution table lists the critical values for various degrees of freedom and levels of significance. For each level of significance (e.g., 0.05 or 0.01),
The table provides the critical value for each degree of freedom. To use the table, you need to determine the degrees of freedom for your data and then find the appropriate critical value for the desired level of significance.
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What is an example of a histogram?
The example of histogram is dataset of exam scores of 100 students, with scores ranging from 50 to 100
A histogram is a graphical representation of the distribution of a dataset. It is a way to visualize the frequency distribution of a set of continuous or discrete data. Here's an example of a histogram:
Suppose we have a dataset of exam scores of 100 students, with scores ranging from 50 to 100. We can create a histogram to visualize the distribution of scores. The histogram will have a vertical axis representing the frequency of scores and a horizontal axis representing the range of scores. We can divide the horizontal axis into equal intervals, called bins, and count the number of scores falling into each bin.
The histogram is shown in the figure
In this example, the histogram shows that most students scored between 70 and 80, with a few students scoring below 60 and above 90.
The histogram also shows that the distribution of scores is roughly symmetrical, with no outliers.
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Suppose we want to choose 2 letters, without replacement, from the 5 letters A, B, C, D, and E.
How many ways can this be done, if the order of the choices is relevant?
There are 20 ways to choose 2 letters from the set A, B, C, D, and E if the order of the choices is relevant
If the order of the choices is relevant, we are looking for the number of permutations of 2 letters chosen from a set of 5 letters. We can use the permutation formula to calculate this:
nPr = n! / (n - r)!
where n is the total number of items in the set (5 letters in this case), and r is the number of items we want to choose (2 letters in this case).
nPr = 5! / (5 - 2)!
nPr = 5! / 3!
nPr = 5 x 4 x 3 x 2 x 1 / (3 x 2 x 1)
Divide the numbers
nPr = 20
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how to convert 145 kg to lbs?
The value of measuring mass 145 kilograms to pounds after conversion as per standard measurements is equal to kilograms 319.7 pounds ( round off to one decimal )
Kilograms and pounds are the units which used to measure the mass of the given body.Kilograms and pounds are related in standard form as given below :
1 kilograms = 2.20462 pounds ___(1)
Substitute the value 145 kilograms in (1) for the conversion into pounds form we have :
⇒ ( 145 ) kilograms = ( 145 multiply to 2.20462 ) pounds
⇒ 145 kilograms = 319.67 pounds
Finally ,
145 kilograms = 319.7 pounds ( round off to one decimal )
Therefore, after conversion the given unit of mass kilograms into pounds is 145 kilograms = 319.7 pounds ( round off to one decimal ).
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select the graph of y=2sin(pi/2x)-1
Answer:
The correct graph is D
What is the conversion of 26 c to fahrenheit ?
The conversion of 26 Celsius to Fahrenheit is 78.8.
Celsius and Fahrenheit are two scales used to measure temperature.
Celsius, also known as the centigrade scale, is a temperature scale where the freezing point of water is 0 degrees Celsius and the boiling point of water is 100 degrees Celsius at standard atmospheric pressure.
To convert Celsius to Fahrenheit, you can use the following formula:
°F = (°C x 9/5) + 32
where °C is the temperature in Celsius and °F is the temperature in Fahrenheit.
Substituting the value of 26 °C in the formula, we get:
°F = (26 x 9/5) + 32
°F = (46.8) + 32
°F = 78.8
Therefore, 26°C is equivalent to 78.8°F in Fahrenheit.
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Correct Question :
What is the conversion of 26 Celsius to Fahrenheit ?
A delivery driver makes 12 deliveries in 3 hours.
How many deliveries can he make in 5 hours?
Answer:
Step-by-step explanation:
as the driver makes 12 delivery in 3 hrs so the driver makes 12/3 delivery in 1 hr that is 4 delivery in 1 hour so he makes 5*4= 20 delivery in 5 hours
A boat travels 15 miles upstream and then turns around and travels 15 miles downstream. The total time for both trips is 4 hours. If the stream flows at 5 miles per hour, how fast does the boat travel in still water?
If the boat needed to travel 15 miles there and back, while the stream only moves 5 miles per hour, it would take 3 hours to travel there and back. This means that in still water, the boat would take 6 hours to move 15 miles upstream and back.
what is 5 8 as a decimal
The number 5/8 as a decimal is 0.625
As we divide a whole into smaller parts, we get decimals. Hence, there are two parts to a decimal number: a whole number part and a fractional part. The whole component of a decimal number has the same decimal place value system as the complete number. After the decimal point, however, when we proceed to the right, we obtain the fractional portion of the decimal number.
An informal way to read a decimal is to first read the whole number as you would any whole number, then the decimal point as "point," and finally each individual digit of the rational part.
the decimal of 5/8 is
5÷8 = 0.625
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