The average of first 50 numbers is 25.5 because average is computed by adding a set of numbers and then dividing by the total number of those numbers.
Why do you use the word "average"?The average of a list of data is a mathematical expression for the central value of a set of data. The ratio of all the data points to all the units in the list is how it is mathematically defined. The average of a specific set of numerical data is also referred to as the "mean" in statistics.
Which four sorts of averages are there?The four sorts of average that we recognize are mean, mode, median, and range. Although the others are our most popular "measures of central tendency," range is actually a measure of spread or distribution.
The first 50 natural numbers are 1,2,3,...,50
The sum of first n natural numbers = n(n+1)/2
Sum of first 50 natural numbers is 50(51)/2
=25(51)/2=1275
Hence, average of first 50 natural numbers is
1275/50
=25.5
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Line g pae through point (9, 9) and (1, 4). Line h i parallel to line g. What i the lope of line h?
Line g pae through point (9, 9) and (1, 4) and the slope of line h is 0.68.
The coordinates of line g are (9,9) and (1,4).
Substitute the values in the slope formula with (x1, y1) = (9,9) and (x2, y2) = (1, 4).
m = (y2-y1)/(x2-x1)
m = (4-9)/ (1-9)
m = (-5)/ (-8)
m = 0.68
the slope of the line g is 0.68
line h is parallel to line g so parallel lines have the same slope
slope of line h is 0.68
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The Collin Freight Company has an order for three products to be delivered to a
destination. Product I requires 10 cubic feet, weighs 10 pounds, and has a value
of $100. Product II requires 8 cubic feet, weighs 20 pounds, and has a value of $20.
Product III requires 20 cubic feet, weighs 40 pounds, and has a value of $200. If the
carrier can carry 6,000 cubic feet, 11,000 pounds, and is insured for $36,900, how
many of each product can be carried?
A , B, C are the amounts of each product
10A + 8B + 20C = 6000 <--- volume constraints
10A + 20B + 40C = 11000 <---- weight constraints
100A + 20B + 200C = 36900 <---- $$$$
What is product?Byproducts are things created in a process, typically one that is industrial or biological, in addition to the main result. A byproduct of the sugar refining process is sulfured molasses.
the first two equations together:
10A + 8B + 20C = 6000
10A + 20B + 40C = 11000
first is subtracted from second: 12B + 20C = 5000 3B + 5C = 1250 —- identifies this equation. ALPHA
Connect the second and third equations:
10A + 20B + 40C = 11000
100A + 20B + 200C = 36900
The top equation is multiplied by 10:
100A + 200B + 400C = 110000 —— Weight restrictions
100A + 20B + 200C = 36900 <—— $$$$
takes them away:
180B + 200C = 73100
18B + 20C = 7310
9B + 10C = 3655 —- identifies this equation. ALPHA BETA: BETA: 9B + 10C = 3655 3B + 5C = 1250
ALPHA is multiplied by 3:
9B + 15C = 3750
9B + 10C = 3655
takes them away:
5C = 95\s C = 95/5 = 19
Plugging into BETA yields the following results: 9B + 10(19) = 3655 9B = 3655 - 190 B = 385
Adds to the initial first equation:
10 A + 8(385) + 20(19) = 6000 A=254\s A=254\sB=385\sC=19
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Find the component form of the vector that translates A(-4,8) to A'(7,-9)
The component form of the vector that translates A to A' is (11, -17)
A translation is a type of transformation that takes each point in a figure and slides it the same distance in the same direction.
In translation, the shape of the figure does not change but its size may change.
Other transformation processes are reflection and rotation.
The component form of the vector is governed by the rule; A' - A
so we subtract corresponding x- coordinates and corresponding y- coordinates
A' - A = (7, -9) - (-4, 8)
= ( 7 - - 4, -9 - 8)
-= ( 11, -17)
In conclusion, the vector that translates A to A' is ( 11, -17 )
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Etimate each product. Then write whether the etimate i greater than or le than the actual product. There are 325 row of 9 chair in the theater. There are 102 chair in the balcony. About how many chair are there?
There are total 3027 chairs in the balcony and whole theater.
According to the Question,
There are total 325 rows, each rows have 09 chairs.
The number of chairs contains in theater are:
total number of rows × total chairs in rows
= 325 × 9 = 2925.
Again, there are additional 102 chairs in the balcony.
∴ 2925 + 102 = 3027
∴ There are total 3027 chairs in the whole theater.
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excel's binom.dist function can be used to compute . a. cumulative binomial probabilities b. binomial probabilities c. bin width for histograms d. binomial probabilities and cumulative binomial probabilities
Excel's binom.dist function can be used to compute both binomial probabilities and cumulative binomial probabilities
The Excel BINOM.DIST function returns the individual term binomial distribution probability. You can use BINOM.DIST to calculate probabilities that an event will occur a certain number of times in a given number of trials. BINOM.DIST returns probability as a decimal number between 0 and 1.
We use BINOM.DIST in problems with a fixed number of tests or trials, when the outcomes of any trial are only success or failure, when trials are independent, and when the probability of success is constant throughout the experiment.
For example, BINOM.DIST can calculate the probability that two of the next three babies born are male.
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In expression (-6)4 what is the power and exponent?
In the expression (-6)⁴, the power and exponent is 4
What is an exponent?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations. As an illustration, the expression x + y has the terms x and y with an addition operator between them.
The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.
In this case, the power or exponents us the number of times the number is raised which is 4.
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Estimate each product. then write whether the estimate is greater than or less than the actual product. there are 325 rows of 9 chairs in the theater. there are 102 chairs in the balcony. about how many chairs are there?
Estimate each product then write whether the estimate is greater than or less than the actual product.
= 3027 chairs are there.
There are 325 rows of 9 chairs in the theater.
There are 102 chairs in the balcony.
The total number of chairs there are in the theater and balcony is equal to 3027 chairs.
According to the question;
There are 325 rows in the theater.
Each row contains 9 chairs.
Additionally, there are 102 chairs in the balcony.
In essence, the number of chairs in the theater is;
= 325 × 9
= 2925 chairs.
Additionally, there are 102 chairs in the balcony;
In essence, the total number of chairs is;
= 2925 + 102
= 3027 chairs.
Hence the answer is, = 3027 chairs are there.
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please help me with this math problem
Answer:
(7/15)
Step-by-step explanation:
2 1 10 3 7
------- - ------- = ------- - ------- = -------
3 5 15 15 15
I hope this helps!
What is the area of a rectangle ABCD with vertices at
A(-1, 11)
B(7, 9)
C(10, 13)
D(2, 7)
The Area of the rectangle is 32 square units
Finding the Area of Rectangle with vertices:The area of the rectangle can be defined as 'the region covered by the rectangle in a 2-D plane. The formula for the area of the Rectangle or the Quadrilateral with vertices is given below
Area of Quadrilateral
= (¹/₂) | x₁y₂+ x₂y₃+ x₃y₄ +x₄y₁ - (x₂y₁ +x₃y₂ +x₄y₃ +x₁y₄) |
Where (x₁, y₁); (x₂, y₂); (x₃, y₃) and (x₄, y₄) are vertices of the quadrilateral
Here we have
Vertices of rectangle are A(-1, 11), B(7, 9), C(10, 13) and D(2, 7)
If we draw the given vertice in a graph then the order of the sides will be 'ACBD' [ For more understanding observe the given figure ]
From the above formula,
Area of rectangle
= (¹/₂) | (-1)(13) + (10)(9) + (7)(7) + (2)(11) - [ (10)(11)+(7)(13) +(2)(9) +(-1)(7) ] |
= (¹/₂) | -13 + 90 +49 + 22 - [ 110+ 91 + 18 - 7 ] |
= (¹/₂) | -13 + 90 +49 + 22 - [ 110+ 91 + 18 - 7 ] |
= (¹/₂)(64)
= 32 Square units
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explain how a number line can be used to compare two negative integers.
On a number line, plot the negative integers. The number that is further to the left will be less than the other.
What is the number?A number is a mathematical entity that can be used to count, measure, or name things. For example, 1, 2, 56, etc. are the numbers.
We have to explain how a number line can be used to compare two negative integers.
Integers are whole numbers they can be negative whole numbers or positive whole numbers for example 2, 4, 1, -8, 0, etc.
Plot the negative integers on a number line. It will be smaller than the other number if it is further to the left.
The numbers always go up (become "more positive") to the right and down (become "more negative") to the left on a number line. Numbers to the right are bigger than numbers to the left, and the opposite is true the other way around.
Thus, on a number line, plot the negative integers. The number that is further to the left will be less than the other.
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What’s 55 divided by 50,325?
Answer:
Step-by-step explanation:
0.0010928961748634
but 50,325 divided by 55 is 915
Find the value of r so the line that passes through the pair of points has the given slope.
(12, 10), (−2, r), m=−4
Based on the concept of the slope intercept form, the value of r is 66.
Slope intercept form:
The general formula to calculate the slope intercept form equation is written as,
y = mx + c
where
(x, y) represents the point
m represents the slope
c represents the y-intercept.
Given,
Here we know the pair of points (12, 10), (−2, r) and the value of slope which is m = -4.
And we need to find the value of r.
We know that the formula for of the slope intercept form is
y = mx + c
So, we have to use the slope and the point (12, 10), to find the intercept of the line,
When we apply the value on the formula, then we get,
=> 10 = -4(12) + c
=> 10 = -48 + c
=> c = 58
Therefore, the slope intercept form equation is written as
=> y = -4x + 58
Now, we have to find the value of r, by apply the point (-2,r) on the equation, then we get,
=> r = -4(-2) + 58
=> r = 8 + 58
=>r = 66
Therefore, the value of r for the given pair of points is 66.
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5x + 3x + 7 which expressions are equal to it 15x +7 , 8x+ 7 ,15x , 5x+ 10
Answer:
8x + 7
Step-by-step explanation:
5x + 3x = 8x
A line has a slope of 1/7 and includes the points (0,–4) and (u,–5). What is the value of u?
Answer:
u : -7
So the points are (0,-4) and (-7,-5)
Slope: 1/7
Which statement explains whether 0.1515 is rational?
A Yes, because 0.1515 is a repeating decimal, so it can be expressed as a ratio of integers.
B Yes, because 0.1515 is a terminating decimal, so it can be expressed as a ratio of integers.
(c) No, because 0.1515 is a repeating decimal, so it cannot be expressed as a ratio of integers.
D No, because 0.1515 is a terminating decimal, so it cannot be expressed as a ratio of integers.
A statement that explains whether 0.1515 is rational: Yes, because 0.1515 is a repeating decimal, so it can be expressed as a ratio of integers.
The correct answer is an option A
We need to select a correct statement that explains whether 0.1515 is rational.
We can observe that 0.1515 is the recurring decimal 0.15
This decimal can be written as a ratio of two integers.
Consider numerator = 5 and the denominator = 33.
So, 5/33 = 0.1515..
This means, 0.1515 can be expressed as p/q where p, q are integers with q ≠ 0
Therefore, a statement that explains whether 0.1515 is rational: Yes, because 0.1515 is a repeating decimal, so it can be expressed as a ratio of integers.
The correct answer is an option A
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A rectangular box which i open at the top can be made from an 12-by-30-inch piece of metal by cutting a quare from each corner and bending up the ide. Find the dimenion of the box with greatet volume, where h = height, l = length, and w = width. (Note: let the width be determined by the 12-inch ide and the length by the 30-inch ide. )
The dimension of the box with greatest volume is h = 2.64 in, l = 24.72 in, and w = 6.72 in.
If squares of equal sizes are to be cut out from the four corners so the four sides can be bent upwards, then the length of these squares will be the height of the box. Also twice of this length subtracted from the initial length and width of the material will be the new length and width of the box, respectively.
let x = length of square to be cut = height of the box
length of the box = 30 - 2x
width of the box = 12 - 2x
The volume of the box, which is a rectangular prism, is the product of the length, height and width.
V = l x w x h
V = (30 - 2x)(12 - 2x)(x)
V = 360x - 84x² + 4x³
To obtain the largest volume possible, the first derivative of the volume should be equal to zero.
V'(x) = 0
V = 360x - 84x² + 4x³
360 - 168x + 12x² = 0
Simplify and solve for the value of x.
360 - 168x + 12x² = 0
x² - 14x + 30 = 0
x = 7 ± √19
x₁ = 11.35
x₂ = 2.64
Check each value.
When x = 11.35 = h
l = 30 - 2x = 7.3
w = 12 - 2x = -10.7 (dimension should be positive)
When x = 2.64 = h
l = 30 - 2x = 24.72
w = 14 - 2x = 6.72
Hence, the length of square to be cut is 2.64 in.
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how many two-digit prime numbers can be formed by choosing two different digits from the set $\{2, 7, 8, 9\}$ to be used as the tens digit and units digit?
Two digit prime numbers formed by choosing two different digits from the given {2,7,8,9} set of numbers are 97, 29, 79, 89.
As given in the question,
Given set of numbers are :
{ 2,7,8,9}
Two digit prime numbers formed by given set of numbers are as follow:
When 2 and 8 are at unit place, number formed is a even composite number which is not prime.
Number formed when 7 at unit place are:
27, 87, 97 from which only 97 is prime.
Number formed when 9 at unit place are:
29, 79, 89 all three are prime numbers.
Therefore, two digit prime numbers formed by choosing two different digits from the given {2,7,8,9} set of numbers are 97, 29, 79, 89.
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Evaluate x³ + 16 ÷ 4 for x = 2
Answer: 6
Step-by-step explanation:
2x2=4x2=8
8+16=24
24÷4=6
You traveled 300 miles the first day of your trip and then drove 60mph after this day.
Write an equation in slope intercept form to represent the situation.
The slope intercept form of the given situation is:
y = 60x+300
Given,
You traveled 300 miles the first day of your trip and then drove 60mph after this day.
we are asked to determine the slope intercept form of the given situtation.
we know the slope intercept form as:
y = mx+c
we know that at first day we traveled = 300 miles
then after that the graph declines to 60 miles per hour
y = 60x+300
Hence we get the equation as y = 60x+300
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Given line segment GH is a mid segment of triangle DEF
Find value of x and y
What is the length of line segment DF?
The value of x and y for the triangle is 17 units and 2 units respectively. The length of side DF is 20 units.
What is the midsegment theorem in a triangle?A triangle's midsegment is a line segment that connects the midpoints or centers of two of its opposite or adjacent sides.
According to the midsegment theorem, every line segment joining any two triangle sides' midpoints is parallel to and comprises half of the third side.
DH is the midsegment of the triangle DEF, so the value of x can be given by
(1/2)(28) = x -3
x - 3 = 14
x = 14 + 3
x = 17 units
As given, x - 7 = y + 8. So, put x = 17 in it
17 - 7 = y + 8
10 = y + 8
y = 10 - 8
y = 2 units
The side DF = DH + HF
DF = y + 8 + x - 7
= 2 + 8 + 17 - 7
= 10 + 10
= 20 units
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Solve for x given the triangle above?
Answer:
Step-by-step explanation:
you can find out the answer by subtracting 48 by 32, and if that number(16) times 3 equals 48( which it does) Then you know you are in the good.
can someone pls helppp!!!!!!
Answer:
(a) 2x + x + 39 = 90
(b) m<1 = 34°; m<2 = 56°
Step-by-step explanation:
Use the angle addition postulate. Angles 1 and 2 add to a right angle. A right angle has a measure of 90°.
(a) m<1 + m<2 = 90
2x + x + 39 = 90
(b)
Solve the equation for x.
2x + x + 39 = 90
3x = 51
x = 17
Use the value of x to find the angle measures.
m<1 = 2x = 2(17) = 34
m<2 = x + 39 = 17 + 39 = 56
Answer:
a.) 3x+39=90
b.) ∠1=34°
∠2=56°
Step-by-step explanation:
According to the graph, ∠1 + ∠2=90°.
∠1=2x and ∠2=x+39
So,
[tex]2x+(x+39)=90\\2x+x+39=90\\3x+39=90\\3x=51\\x=17[/tex]
Rewrite the equations for the two angles substituting 17 for x.
∠1=[2(17)]°=34° and ∠2=[(17)+39]°=56°
A sign at the store says 3 orange’s cost 2.25$ how much would one orange cost.
If 3 oranges cost 2.25$ then the cost of 1 orange is $0.83.
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
Given, A sign at the store says 3 oranges cost 2.25$.
So, The cost of one orange can be obtained by dividing the total cost by the total no. of oranges which is,
= $(2.25/3).
= $0.83.
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The mean of this set of data {23, 30, 27, 30, 20} is
Answer: 26
Step-by-step explanation:
I always look at it like mean is mean because you have to do two steps.
Step one - add them all up 23 +30+ 27+ 30+ 20= 130
Step two - Divide that number (130) by the number of numbers ( that would be 5) EXAMPLE -- 23 is one 30 is two and so on
Sadira estimated the solution of a system of equations is approximately (–3.7, 2.2). What can be concluded of the graph that represents the system of this solution? Check all that apply.
The x-coordinate of the intersection point is between 2 and 3.
The y-coordinate of the intersection point is between 2 and 3.
The y-coordinate of the intersection point is between –3 and –4.
The x-coordinate is closer to –4 than –3.
The y-coordinate is closer to –4 than –3.
Using the solution of system of equations, the y- coordinate of intersection point is between 2 and 3 and the x - coordinate is closer to -4 than -3
System of EquationsIn algebra, a system of equations comprises two or more equations and seeks common solutions to the equations. "A system of linear equations is a set of equations which are satisfied by the same set of variables."
In the question given, we are told the system of equation have a solution of (-3.7, 2.2).
What this implies is that the value of x and y are 3.7 and 2.2 respectively.
In the options given;
The y - coordinate of the intersection point is between 2 and 3The x - coordinate is closer to -4 than -3Learn more on system of equations here;
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Answer:
B) The y-coordinate of the intersection point is between 2 and 3.
D) The x-coordinate is closer to –4 than –3.
Step-by-step explanation:
Match the correlation coefficients with the scatterplots shown below! Will give brainliest to correct answer!
The scatterplot and their corresponding correlation coefficient are as follows;
Scatterplot [tex]{}[/tex] Correlation coefficient
Scatterplot A [tex]{}[/tex] r = -0.42
Scatterplot B [tex]{}[/tex] r = -0.85
Scatterplot C [tex]{}[/tex] r = 0.64
Scatterplot D [tex]{}[/tex] r = 0.86
What is a correlation coefficient?The correlation coefficient is an indication of the strength of a linear relationship that is used to model an observed dataset.
The value of the correlation coefficient ranges from -1 to 1, with a positive correlation indicating that both variables increases proportionately, and a negative correlation indicating that as one variable increases the other decreases.
A low value of the correlation coefficient indicating that there is a weak relationship between the variables such that the prediction of the output from the input has a low reliability.
The scatterplot D shows the strongest correlation, which indicates that it has the highest correlation coefficient of 0.86The scatterplot B also has a strong negative correlation such that as the input variable increases, the output decreases corresponding to r = -0.85The scatterplot A has a weak relationship as the points are scattered on the graph, however, as the output values increase, the input decreases indicating a negative correlation coefficient, which corresponds to the option, r = -0.42The scatterplot C has a week positive correlation, therefore, the scatterplot C corresponds to the option, r = 0.64Learn more about the correlation coefficient here:
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The correlation coefficients that matches the scatterplots are as follows;
Scatterplot A; r = -0.42
Scatterplot B; r = -0.85
Scatterplot C; r = 0.64
Scatterplot D; r = 0.86
How to interpret the correlation coefficient?The correlation coefficient is defined as a statistical measure of the strength of a linear relationship that exists between two variables. Its' values can range from -1 to 1.
Now, a correlation is considered to be a positive correlation when both variables increases or decreases in tandem which is the same direction. Meanwhile, a negative correlation is defined as on whereby one variable increases as the other decreases.
Now, the farther away the data points are from each other the greater the value of the correlation coefficient and vice versa.
The scatterplot A is a negative correlation because the output increases as the input decreases and vice versa. This is more scattered than the other negative correlation; r = -0.42
The scatterplot B also has a stronger negative correlation than scatter plot A since r = -0.85
The scatterplot C has a positive correlation, but not so strong as seen by the spacing of the scatter dot points. Thus, the scatterplot C has a correlation coefficient of r = 0.64
The scatterplot D has a stronger positive correlation coefficient than C as seen in the dot scatter points and as such its' correlation coefficient is 0.86
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An orange grower harvested oranges from 4 acres of land and collected 720 bushels of oranges. The next day, the farmer harvested oranges from 7 acres of land and collected 1,260 bushels of oranges.
Is there a proportional relationship between the number of bushels of oranges collected and the number of acres harvested over the two days? Explain.
No, it is not proportional because both variables cannot be zero at the same time.
No, it is not proportional because all ratios between the number of bushels collected and the number of acres harvested are not equivalent.
Yes, it is proportional because the farmer collected 18 bushels for every 1 acre harvested.
Yes, it is proportional because the farmer collected 180 bushels for every 1 acre harvested.
Answer:
(d) Yes, it is proportional because the farmer collected 180 bushels for every 1 acre harvested.
Step-by-step explanation:
You want to know if the ratios 4 acres : 720 bushels and 7 acres : 1260 bushels represent a proportional relationship.
ProportionA relationship is proportional if the ratio of the dependent variable to the independent variable is a constant. We can check this for the numbers given:
(720 bu)/(4 ac) = 180 bu/ac
(1260 bu)/(7 ac) = 180 bu/ac
The ratios are the same, 180 bushels for each acre, so the relationship is proportional.
Answer:
(d) Yes, it is proportional because the farmer collected 180 bushels for every 1 acre harvested.
Step-by-step explanation:
I took the exam and got it right
what is the slope of the line?
Answer:
The slope is 2/3
Step-by-step explanation:
y is 4 and x is 6 so it will be 4/6 then divide 2
4:2 = 2
6:2 = 3
2/3
At a local prechool there i a ratio of 3 boy to every 4 girl. If there are 245 total prechooler how many are boy
If there are 245 total preschoolers, there will be 105 boys.
What is unitary method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. What can be values and units.Let's say you go to the store to buy six apples. You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples.Recognizing the units and values is crucial when using the unitary technique to a problem.Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things. We are aware of the quantity of apples and the amount of money in the aforesaid problem.acc to our question-
Fraction of boys = 3/7Fraction of girls = 4/7Total number of students = 245The number of boys will be:= 3/7 × 245.= 105 boysTherefore, there are 105 boys in the school.
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Can someone please fill in blank ASAP
Answer:
The quotient is 48.
Step-by-step explanation:
Estimate the quotient using compatible numbers:
45 (or I guess any number close the answer above, not sure tbh)
Multiply the estimate by 21:
945
45*21
Is the estimate to high or too low?
too low
Adjust and continue until the product is 1008.
1008/21=48
Have a good day/evening! I hope my answer is correct!
