the factors of 28 are : 1, 2, 4, 7, 14, and 28.
the prime factors of 28 are : 2, 2, and 7.
which of the following is an example of a paired design? question 7 options: a teacher compares the scores of students in her class on a standardized test with the national average score. a teacher compares the pre-test and post-test scores of students. a teacher calculates the average score of students on a pair of tests and wishes to see if this average is larger than 80%. a teacher compares the scores of students using a computer-based method of instruction, with the scores of other students using a traditional method of instruction. question 8 (1 point)
The statement “A teacher compares the pretests and posttest scores of students” is an example of matched pairs design.
Given data;
A teacher contrasts the results of her class's standardized test with the entire country's results. An instructor contrasts the results of the students' pre-and post-tests. A teacher computes the average grade received by students on two tests and checks to see if it is greater than 80%. An instructor contrasts the results of students who were taught using a computer-based method with those of post-students whose students ought to use a more conventional approach.
⇒
The statement “A teacher compares the pretests and posttest scores of student” using here would be approach-test because the sample “the students’ scores” are being compared with the two different treatments” and pretest and posttest scores.
A matched pairs design is demonstrated with the sentence "A teacher compares the pretests and posttest scores of students."
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the food and drug administration (fda) is a u.s. government agency that regulates (you guessed it) food and drugs for consumer safety. one thing the fda regulates is the allowable insect parts in various foods. you may be surprised to know that much of the processed food we eat contains insect parts. an example is flour. when wheat is ground into flour, insects that were in the wheat are ground up as well. the mean number of insect parts allowed in 100 grams (about 3 ounces) of wheat flour is 75. if the fda finds more than this number, they conduct further tests to determine if the flour is too contaminated by insect parts to be fit for human consumption. the null hypothesis is that the mean number of insect parts per 100 grams is 75. the alternative hypothesis is that the mean number of insect parts per 100 grams is greater than 75. is the following a type i error or a type ii error or neither?
Since in the question we reject the alternative hypothesis hence type II error occurs.
What is Type I error?
When the null hypothesis is true but rejected in hypothesis testing, type 1 errors often confused with false positives occur. A general assertion or default attitude that there is no connection between two measurable phenomena is known as the null hypothesis.
What is Type II error?
Type II errors take place when you fail to reject the null hypothesis even though it is untrue.
The average number of insect parts per 100 gm in this problem is 75. This number cannot be demonstrated by the test to be larger than 75. This indicates that the test is producing a "false negative" since it is not detecting these insect parts.
Hence, this is a Type II error.
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What is meant by the degree of a function?
Answer:
The highest power of a variable in a function is known as its degree.
Step-by-step explanation:
Examples:
x + 5 is 1st degree, since x is to the power of 1.
5[tex]x^{3}[/tex] + 3x + 5 is 3rd degree.
[tex]x^{21}[/tex] +99 is 21st degree.
If 6s = 24, does 6s ÷ 6 = 24 ÷ 6? Why or why not?
Answer:
Yes.
Step-by-step explanation:
if 6s=24, s = 4 because 6 x 4 = 24
so
6s divided by 6 = 24 divided by 6 because 6 x s = 24
SOO
24 divided by 6 = 24 divided by 6
Graph the solution of the inequality 2x - (3-x) > x + 1 on the number line.
Ο Α.
-5 -4 -3 -2 -1 0 1
OB.T
0 с.
2
+
-5 -4 -3 -2 -1 0 1 2
F
OD. |▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬
+ +
3
10Ø|||
-5 -4 -3 -2 -1 0 1 2 3
-5 -4 -3 -2 -1 0 1 2
+43
3
4 5
14
4 5
++
4 5
+
4 5
The solution of the inequality 2x - (3 – x) > x + 1 is the values greater than 2.
From the question, we have
2x -3+x>x+1
⇒3x-3>x+1
Subtract x from both sides, we get
⇒3x-3-x>x+1-x
⇒2x-3>1
⇒2x>4
⇒ x > 2
The solution of the inequality 2x - (3 – x) > x + 1 is the values greater than 2.
Subtraction:
Subtraction serves as a representation for the act of removing items from a collection. The negative symbol stands for subtraction. For example, if four of the nine oranges that are stacked together (as in the above illustration) are then transported to a basket, the stack will now contain five oranges rather than nine. Therefore, the difference between 9 and 4 is 5, which equals 9 minus 4. In addition to applying it to natural numbers, subtraction can also be used with other kinds of numbers. The letter "-" represents subtraction. Minuend, subtrahend, and difference are the three numerical components that make up the subtraction operation.
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HELP ME ASAP!! PLEASEEE I GOTTA SUBMIT THIS IN 6 MINUTES
The domain and range of the function is given by D:{x|∞<x<∞} and
R:{y|∞<y<∞}
In the given graph we can see that the graph is of straight line .
We know that the straight line graph of the function is of the form
y = mx + c
Now we can say that the graph of the given function is of that form.
The graph passes through (-7,0) and (-5,3)
Slope of the line= 3 / 2
Equation of the line is
y-3 = -3/2(x+5)
or, 2y+3x+9 = 0
Here the domain will be all possible values of x and range will be all possible values of y.
Domain : {x|∞<x<∞}
Range : {y|∞<y<∞}
A function's domain and range are its constituent parts. A function's range is its potential output, whereas its domain is the set of all possible input values.
A is the domain and B is the co-domain if a function f: A →B exists that maps every element in A to an element in B. 'b', where (a,b) R, provides the representation of an element 'a' under a relation R.
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Which of the following is true of prime numbers?
A.
A prime number may be an even number or an odd number.
B.
A prime number is always an even number.
C.
A prime number is always an odd number.
D.
A composite number may be an even number or an odd number.
Answer:
a is right (prime number is always a even number)
Answer:
A.
a prime number may be an even or an odd number
Suppose that F(x) = x² and G(x) = -1/4 (x+7)². Which statement best compares
the graph of G(x) with the graph of F(x)?
A. The graph of G(x) is the graph of F(x) stretched vertically, flipped
over the x-axis, and shifted 7 units to the right.
B. The graph of G(x) is the graph of F(x) stretched vertically, flipped
over the x-axis, and shifted 7 units to the left.
C. The graph of G(x) is the graph of F(x) compressed vertically,
flipped over the x-axis, and shifted 7 units to the right.
OD. The graph of G(x) is the graph of F(x) compressed vertically,
flipped over the x-axis, and shifted 7 units to the left.
The statement that best compares the graph of G(x) with the graph of F(x) is the graph of G(x) is the graph of F(x) compressed vertically, flipped over the x-axis, and shifted 7 units to the left.
According to the question,
We have the following information:
F(x) = x² and G(x) = -1/4 (x+7)²
Now, the graph of G(x) will be the graph of F(x) but there will be certain changes in the graph according to its function.
Now, in this function, 7 is added to x then it means that it will shift 7 units to left.
There is a negative sign before the function which says that is flipped over the x-axis.
Now, the factor 1/4 in the multiplication says that it has been compressed.
Hence, the correct option is D.
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Sami made $23,400 last year in income from his job. He worked 30 hours per week and worked all 52 weeks of the year, What was his hourly pay
rate?
Sami made !
per hour and $
per week.
So, lets think about the information we are given.
Sammy earns 23,400 in a given year.
In a year, he works 52 weeks.
Per week, he works 30 hours.
Find hours -> find pay.
To find hours, multiply number of weeks by hours
52 * 30 = 1560
He works 1560 hours per year.
To find hourly income, divide total money per year by hours per year. He makes 15 dollars per hour.
Find $ per week.
Hourly rate by hours per week
15 * 30 =450 per week
Hope this helps :)
Answer:
Sami had an hourly pay rate of $15 an hour
Step-by-step explanation:
Multiply 52 by 30 and you get 1,560, this is the total number of hours sami worked in a year.
If Sami made $23,400 in one year and worked 1,560 hours, you divide the total amount of hours work and total amount of money made to get an hourly pay rate of $15 an hour.
If LEFH= (2x + 2)° and its complement
LHFI = (x+1), then what is the value of x?
If ∠EFH and ∠HFI are complementary angles,∠EFH = (2x + 2)° and ∠HFI= (x+1), the measure of x will be 29°.
What is an angle?When two lines or rays converge at the same point, the measurement between them is called an "Angle."
It is given that, ∠EFH and ∠HFI are complementary angles,∠EFH = (2x + 2)° and ∠HFI= (x+1),
Complementary angles are those where the sum of the two angles is 90 degrees. In other words, two angles are considered complementary if they combine to form a right angle. The two angles are said to complement one another in this context.
Since ∠EFH and ∠HFI are complementary angles,
∠EFH + ∠HFI = 90
(2x + 2)+ (x+1) =90
3x+3=90
x+1=30
x=29°
Thus, if ∠EFH and ∠HFI are complementary angles,∠EFH = (2x + 2)° and ∠HFI= (x+1),the measure of x will be 29°.
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ons
gr...
Complete the equation of the line through (-8, 8) and (1,-10).
Use exact numbers.
[tex](\stackrel{x_1}{-8}~,~\stackrel{y_1}{8})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{-10}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-10}-\stackrel{y1}{8}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{(-8)}}} \implies \cfrac{-18}{1 +8} \implies \cfrac{ -18 }{ 9 } \implies - 2[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{8}=\stackrel{m}{- 2}(x-\stackrel{x_1}{(-8)}) \implies y -8 = - 2 ( x +8) \\\\\\ y-8=-2x-16\implies {\Large \begin{array}{llll} y=-2x-8 \end{array}}[/tex]
11 Find the value of x.
(x+8)
fo
-(6x-58)
12 FT
2. Use the areas of the two identical squares to explain why 5² + 12² = 13² without
doing any calculations.
The equation can be proved by taking Pythagorean Triplets into consideration, therefore 5^{2} + 12^{2} = 13^{2}
What are Pythagorean Triplets?
The "Pythagorean Triple" is a collection of three positive numbers, a, b, and c, that satisfy the following rule:
a^{2} + b^{2} = c^{2}
From the figure two in the attached image it can be very well observed that 5,12 and 13 are making a pythagorean triplets, therefore it can be said 5^{2} + 12^{2} = 13^{2}
Hence Proved.
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For his phone service, Chang pays a monthly fee of $27, and he pays an additional $0.07 per minute of use. The least he has been charged in a month is
$121.71.
What are the possible numbers of minutes he has used his phone in a month?
Use m for the number of minutes, and solve your inequality for m.
1353 numbers of minutes he has used his phone in a month.
What do you mean by algebraic expression?
In mathematics, an algebraic expression is an expression composed of integer constants, variables, and algebraic operations (addition, subtraction, multiplication, division, and exponentiation by exponents that are rational numbers).
Algebraic equations are equations that contain only algebraic expressions.
Algebraic expression is the idea of using letters or alphabets to represent numbers without specifying the actual value. Algebra Basics taught us how to use letters like x, y, and z to represent unknown values. These characters are called variables here.
It is given that Chang pays a monthly fee of $27, and he pays an additional $0.07 per minute of use.
Let m be the additional minutes
Then charge for additional minutes is $0.07m
Now , it is also given that least he has been charged in a month is
$121.71.
⇒ 0.07m + 27 = 121.71
⇒ 0.07m = 121.71 - 27
⇒ 0.07m = 94.71
⇒ m = 94.71/0.07 = 1353
Therefore, 1353 numbers of minutes he has used his phone in a month.
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A farmer wants to fence an area of 24 million square feet in a rectangular field and then divide it in half with a fence parallel to one of the sides of the rectangle. What should the lengths of the sides of the rectangular field be (in ft) in order to minimize the cost of the fence? smaller value ft larger value ft.
The lengths of the sides of the rectangular field in order to minimize the cost will be length = 6000 feet and width = 4000 feet .
In the question ,
it is given that ,
the area that farmer need to fence = 24 million square feet
let the length of field be [tex]=[/tex]"x" and
let the width of rectangular field be [tex]=[/tex]"y" .
So , the area of the rectangular field = x.y = 24
So , y = 24/x .
given that the field is divided into half ,
So , the required fencing will be
S = 2x + 3y
Substituting y = 24/x in the equation,
we get ,
S = 2x + 3(24/x)
S = 2 + 72/x
Differentiating the equation "S [tex]=[/tex] 2 [tex]+[/tex] 72/x" with respect to "x" ,
dS/dx = 2 - 72/x²
to minimize the cost of fencing , we equate ds/dx to 0 ,
we get
2 - 72/x² = 0
x² = 36 million feet
x² = 36000000
x = 6000 feet
and y = 24/x = 24million/6000
= 24000000/6000
= 4000 feet
Therefore , The length of the rectangular field is 6000 feet and the width of the rectangular field is 4000 feet .
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An element with a mass of 200 grams decays by 15.7% per minute. To the nearest minute, how long will it be until there are 60 grams of the element remaining?
Answer:
3.82%
Step-by-step explanation:
Triangle ABC ~ Triangle DEF. Triangle ABC has
side lengths of 7, 9, and II. Triangle DEF has side
lengths of 17.5, 22.5, and x. Find the length of the
longest side of triangle DEF
192.5 the length of the longest side of triangle DEF .
What do you mean by congruent?
It is claimed that two figures are "congruent" if they can be positioned exactly over one another. Both the shape and size of the bread slices are same if you lay one slice on top of the other. Congruent refers to having precisely the same shape and size.Triangle ABC ~ Triangle DEF.
SO, both triangle sides are equal .
7/17.5 = 9/22.5 = 11/x
1/17.5 = 11/x
x = 11 * 17.5
x = 192.5
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28/63 en la forma más simple
plss ayuda para que suba al 70% en el khann
The value of the fraction 28/63 in the simplest form is 4/9.
What is a fraction?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.
In this case, we want to reduce 28/63 yo the simplest term. This will be illustrated thus:
= 28/63
= (7 × 4) / (9 × 7)
= 4 / 9
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How do you approximate on a calculator?
Answer:
enter a function and from there you approximate hope it helps
Simplify (4x to the power of 3) power of 2
The correct answer is: " 4096 x⁶ " .
Step-by-step explanation:
Given: [(4x)³] ² ; Simplify.
Method 1)
Note the following multiplication property of exponents:
⇒ (aᵇ)ᶜ = a⁽ᵇ*ᶜ⁾ ;
As such:
[ [(4x)³] ² = (4x)⁽²ˣ³⁾ = (4x)⁶ ;
Now; note the following property of exponents:
(ab)ᶜ = aᶜ * bᶜ ;
As such: (4x)⁶ = 4⁶ * x⁶ ;
Now; we can simplify 4⁶ ; by using a calculator:
→ 4⁶ = 4096 ;
Or: 4⁶ = 4 * 4 * 4 * 4 * 4 * 4 ;
= (4 * 4) * 4 * 4 * 4 * 4 ;
= 16 * 4 * 4 * 4 * 4 * ) ;
= (16 * 4) * 4 * 4 * 4 ;
= 64 * 4 * 4 * 4 ;
= (64 * 4) * 4 * 4 ;
= (126 * 4) * 4
= (256) * 4 ;
= 4096 .
_______
or: 4⁶ = 4 * 4 * 4 * 4 * 4 * 4 ;
= (4 * 4) * (4 * 4) * (4 * 4) ;
= 16 * 16 * 16 ;
= (16 * 16) * 16 ;
= (256) * 16 , = 4096.
_______
So: [(4x)³] ² = 4⁶ * x⁶ = 4096 x⁶ ;
_______
Method 2) Given: [(4x)³] ² ;
(4x)³ = 4x * 4x * 4x ;
[(4x)³]² = (4x * 4x * 4x)²
= (4x * 4x * 4x) * (4x * 4x * 4x) ;
= (4 * 4 * 4 * x * x * x * 4 * 4 * 4 * x * x * x ;
= 4 * 4 * 4 * 4 * 4 * 4 * x * x * x * x * x * x ;
⇒ (4 * 4 * 4 * 4 * 4 * 4) = 4⁶ = 4096 ; (see Method 1 above).
⇒ (x * x * x * x * x * x) = x⁶ ;
⇒ [(4x)³] ² = 4⁶ * x⁶ = 4096 x⁶ ;
_______
Method 3)
[(4x)³] ² = (4x)⁽²ˣ³⁾ = (4x)⁶ ;
(4x)⁶ = 4x * 4x * 4x * 4x * 4x * 4x ;
= 4 * 4 * 4 * 4 * 4 * 4 * x * x * x * x * x * x ;
= (4 * 4 * 4 * 4 * 4 * 4) * (x * x * x * x * x * x) ;
⇒ (4 * 4 * 4 * 4 * 4 * 4) = 4⁶ = 4096 ; [see Method 1 above].
⇒ (x * x * x * x * x * x) = x⁶ ;
⇒ [(4x)³] ² = 4⁶ * x⁶ = 4096 x⁶ .
_______
The correct answer is: " 4096 x⁶ " .
_______
Hope this is helpful.
Best wishes in your academic endeavors!
_______
Answer:
Simplify (4x to the power of 3) power of 2
Step-by-step explanation:
The school I go to tells me to do this:
(4x^3)^2
(4x^3)(4x^3)
(4)(4) - 16
(x^3)(x^3) - x^6 bc you add the exponents
16x^6 which is correct bc my teacher has checked us on that before in class bc we have had equations like that ^_^
Help please! 50 Points
A runner is training for a marathon. The first week, she runs 4 miles during each training session. Each week, she increases her distance by 1.5 miles. Write a recursive definition for this sequence and use this definition to find her training distance in the tenth week.
17.5 miles is the runner training distance in the tenth week.
What is Sequence?A sequence is an enumerated collection of objects in which repetitions are allowed and order matters.
Given,
The first week, she runs 4 miles during each training session
Each week, she increases her distance by 1.5 miles.
4,5.5,7,8.5....
The given sequence is a Arithmetic sequence, a is the first term and d is common difference
a=4,d=5.5
We need to find the distance in the tenth week.
n=10
aₙ=a+(n-1)d
a₁₀=4+(10-1)(1.5)
a₁₀=4+9(1.5)=4+13.5=17.5
Hence 17.5 is the runner training distance in the tenth week.
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In the tenth week, the runner will run 17.5 miles.
What are arithmetic and geometric sequence?An arithmetic sequence is a set of numbers in which every no. next to the previous number has the same common difference
d = aₙ - aₙ₋₁ = aₙ₋₁ - aₙ ₋₂.
In a geometric sequence numbers are written in the same constant ratio(r).
It means every next number is a multiple of a common constant and the previous number.
r = aₙ/aₙ₋₁ = aₙ-₁/aₙ₋₂.
Given, A runner is training for a marathon.
The first week, she runs 4 miles during each training session.
Here a₁ = 4.
Each week, she increases her distance by 1.5 miles.
d = 1.5
We know the nth term of an AP is aₙ = a₁ + (n - 1)d.
∴ In tenth week which is a₁₀ the runner will run,
a₁₀ = a₁ + (10 - 1)×1.5
a₁₀ = 4 + 9(1.5).
a₁₀ = 4 + 13.5.
a₁₀ = 17.5 miles.
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-18t=-3(t+5) distributive property and using division first HELP PLEASE
Answer: T= 1
Step-by-step explanation:
Please help
What is the area, in square feet, of the shape below? Express your answer as a fraction in simplest form.
2/3 ft
4/3 ft
Answer:
4/9
Step-by-step explanation:
Area of a triangle is 1/2*base*height
1/2*2/3*4/3 = 8/18 = 4/9
Pls answe only 9 and 10 and this is due tomorrow
The value is 5/2 and 35/2 pounds.
What is meant by ratio?Comparing two amounts of the same units and determining the ratio tells us how much of one quantity is in the other. Two categories can be used to categorize ratios.
Part to whole ratio is one, and part to part ratio is the other. The part-to-part ratio shows the relationship between two separate entities or groupings.
For instance, a class has a 12:15 boy-to-girl ratio, whereas the part-to-whole ratio refers to the relationship between a particular group and the entire.
The ratios of the given table
Table 10,
[tex]\begin{aligned}&\Rightarrow \frac{5}{3}=\frac{1}{x} \\&\Rightarrow x=\frac{3}{5} \\&\Rightarrow \frac{5}{3}=\frac{12}{x}=\frac{12+3}{15} \\&\Rightarrow x=\frac{12}{5}\end{aligned}[/tex]
Table 9,
[tex]\begin{aligned}&\frac{10}{4}=\frac{5}{2} \\&\frac{5}{2}=\frac{x}{1} \\&x=\frac{5}{2} \\&\frac{5}{2}=\frac{x}{7} \\&x=\frac{35}{2}\end{aligned}[/tex]
[tex]\begin{array}{rccc}\text { 9) pounds } & 10 & \frac{5}{2} & \frac{35}{2} \\\text { Weeks } & 4 & 1 & 7 \\\text { 10) tons } & 5 & 1 & 12 \\\text { days } & 3 & \frac{3}{5} & \frac{12}{5}\end{array}[/tex]
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Determine the size of all missing angles:
angle a =
angle b =
angle c =
angle d =
angle e =
Answer:
angle a = 74 degrees
angle b = 106 degrees
angle c = 106 degrees
angle d = 65 degrees
angle e = 65 degrees
Step-by-step explanation:
Angle a:
the Alternate Interior Angles Theorem makes angle a equal to 74 degrees
Angle b:
First find angle c, and angle b is equal to angle c because angle b and c are Corresponding angles
Angle c:
angle c = 180 degrees - 74 degrees
angle c = 106 degrees
Angle d:
angle d corresponds with 65 degrees, therefore the are the same.
Angle e:
angle d and e are opposite angles, therefore they are the same.
Tyrone can type 87 words in three minutes at this rate how long will it take him to type 1624 words
Which of the following is an equation for the constant of proportionality? A k=y+xk=y+x B k=yxk=yx C k=xyk= y x D k=y−xk=y−x E k=yxk= x y
An equation for the constant of proportionality is (b) y = kx
How to determine the constant of proportionality?From the question, we have the options to represent the given parameters
An equation that represents a constant of proportion passes through the origin
So, we have the following points
(x, y) = (0, 0) and (x, y)
The slope (k) is then calculated as
Slope = (y₂ - y₁)/(x₂ - x₁)
So, we have
k = (y - 0)/(x - 0)
Evaluate the difference
k = y/x
Make y the subject
y = kx
Hence, the constant of proportionality has an equation of (b) y = kx
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In a class of 25 students, 14 are boys and 11 are girls. On a unit test, 6 boys and 6 girls made an A grade. If a student is chosen at random from the class, what is the probability of choosing a boy or an A student?
If in a class of 25 students, 14 are boys and 11 are girls. On a unit test, 6 boys and 6 girls made an A grade. If a student is chosen at random from the class, The probability of choosing a boy or an A student 4 / 5
How to solve for the probabilityFrom the question, we have the following data
Total number of students = 25
The total number of boys = 14
The students that are A male students = 6
Then we would have probability of having an A male student to be:
Total boys + A male students / total
= 14 + 6 / 25
= 4 / 5
Hence the probability is 4 / 5
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ldhjahwkwueyebr. help pls
Answer:
34
Step-by-step explanation:
Triangle is an isosceles triangle, where two angles are the same. BA=BC
Answer:34
Step-by-step explanation:
its an isosceles triangle because two sides are equal
A tudy invetigated the tatitical quetion: ""How many hour per week do teenager pend playing a port or outdoor game?"" Here are the data that wa collected from a ample of 10 teenager howing the number of hour per week pent playing a port or a game outdoor: 3; 2; 0; 6; 3; 3; 3; 1; 1; 2
The numbers of hours per week teenagers spend playing a sport or outdoor game is 2.4 or 2[tex]\frac{1}{15}[/tex] hours.
What is Averaging?
This refers to the mean value, which is equal to the ratio of all the numbers added and divided by the number of a given set of values present in the set of values.
Average= x₁+x₂+x₃+x₄..........xn
n
Where,
x₁+x₂+x₃+x₄..........xn = Given set of values
n= Number of a given set of values
From the question:
The number of hour per week spent playing a port or a game outdoors:
3; 2; 0; 6; 3; 3; 3; 1; 1; 2
number of teenagers,n =10
Average= 3+ 2+ 0+ 6+3+3+3+ 1+ 1+2
10
=2.4 or 2[tex]\frac{1}{15}[/tex] hours.
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