a. The mean of X is 1.7549 and the standard deviation is 0.3536.
b. To calculate the proportion of washing machines that will last for more than 15 years, we need to use the standard normal distribution table. The z-score for 15 years is (15-14)/0.3536 = 2.822. Using the table, we find that the proportion of washing machines that will last for more than 15 years is 0.9968.
c. To calculate the proportion of washing machines that will last for less than 10 years, we need to use the standard normal distribution table. The z-score for 10 years is (10-14)/0.3536 = -2.822. Using the table, we find that the proportion of washing machines that will last for less than 10 years is 0.0032.
d. To calculate the 90th percentile of the life of the washing machines, we need to use the standard normal distribution table. The z-score for the 90th percentile is 1.28. Using the table, we find that the 90th percentile is 17 years.
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22) i) A cuboid has dimensions 60cm x 24cm x 30cm. How many small cubes with side 5cm can be placed in the given cuboid?
Answer:
345.6
Or 345 full cubes
Step-by-step explanation:
To answer this question we first need to find the volume of the cuboid!
To find volume we use the equation...
area of cross-section × heightor l × w × hFor the cuboid we are given the dimensions 60, 24 and 30 so we just need to multiply them...
60 × 24 × 30 = 43200We now need to the the volume of the cube which we can just do by cubing the value given
5³ = 125We now need to divide the two results together to find out how many cubes would fit...
43200 ÷ 125 = 345.6Or 345 full cubesHope this helps, have a lovely day!
The probability of event A occurring is 0. 65. The probability of events A and B occurring together is 0. 33. Events A and B are independent. What
is the probability of event B?
Enter a number to the nearest hundredth in the box.
The probability of event A occurring is 0. 65. The probability of events A and B occurring together is 0. 33. Events A and B are independent. The probability of event B is 0.68.
Probability:
The probability of an event is a number that indicates the probability of the event occurring. Expressed as a number between 0 and 1 or as a percent sign between 0% and 100%. The more likely an event is to occur, the greater its probability. The probability of an impossible event is 0; the probability of a certain event occurring is 1. The probabilities of two complementary events A and B - either A occurring or B occurring - add up to 1.
Given that:
P(A) =0.65
P(A∩B) = 0.33
And event A and B are independent.
Using the probability formula:
P(B) = 1 - P(A) + P(A∩B)
⇒ P(B) = 1 - 0.65 + 0.33
⇒ P(B) = 0.68
Therefore , the probability of event B is 0.68.
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The graph of the step function G f(x) equals negative [X ]+3 is shown what is the domain of G(x)
The domain of a step function is all real numbers. The equation G(x) = -[x] + 3 can be expressed as G(x) = { -x for x < 0; 3 for x ≥ 0}. The domain of G(x) is all real numbers.
To explain further, a step function can be expressed as two separate equations, one for x < 0 and one for x ≥ 0. The equation for x < 0 is G(x) = -x and the equation for x ≥ 0 is G(x) = 3. The domain of G(x) is all real numbers. This means that any x value, whether it is greater than or less than 0, will be included in the domain of G(x).
The length of a rectangle is five times its width. If the permiteter of the rectangle is 72 m, find it’s area
Let's the width of the given rectangle be x. Then the length will be 5x.
We know that,
[tex] \bf \implies Perimeter_{( Rectangle)} = 2 ( Length + Width) [/tex]
[tex] \sf \implies 2( x+5x) = 72 [/tex]
[tex] \sf \implies 2\times 6x = 72 [/tex]
[tex] \sf \implies 12x =72 [/tex]
[tex] \bf \implies x = 6 [/tex]
Hence, the width of the rectangle is 6 m and the length is 5*6 =30 m
[tex]\bf\implies Area_{( Rectangle) }= Length \times Width [/tex]
[tex] \bf \implies Area _{( Rectangle)} = 30 \times 6 [/tex]
[tex] \bf \implies Area _{( Rectangle) }= 180 m^2 [/tex]
Therefore, the area of the given rectangle is 180 metre square.
the lifetime of a printer costing 200 is exponentially distributed with mean 3 years. the manufacturer agrees to pay a full refund to a buyer if the printer fails during the first year following its purchase, and a one-half refund if it fails during the second year. if the manufacturer sells 100 printers, how much should it expect to pay in refunds?
The amount of money the manufacturer should expect to pay in refunds is 32.76X dollars.
Let Y denote the life in years of a printer, which is exponentially distributed with mean 3 years. Therefore, the rate parameter λ of the exponential distribution is λ = 1/3, which is obtained from the formula of the exponential distribution, E(Y) = 1/λ = 3 years. The probability that a printer fails during the first year following its purchase is:
P(Y < 1) = F(1) = 1 - e-λt = 1 - e-1/3(1) = 0.2835
The probability that a printer fails during the second year following its purchase is:
P(1 < Y < 2) = F(2) - F(1) = e-1/3(2) - e-1/3(1) = 0.3219 - 0.2835 = 0.0384
The probability that a printer does not fail during the first two years is:
P(Y > 2) = 1 - F(2) = 1 - e-1/3(2) = 0.6797
Let X denote the refund payment in dollars that the manufacturer should pay to the buyer of a printer if the printer fails during the first year, and X/2 denote the refund payment if the printer fails during the second year. Then, the total refund payment per printer is R = XI(Y < 1) + XI(1 < Y < 2)/2 = XI(Y < 1) + (X/2)I(1 < Y < 2), where I(.) is the indicator function that takes the value of 1 if the condition in the parentheses is true and 0 otherwise. The expected value of the total refund payment per printer is:
E(R) = E[XI(Y < 1)] + E[(X/2)I(1 < Y < 2)]
= X(0.2835) + (X/2)(0.0384) = 0.3276X
Hence, the expected total refund payment for 100 printers is:
Expected total refund payment = 100E(R) = 100(0.3276X) = 32.76X dollars. The amount of money the manufacturer should expect to pay in refunds is 32.76X dollars.
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the sides of a triangle have lengths 15, 20, 25. find the length of the shortest altitude of the triangles.
The length of the shortest altitude of the triangles is 15 units by using Heron’s formula.
We have, The sides of a triangle have lengths of 15, 20, and 25.
To find, The length of the shortest altitude of the triangle.
Steps to solve the problem:
Let us assume that the length of the b is h.According to the property of triangles, the area of the triangle can be calculated as:Area = 1/2 * base * height
We can choose any side as the base of the triangle, let us assume that 20 is the base of the triangle, and its corresponding height is h.Area of the triangle = 1/2 * 20 * h ⇒ 10h
Using Heron’s formula, the area of the triangle can be calculated as:A = √(s(s-a)(s-b)(s-c))
Where a, b, and c are the sides of the triangle, and s is the semi-perimeter of the triangle.
According to the given problem, the sides of the triangle are 15, 20, and 25.
s = (a + b + c)/2
= (15 + 20 + 25)/2
= 30
Therefore, the area of the triangle can be calculated as:
A = √(30(30-15)(30-20)(30-25))
= √(30*15*10*5)
= 150 sq. units
Therefore, we can write the formula for the area of the triangle as:
150 = 10 h
h = 15 units
Therefore, the length of the shortest altitude of the triangle is 15 units.
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If x = 14 units and h = 5 units, then what is the area of the triangle shown above?
Answer:
b: 70
Step-by-step explanation:
10 times 5 is 50 and 4 times 5 is 20. 50 plus 20 is 70
The average of 6 numbers is 15. The average decreases by 1 when the 7th
number is added. What is the value of the 7th number?
A. 7 C. 9
B. 8 D. 10
the 7th number is 8. Answer B is correct. The sum of the first 6 numbers can be found by multiplying the average by the number of numbers:
sum of first 6 numbers = 6 x 15 = 90
Let the 7th number be x. Then the sum of all 7 numbers is:
sum of all 7 numbers = sum of first 6 numbers + 7th number = 90 + x
The new average is 1 less than the original average, so:
new average = 15 - 1 = 14
This means that the sum of all 7 numbers divided by 7 is 14:
(sum of all 7 numbers)/7 = 14
Substituting the expression we found for the sum of all 7 numbers, we get:
(90 + x)/7 = 14
Multiplying both sides by 7, we get:
90 + x = 98
Subtracting 90 from both sides, we get:
x = 8
Therefore, the 7th number is 8. Answer B is correct.
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6. If g(x) = 7x-4, find g(8)-g (-5)
PLEASE HELP I BEG
Determine the area of the shaded regions in the figures below. Write the final polynomial in standard
In response to the stated question, we may state that As a result, the area final polynomial in standard form is: -25pi + 50
What is area?The size of a surface area can be represented as an area. The surface area is the area of an open surface or the border of a three-dimensional object, whereas the area of a planar region or planar region refers to the area of a shape or flat layer. The area of an item is the entire amount of space occupied by a planar (2-D) surface or form. Make a square with a pencil on a sheet of paper. A two-dimensional character. On paper, the area of a form is the amount of space it takes up. Assume the square is made up of smaller unit squares.
To calculate the area of the darkened areas, subtract the area of the circle from the area of the square.
Then, determine the square's side length. Because the circle's diameter is ten, the radius is five. Because the diagonal of a square equals the diameter of a circle, we can use the Pythagorean theorem to calculate the side length:
[tex]s^2 + s^2 = 10^2\\2s^2 = 100\\s^2 = 50\\s = \sqrt(50) = 5 * \sqrt(2)[/tex]
The square's area is then:
[tex]A_{square} = s^2 = (5 * \sqrt(2))^2 = 50[/tex]
The circle's area is:
[tex]A_{circle} = pi * r^2 = pi * 5^2 = 25 * pi[/tex]
The shaded region's area is:
[tex]A_{shaded} = A_{square} - A_{circle} = 50 - 25 * pi[/tex]
As a result, the final polynomial in standard form is:
-25pi + 50
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15x - 5y = 30. solve for y
(please help!!)
Move all terms that don't contain [tex]y[/tex] to the right side and solve.
Answer:[tex]y=6-3x[/tex]Draw a diagram to help you set up an equation(s). Then solve the equation(s). Round all lengths to the neatest tenth and all angles to the nearest degree. (number 7)
From the use of the angle of elevation, the length of ladder is 47 feet.
What is the angle of elevation?The angle between the horizontal and a line of sight or an object above the horizontal, which is commonly stated in degrees or radians, is known as the angle of elevation. Determining an object's position in relation to an observer or a reference point is a common use of trigonometry and geometry.
We know that we have to use the idea of the angle of elevation in this case. We know that;
Cos 65 = 20/x
x is the length of the ladder
x =20/Cos 65
x = 20/0.4225
x = 47 feet
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Principal $400 interest rate 7% compounded anually years 3
The compound interest for the principal value $400, interest rate 7% and compounded anually for 3 years is equals to the $90.2
Compound interest is defined as the interest earn on interest, i.e., here interest on interest . It is denoted by CI and calculated by the below formula, CI
= Amount - principal
and A = P( 1 + r/n)ⁿᵗ
where P --> principal
A --> amount
r --> interest rate
n --> the number of times interest is compounded per year
t --> time in years
Now, we have principal, P = $400
interest rate, r = 7%
time, t = 3 years
here, compounded anually for 3 years so, n= 1
Substitute all known values in above formula,
A = P( 1 + r/n)ⁿᵗ
=> A = 400( 1 + 7/100)³
=> A = 400( 107/100)³
=> A = $490.02.
So, compound interest = A - P
=> CI = $90.2
Hence, required value is $90.2.
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Complete question:
Principal $400 interest rate 7% compounded anually years 3. Calculate the compound interest three years.
given the following limit lim(x;y)!(0;0) xy x y , show that the function f (x; y) does not have a limit as (x; y) ! (0; 0).
To show that a function does not have a limit as (x, y) approaches (0, 0), we need to examine the limit along different paths .
How can we show that a function does not have a limit as (x, y) approaches (0, 0)?
To show that the function f(x, y) does not have a limit as (x; y) ! (0; 0), we need to examine the limit lim
(x;y)!(0;0) xy x y .
Convert the given limit into a more recognizable form. The given limit is
lim(x, y) -> (0, 0) (xy / (x + y)).
Analyze the limit along different paths. Let's examine the limit along two distinct paths - the
x-axis (y = 0)
and
the y-axis (x = 0).
For the x-axis (y = 0), the limit becomes
lim(x, 0) -> (0, 0) (x * 0 / (x + 0))
= lim(x, 0) -> (0, 0) (0) = 0.
For the y-axis (x = 0), the limit becomes
lim(0, y) -> (0, 0) (0 * y / (0 + y))
= lim(0, y) -> (0, 0) (0) = 0.
Compare the results of the two paths. Both limits along the x-axis and y-axis are equal to 0. However, this is not enough to conclude that the function f(x, y) has a limit as (x; y) ! (0; 0).
Examine another path, such as the line y = x. In this case, the limit becomes
lim(x, x) -> (0, 0) (x * x / (x + x))
= lim(x, x) -> (0, 0) (x^2 / 2x)
= lim(x, x) -> (0, 0) (x / 2)
= 0 / 2 = 0.
Consider another path, like
y = -x.
For this path, the limit becomes
lim(x, -x) -> (0, 0) (x * -x / (x - x))
which is undefined, since the denominator is zero.
Since we have found a path
(y = -x)
where the limit is undefined, we can conclude that the function f(x, y) does not have a limit as (x; y) ! (0; 0).
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what is the answer to 1.4(x+5) +1.6x=52
Answer: x = 15
Step-by-step explanation:
Expand 1.4(x+5): 1.4x+7+1.6x = 52
Combine like terms: 3x+7 = 52
Subtract 7 from both sides: 3x = 45
Divide both sides by 3: x = 15
Answer:
The answer is x=15
Please give me Brainliest :)
1. Expand the expression
1.4x+7+1.6x=52
2. Simplify
3x+7=52
3. Separate the constants and variables
3x=52−7
4. Add or subtract numbers
3x=45
5. Divide both sides by 3
6. Simplify
x=15
Over 9 days Jaison jogged ----- 10m, 6m, 6m, 7m, 5m, 7m, 5m, 8m, 9m
Find the mean distance Jaison jogged
The mean distance Jaison jogged over 9 days is 7 meters per day. This was calculated by adding up all the distances he jogged and dividing by 9.
To calculate the average distance that Jaison jogged over the 9 days, we used the formula for mean, which involves summing up all the distances he jogged and dividing by the total number of days. After adding up the distances, we found that the total distance Jaison jogged was 63 meters. Dividing this by the 9 days gives us an average distance of 7 meters per day. Therefore, Jaison jogged an average of 7 meters each day over the 9-day period.
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Hi I need help on this question It's teacher conferences week and I want to get this done before this week
Answer:
y = -3/8x + 3
Step-by-step explanation:
The slope intercept form is y = mx + b
Our equation is 3x + 8y = 24
3x + 8y = 24
8y = -3x + 24
y = -3/8x + 3
So, the answer is y = -3/8x + 3
Groups A, B, and C have means of 4, 6, and 8, respectively. There are 15 cases in total, with equal sample sizes in each group. SSwithin is 120. 16-7. For 16-4a, what is omega-squared? 0 .12 0.25 d .33 O2
Groups A, B, and C have means of 4, 6, and 8, respectively. There are 15 cases in total, with equal sample sizes in each group. Within is 120. 16-7. 16-4a, the value of omega-squared is 0.25.
What is omega-squared?
In statistics, omega-squared is a measure of effect size that can be used for one-way ANOVA to determine how much variance is due to the treatment or independent variable. It is calculated by dividing the between-group variance by the total variance, which includes both the within-group and between-group variance.
Omega-squared is used to determine the percentage of variance accounted for by a particular factor or treatment. It is represented as ω2 and ranges from 0 to 1, with higher values indicating a stronger relationship between the independent variable and the dependent variable.
The formula for omega-squared is as follows:
ω2=SSBetween / SSTotalSSWithin
= SSTotal - SS Between
Where SSTotal is the sum of squares for the total variance.SSBetween is the sum of squares between the groups, and within is the sum of squares within the groups.
The given information is:
Mean of group A = 4Mean of group
B = 6Mean of group
C = 8Total cases
= 15SSWithin
= 120
We can calculate the sum of squares between the groups as follows:
SSTotal = SSBetween + SSWithinSSTotal
= (nA + nB + nC - 1) × (σA² + σB² + σC²)SSBetween
= SSTotal - SS Within SS Between
= (3 - 1) × (42 + 62 + 82) - 120SSBetween
= 80 Next,
we can calculate the total variance as:
SSTotal = SSWithin + SSBetweenSSTotal
= 120 + 80SSTotal
= 200
Now, we can calculate omega-squared as follows:
ω2 = SSBetween / SSTotalω2
= 80/200ω2
=0.4
Hence, the value of omega-squared is 0.25.
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find the nth term of this quadratic sequence 4, 7, 12, 19, 28, . ..
Answer:
an = a1 + (n-1)d
Untuk barisan ini, kita dapat menentukan a1 = 4 dan d = 3, karena selisih antar suku bertambah 3. Jadi, rumusnya menjadi:
an = 4 + (n-1)3
a5 = 4 + (5-1)3
a5 = 4 + 12
a5 = 16
Jadi, suku ke-5 dari barisan ini adalah 16.
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How many sides has a polygon if the sum of its
interior angles is 1440⁰
Answer:
10 sides
Step-by-step explanation:
We can use the formula for the sum of the interior angles of a polygon to solve this problem. The formula for the sum of the interior angles of a polygon with n sides, where S is the sum of the interior angles, and n is the number of sides of the polygon is:
S = (n - 2) x 180 degrees
If the sum of the interior angles is 1440 degrees, we can set this equal to the formula and solve for n:
1440 = (n - 2) x 180
Dividing both sides by 180, we get:
8 = n - 2
Adding 2 to both sides, we get:
n = 10
Therefore, a polygon with a sum of interior angles of 1440 degrees has 10 sides.
Click to show the supplementary angle of each angle.
26∘
44∘
45∘
136∘
135∘
154∘
The supplementary angles of the given angles are 154 degrees, 136 degrees, 135 degrees, 44 degrees, 45 degrees, and 26 degrees, respectively.
Supplementary Angles of Given AnglesSupplementary angles are pairs of angles that add up to 180 degrees. To find the supplementary angle of each given angle, we simply subtract the angle from 180 degrees.
Therefore, the supplementary angles of the given angles are:
The supplementary angle of 26 degrees is 154 degrees (180 - 26 = 154).The supplementary angle of 44 degrees is 136 degrees (180 - 44 = 136).The supplementary angle of 45 degrees is 135 degrees (180 - 45 = 135).The supplementary angle of 136 degrees is 44 degrees (180 - 136 = 44).The supplementary angle of 135 degrees is 45 degrees (180 - 135 = 45).The supplementary angle of 154 degrees is 26 degrees (180 - 154 = 26).Therefore, the supplementary angles of the given angles are 154 degrees, 136 degrees, 135 degrees, 44 degrees, 45 degrees, and 26 degrees, respectively.
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For what values of c does the quadratic equatrion x^2-2x+c=0 have two roots of the same sign
The roots have positive or same signs when c>0.
Note that only real numbers can be positive or negative. This concept does not apply to complex non real numbers. So first we have to make sure that the roots are real which occurs when discriminant is greater or equal to 0.
[tex]b^{2} -2ac > 0\\2^{2} -2(-1) (c) > 0\\4-2c > 0\\c > -2[/tex]
Roots of quadrant equation have Samsame sign if product of roots >0.
[tex]\frac{a}{c} > 0\\\frac{c}{-1} > 0\\c < 0[/tex]
Roots of quadratic equation have positive sign if product of roots<0.
c>0.
Combining results, we get:-
roots have positive signs when:-
c>0.
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A statue casts a shadow that is 16 feet long. A nearby maple tree casts a shadow that is 10 feet long. If the statue is 20 feet tall, how tall is the maple tree, to the nearest tenth of a foot?
We can solve this problem by using proportions. 20/16 = x/10 => x = 12.5 Therefore, the height of the maple tree is approximately 12.5 feet, to the nearest tenth of a foot.
what is proportions ?
proportions are statements that two ratios or fractions are equal. A ratio is a comparison of two quantities, typically expressed as the quotient of one quantity divided by the other. For example, if we have 5 apples and 3 oranges, the ratio of apples to oranges is 5/3.
what is height ?
Height typically refers to the measurement of how tall or high something is, usually from its base to its top. In geometry, height is often used to refer to the perpendicular distance
In the given question ,
Let x be the height of the maple tree in feet. Then we have:
(height of statue) / (length of statue's shadow) = (height of maple tree) / (length of maple tree's shadow)
Substituting the given values, we get:
20/16 = x/10
on solving this equation, we can cross-multiply to get:
16x = 200 => x = 12.5
Therefore, the height of the maple tree is approximately 12.5 feet, to the nearest tenth of a foot.
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a cylindrical glass is half full of lemonade. the ratio of lemon juice to water in the lemonade is $1:11$. if the glass is $6$ inches tall and has a diameter of $2$ inches, what is the volume of lemon juice in the glass? express your answer as a decimal to the nearest hundredth.
The volume of lemon juice in the glass is 0.38 cubic inches.
Explanation:
Given,
Let the volume of the lemonade in the glass be V cubic inches
Therefore, the volume of lemon juice in the lemonade is [tex]$\frac{1}{12}$[/tex] V cubic inches
Volume of water in the lemonade is [tex]$\frac{11}{12}$[/tex] V cubic inches
The volume of the cylindrical glass is given by:
[tex]$V_{\text{cylindrical glass}} = \pi r^2h$[/tex]
Here,
Radius r = 1 inch
Height h = 6 inches
[tex]$V_{\text{cylindrical glass}} = \pi r^2h = \pi (1)^2(6) = 6 \pi$[/tex]
Since the glass is half full of lemonade, the volume of lemonade in the glass is:
[tex]$V_{\text{lemonade}} = \frac{1}{2}V_{\text{cylindrical glass}} = \frac{1}{2} 6 \pi = 3\pi$[/tex]
The volume of lemon juice in the lemonade is given by:
[tex]$V_{\text{lemon juice}} = \frac{1}{12}V$[/tex]
Therefore
[tex]$V_{\text{lemon juice}} = \frac{1}{12}3\pi = \frac{1}{4}\pi = 0.7854$[/tex] cubic inches
Hence, the volume of lemon juice in the glass is 0.38 cubic inches (rounded to the nearest hundredth).
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Find the area of the triangle.
3 in.
5 in
; 2.5 in.
6 in.
Answer:
We can use the formula for the area of a triangle which is given by:
Area = (1/2) x base x height
Where the base and height are the two sides that form the right angle.
Looking at the given triangle, we can see that the sides 3 in. and 5 in. form the right angle, so the base is 3 in. and the height is 5 in.
Therefore, the area of the triangle is:
Area = (1/2) x 3 in. x 5 in.
Area = 7.5 in²
Alternatively, we could also use the sides 2.5 in. and 6 in. to find the area of the triangle. In this case, the base would be 2.5 in. and the height would be 5 in. (since the 6 in. side is not perpendicular to the 2.5 in. side). So the area of the triangle would still be:
Area = (1/2) x 2.5 in. x 5 in.
Area = 6.25 in²
Either way, the area of the triangle is approximately 7.5 in² or 6.25 in², depending on which set of sides we use.
Step-by-step explanation:
solve for x.Figures are not necessarily drawn to scale
What is the volume of the prism below?
Answer:30
Step-by-step explanation: the formula is base x height over 2, so (6x10)/2 is 30.
The ratio of distance runners to sprinters on a track is 5:3 how many distance runners and sprinters could be on the track team
Runners and sprinters could be on the track team is 25 distance.
Distance:
Distance is a qualitative measurement of the distance between objects or points. In physics or common usage, distance can refer to a physical length or an estimate based on other criteria (such as "more than two counties"). The term Distance is also often used metaphorically to refer to a measure of the amount of difference between two similar objects.
According too the Question:
Based on the based Information:
15× 5÷3
canceling all the common factor, we get:
5 × 5 = 25
Now, the Product or Quotient is 25.
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3) One piece of fencing is 71/8 feet long. How long will a fence be that is made up of 9 of these pieces?
Answer:
Step-by-step explanation:
71/8*9 which it 639/8 feet long
Put the steps in correct order to prove that if n is a perfect square, then n + 2 is not a perfect square.1).Lets assume m ≥ 1.2) If m = 0, then n + 2 = 2, which is not a perfect square. The smallest perfect square greater than n is (m + 1)^2.3) Hence, n + 2 is not a perfect square4) Expand (m + 1)^2 to obtain (m + 1)^2 = m2 + 2m + 1 = n + 2m + 1 > n + 2 + 1 > n + 2.5) .Assume n = m2, for some nonnegative integer m
The following is the correct sequence of steps to prove that if n is a perfect square, then n + 2 is not a perfect square:
Step 1: Assume n = m², for some non-negative integer m.
Step 2: If m = 0, then n + 2 = 2, which is not a perfect square. The smallest perfect square greater than n is (m + 1)².
Step 3: Expand (m + 1)² to obtain (m + 1)² = m² + 2m + 1 = n + 2m + 1 > n + 2 + 1 > n + 2.
Step 4: Let's assume m ≥ 1.
Step 5: Hence, n + 2 is not a perfect square.
The first step in the sequence involves making an assumption to start the proof. The second step entails the derivation of the smallest perfect square greater than n. In the third step, we expand the (m + 1)² expression to get n + 2m + 1. The fourth step is an important one, as it shows that m must be greater than or equal to 1.
In the final step, we conclude that n + 2 is not a perfect square.
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