The conclusion that 40% of the students have visited a science museum based on a sample of 50 may not be accurate because the Sample Size may be too small and unrepresentative of the school population. Other factors like Response Rate and random sampling are essential for validity, and a Hypothesis Test could provide more solid evidence.
The conclusion that 40% of the students in the school have visited a science museum based on a survey of 50 students is not fully valid without considering additional factors. When conducting a survey, the concept of Sample Size is crucial. A sample size of 30 is the minimum required to start establishing statistical confidence, but larger samples are generally better to reduce sampling error. In this case, sampling only 50 students might not be representative of the entire student body, depending on the school's population. Moreover, the Response Rate and the randomness of the sample are essential in determining the validity of survey results. The survey must have a relatively high response rate and the sample must be chosen randomly from the entire population to avoid bias. This helps in better reflecting the overall characteristics of the population.
Conducting a Hypothesis Test would also help validate the findings. This statistical tool helps determine whether the observed proportion significantly deviates from the expected proportion (if known) or not. Furthermore, one important aspect is to avoid making statistics imply something they do not, which is common in cases where the sample size is small or the sample is unrepresentative. Lastly, discrepancies in survey results, like those seen in vaccination rates from two different researchers, can occur even when the right procedures are followed due to inherent variability in sampling.
what angles do perpendicular lines form?
Answer:
Two intersecting lines that form right angles (90 degree angles). All perpendicular line intersections will form .
Step-by-step explanation:
Answer: 90° angle
Step-by-step explanation: In the image provided, you can see that the 2 lines cross at a point so they're intersecting lines. However, notice the box that is used at the point where the lines meet. This box means that the lines meet at a 90° angle or a right angle and 2 lines that intersect at a right angle are called perpendicular lines which means that the lines are perpendicular.
Ahmed lent amir Rs8000 at simple interest for 3 years at the rate of 5% per annum. How much more would he have gained if he had lent it at compound interest?
Ahmed could have gained 61 rupees more, if had given had given in compound interest.
Solution:
Given that Ahmed lent amir Rs8000 at simple interest for 3 years at the rate of 5% per annum
Simple Interest calculation:
Principal = 8000
Rate of interest = 5%
Time = 3
Formula:
[tex]S.I=\frac{p\times n\times r}{100}[/tex]
Where , "p" is the principal and "n" is the number of years and "r" is the rate of interest
Substituting the values in formula,
[tex]S.I = \frac{8000 \times 3 \times 5}{100}\\\\S.I = 80 \times 3 \times 5 = 240 \times 5\\\\S.I = 1200[/tex]
Compound Interest calculation:
Principal = 8000
Rate of interest = 5% compounded annually
Time = 3
Formula:
[tex]C.I=P(1+\frac{R}{100})^n-P[/tex]
Substituting the values in formula,
[tex]\Rightarrow C.I=8000(1+\frac{5}{100})^3-8000\\\\\Rightarrow C.I=9261-8000\\\\\Rightarrow C.I=1261[/tex]
Therefore, the difference between the interests:
1261 - 1200 = 61
Thus he could have gained 61 rupees more, if had given had given in compound interest.
Four friends Ram, Mohan, Ajay and Sanjay are playing in a rectangular playground. Ram suggested his friends to get the position by keeping a stone in the middle of the park and he told the stone is the origin for their position. Now, they got the position of all four friends as (– 4, – 2), (– 3, – 5), (3, – 2) and (2, 3). Mohan claimed that their position will form a quadrilateral if taken in order. Ajay and Sanjay are now trying to calculate the area of the quadrilateral formed by their position if taken in order. How much area they calculated.
The area calculated by them is 21.
Step-by-step explanation:
The given points are (-4,-2),(-3,-5),(3,-2) and (2,3).
The area of the quadrilateral:
A= [tex]\frac{(x1 y2+x2y3+x3y4+x4y1)-(x2y1+x3y2+x4y3+x1y4) }{2}[/tex].
From the given points,
A=[tex]\frac{(20+6+9-4)-(6-1-4-12) }{2}[/tex]
A=[tex]\frac{(31)-(-11) }{2}[/tex]
A= [tex]\frac{42}{2}[/tex]
The area of the quadrilateral = 21.
Answer:
The are is 28
Step-by-step explanation:
Given:
Point 1: (– 4, – 2)
Point 2: (– 3, – 5)
Point 3: (3, – 2)
Point 4: (2, 3)
then, the coordinates of the first point are x1 = -4, y1 = -2; of the second point x2 = -3, y2 = -5; and so on.
We can compute the area of the quadrilateral with the shoelace formula as follows:
area = 1/2 * |x1*y2 + x2*y3 + x3*y4 + x4*y1 - x2*y1 - x3*y2 - x4*y3 - x1*y4 |
area = 1/2 * |(-4)*(-5) + (-3)*(-2) + 3*3 + 2*(-2) - (-3)*(-2) - 3*(-5) - 2*(-2) - (-4)*3 |
area = 1/2 * 56 = 28
What is the standard form of this complex number?
1 / (3 - sqrt-4)
A. 3/13 + 2/13i
B. 3/5 + sqrt-2/5
C. 3 - 2i
D. 3 + 2i
Answer: A
Step-by-step explanation:
The standard form of this complex number is A. 3/13 + 2/13i
=3+2i/9-4(-1)
=3+2i/9+4
=3+2i/13
What is an example of a complex number?
Complex numbers in mathematics. Complex numbers are numbers expressed in the form of a + ib. Here, a and b are real numbers, and "i" is an imaginary number called "iota". The value of i = (√-1). For example, 2 + 3i is a complex number, 2 is a real number (Re), and 3i is an imaginary number.
Complex numbers are numbers that consist of two parts: real and imaginary. Complex numbers are more complex mathematical components such as algebra. They can be applied to many aspects of real life, especially electronics and electromagnetism.
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simplify (5^x+2-5^x)/5^x×4
Answer:
6
Step-by-step explanation:
The given expression is,
[tex]\frac{5^{x+2}-5^x }{5^x\times4}[/tex]
Now, we know that,
[tex]a^{m+n} = a^m . a^n[/tex]
Then,
[tex]5^{x+2}=5^x . 5^2[/tex]
So,
[tex]\frac{5^{x+2}-5^x}{5^x\times4}=\frac{5^x.5^2-5^x}{5^x\times4}[/tex]
Now, taking [tex]5^{x}[/tex] common from the numerator of the given expression, then
[tex]\frac{5^{x+2}-5^x}{5^x\times4}=\frac{5^x(5^2-1)}{5^x\times4}[/tex]
[tex]\implies\frac{5^{x+2}-5^x }{5^x\times4}=\frac{5^2-1}{4}[/tex]
[tex]\implies\frac{5^{x+2}-5^x}{5^x\times4}=\frac{5\times5-1}{4}=\frac{25-1}{4}[/tex]
[tex]\implies\frac{5^{x+2}-5^x}{5^x\times4}=\frac{24}{4}=6[/tex]
So, the simplified form of the given expression gives the result 6.
Adrienne operates the milkshake machine at Burgers and Shakes. on Monday she added whipped cream to 210 shakes.This was 70% of the total milkshakes sold. how many milkshakes were sold at Burgers and Shakes on Monday? How many shakes did not have whipped cream?
Answer:
Total number of milkshakes sold on Monday = 300
Number of milkshakes without whipped cream = 90
Step-by-step explanation:
Given:
Adrienne adds whipped cream to 210 milk shakes which is 70% of the total milk shakes sold.
To find the total milkshakes sold.
Solution:
Let the total number of milkshakes sold on Monday be = [tex]x[/tex]
Percentage of milkshakes with whipped cream added to them = 70%
Number of milk shakes with added whipped cream can be given as:
⇒ [tex]70\% \textrm{ of the total number of milkshakes}[/tex]
⇒ [tex]70\% x[/tex]
⇒ [tex]\frac{70}{100}x[/tex] [Representing percent in fraction form]
⇒ [tex]0.7x[/tex] [evaluating in decimals]
We know that the number of milkshakes with whipped cream added to them = 210.
So, we have:
[tex]0.7x=210[/tex]
Solving for [tex]x[/tex]
Dividing both sides by 0.7
[tex]\frac{0.7x}{0.7}=\frac{210}{0.7}[/tex]
∴ [tex]x=300[/tex]
Thus, total number of milkshakes sold on Monday = 300
Number of milkshakes without whipped cream = [tex]300-210[/tex]= 90
Convert the following equation to standard form: y = -3x + 2
o3х – у = 2
3х + y = 2
3х + y = -2
—37 — у = 2
ооо
For this case we have that by definition, the equation of a line in its standard form is given by:
[tex]ax + by = c[/tex]
We have the following equation in the slope-intersection form:
[tex]y = -3x + 2[/tex]
Where:
-3: It's the slope
2: It is the cut-off point with the y axis.
We manipulate algebraically:
Adding 3x to both sides of the equation we have:
[tex]y + 3x = 2\\3x + y = 2[/tex]
Thus, the correct option is option B.
Answer:
Option B
Myra is evaluating the expression –31.7 + 4.5x, when x = 2.1.
–31.7 + 4.5(2.1)
–27.2(2.1)
–57.12
What was Myra’s error?
Answer:
-22.25
Step-by-step explanation:
-31.7+4.5(2.1)
-31.7+9.45
-22.25
If 3 boxes can hold 27 books, how many boxes can hold 108 books?
1 box holds 9 so u divide 108 by 9 to get 12.
U can also multiply 3 and 27 until u get 108. First divide 108 by 27 and get 4. so u then multiply 4 times 3 to get 12.
Answer:
Step-by-step explanation:
No of books that 3 boxes can hold = 27 books
No of boxes required =(3/27) * 108 = 3*108 / 27 = 3 *4 = 12
12 boxes are required
how does this polynomial identity work on numerical relationships?
(y + x) (ax + b)
Answer:
Let us take 'a' in the place of 'y' so the equation becomes
(y+x) (ax+b)
Step-by-step explanation:
Step 1:
(a + x) (ax + b)
Step 2: Proof
Checking polynomial identity.
(ax+b )(x+a) = FOIL
(ax+b)(x+a)
ax^2+a^2x is the First Term in the FOIL
ax^2 + a^2x + bx + ab
(ax+b)(x+a)+bx+ab is the Second Term in the FOIL
Add both expressions together from First and Second Term
= ax^2 + a^2x + bx + ab
Step 3: Proof
(ax+b)(x+a) = ax^2 + a^2x + bx + ab
Identity is Found .
Trying with numbers now
(ax+b)(x+a) = ax^2 + a^2x + bx + ab
((2*5)+8)(5+2) =(2*5^2)+(2^2*5)+(8*5)+(2*8)
((10)+8)(7) =(2*25)+(4*5)+(40)+(16)
(18)(7) =(50)+(20)+(56)
126 =126
ratio of girls to boys at a movie is 5:7 if there are 28 boys how many girls are at the movie?
For every 7 boys there are 5 girls.
Divide the number of boys by the ratio for boys: 28 / 7 = 4
Now multiply that by the ratio for girls:
4 x 5 = 20
There are 20 girls.
Help solving this math
Answer:
Rank 1 - plane.
Rank 2- line.
Rank 3- point.
Step-by-step explanation:
Here, I have given the ranks based on what includes what.
Rank 1 is given to plane because infinite lines together makes a planes
and infinite points together makes a line.
so, Rank 1 includes both Rank 2 and Rank 3.
Now, Rank 2 is line because it consists of infinite number of points together
and is used to form a plane.
Rank 3 is point as it is the basic thing for any line or plane
See, it is simple, group of points make a line and group of lines make a plane.
visualize it this way,
When you zoom too in a plane, you see a line and when you zoom too in a line, you see a point.
2/9x+5=2/3
I have to rewrite the equation so it doesn’t have a fraction
Answer:
2x + 45 = 6
Step-by-step explanation:
(2/9)x + 5 = 2/3 Subtract 5 from both sides
(2/9)x +5-5=2/3-5
(2/9)x = - 4 1/3 Multiply by 9
2x = -13/3 * 9
2x = -39
x = -19.5
==============
I see. You don't want it solved. Multiply by 9 to clear the fractions.
==============
2x + 45 = 6
==============
Solve it now. It should be easier.
2x = 6 - 45
2x = - 39
x = -19.5
How many 10s are in a 20
Answer:
2
Explanation:
Another way to write this is:
20 ÷ 10
2 whole tens go into 20.
20 ÷ 10 = 2
Answer: 2
This question is asking you to divide 20 by 10. This means:
20 ÷ 10=2
If 10 can go into a number 2 times, it means that 10•2=20. So, since we dont know how many times 10 goes into 20, we divide 20 by 10.
Below I have attached an image of the long division in case you need to do that as well.
Hope this helps comment below for more questions :)
Which is the MOST REASONABLE approach for the company to take to lessen the number of latecomers to work?
A) Relocate the company to an area with less traffic.
B) Deduct the lost time for any reason from vacation time.
C) Delay the start time of work days when there is bad weather.
D) Implement better procedures at the security gate.
Answer:
D) Implement better procedures at the security gate.
Step-by-step explanation:
INTELLIGENT STUDENT IN TRIG?.Ill give brainlest
Answers:
x = 6
y = 6*sqrt(2)
=======================
Explanation:
To find these values, you can use the general template of a 45-45-90 triangle or you can use trig ratios
tan(45) = 1
tan(angle) = opposite/adjacent
tan(45) = x/6
1 = x/6
6*1 = x
x = 6
-------
sin(45) = 1/sqrt(2)
sin(angle) = opposite/hypotenuse
sin(45) = 6/y
1/sqrt(2) = 6/y
1*y = sqrt(2)*6
y = 6*sqrt(2)
Type the correct answer in each box. (Read picture)
Answer:
The value of x in terms of b is (-3/b)
The value of x when b is 3 is -1
===============================
Step-by-step explanation:
The given function is :
-2 (bx - 5) = 16
Divide both sides by 2
bx - 5 = 16/(-2) = -8
Add 5 to both sides
bx = -8 + 5 = -3
Divide both sides by (b)
∴ x = -3/b
∴ The value of x in terms of b is (-3/b)
When b = 3 ⇒ ∴ x = -3/b = -3/3 = -1
what is the answer to this
Answer:
-81
Step-by-step explanation:
Answer:
1/81
Step-by-step explanation:
Paul brought and sold a computer .he wrote his business activity as followers cost price of computer =$1064 marked price of computer =$1399 discount on marked price =5%
Answer:
Profit = $265.04.
Selling price = $1329.05
Step-by-step explanation:
Paul brought a Computer at a cost price of $1064.
Now ,
The marked price of the computer is given as $1399.
Also,
He is giving a total discount of 5% on the marked price of the computer i.e., $1399.
So, The selling price of computer will become 95 percent of $ 1399 which equals $1329.05.
Thus Paul sold the computer at a profit of $1329.05 - $1064
= $265.04.
Answer:
A) selling price of computer is $1329.05
B) Profit is $265.05
C) Profit percentage = 24.9%
Step-by-step explanation:
Given as :
The cost price of computer = c.p = $1064
The marked price of computer = m.p = $1399
The marked percentage discount = d = 5%
Let The selling price of computer = s.p
Now, According to question
discount% = [tex]\dfrac{m.p - s.p}{m.p}[/tex]
Or, d% = [tex]\dfrac{m.p - s.p}{m.p}[/tex]
Or, 5% = [tex]\dfrac{1399 - s.p}{1399}[/tex]
Or, [tex]\dfrac{5}{100}[/tex] = 1 - [tex]\dfrac{s.p}{1399}[/tex]
Or, [tex]\dfrac{s.p}{1399}[/tex] = 1 - [tex]\dfrac{5}{100}[/tex]
Or, [tex]\dfrac{s.p}{1399}[/tex] = [tex]\dfrac{95}{100}[/tex]
∴ s.p = [tex]\dfrac{95}{100}[/tex] × 1399
Or, s.p = $1329.05
So,The selling price of computer = s.p = $1329.05
Now, Profit = selling price - cost price
or, p = s.p - c.p
Or, p = $1329.05 - $1064
∴ Profit = $265.05
Now, Profit % = [tex]\dfrac{\textrm profit}{c.p}[/tex]
Or, p% = [tex]\dfrac{\textrm 265.05}{1064}[/tex]
∴ p% = 0.249
i.e p = 0.249 × 100
So, profit percentage = 24.9%
Hence, A) selling price of computer is $1329.05
B) Profit is $265.05
C) Profit percentage = 24.9% Answer
BRAINLIEST!!!
Find the probability that a point chosen at random lies in the shaded region.
Answer:
0.56
Step-by-step explanation:
First, we need to look at the size of the image as a whole. It is 10x10, so it has 100 squares within it.
When counted, there are 56 shaded squares.
This gives us [tex]\frac{56}{100} =0.56[/tex]
the answer is 0.56, because there’s 56 shades squares.
Explanation: there’s 100 squares, 56 are shaded 56/100.
Mark bought 8 bags of sand, each weighing 25 lb, for $1.68/bag. One bag ripped and he lost all the sand. What was his true price per pound of sand?
Answer:
4.80 rounded
Step-by-step explanation:
Sole by substitution.
-3x+2y=16
X-2y=-12
Answer:
For the given equations the values of x and y by using substitution method are [tex]x=1[/tex] and [tex]y=\frac{13}{2}[/tex]
Step-by-step explanation:
Given system of equations are
[tex]-3x+2y=16\hfill (1)[/tex]
[tex]x-2y=-12\hfill (2)[/tex]
Solve the given equations by substitution method:
Now (2) implies
[tex]x-2y=-12[/tex]
[tex]x=-12+2y\hfill (3)[/tex]
Now substitute the x value in equation (1)
[tex]-3x+2y=16[/tex]
[tex]-3(-12+2y)+2y=16[/tex]
[tex]36-6y+2y=16[/tex]
[tex]36-4y=16[/tex]
[tex]-4y=16-36[/tex]
[tex]y=-(\frac{-26}{4})[/tex]
[tex]y=\frac{26}{4}[/tex]
Therefore [tex]y=\frac{13}{2}[/tex]
Now substitute the y value in equation (3)
[tex]x=-12+2y[/tex]
[tex]x=-12+2\times \frac{13}{2}[/tex]
[tex]x=-12+13[/tex]
[tex]x=1[/tex]
Therefore [tex]x=1[/tex] and [tex]y=\frac{13}{2}[/tex]
seven friends have a similar cell phone plan
Part C Help me I have a test tomorrow
Given: 2 ≅ 5, AB ≅ DE
Prove: BC ≅ EC
Answer:
See explanation
Step-by-step explanation:
Consider triangles ABC and DEC. In these triangles,
[tex]\angle 2\cong \angle 5[/tex] - given;[tex]AB\cong DE[/tex] - given;[tex]\angle 3\cong \angle 4[/tex] - as vertical angles when lines AD and BE intersect.Thus, by AAS postulate, triangles ABC and DEC are congruent. Congruent triangles have congeruent corresponding sides.
So,
[tex]BC\cong EC[/tex]
The Angle Angle Side postulate (AAS) states that if two angles and the non-included side one triangle are congruent to two angles and the non-included side of another triangle, then these two triangles are congruent.
AA cash register has only one-dollar bills and five-dollar bills, and no change. There are $6$6 times as many one-dollar bills as five-dollar bills. The total amount in the cash register is $231.
Answer:
There are 126 $1 bills and 21 $5 bills.
Step-by-step explanation:
Given,
Total cash Amount = $231
Solution,
Let the number of $1 bill be 'x'.
And the number of $5 bill be 'y'.
Now according to question, one-dollar bills is six times of five-dollar bills.
So, we can frame it in equation form as;
[tex]x=6y[/tex] ⇒ equation 1
Again according to question, there is only one-dollar bills and five-dollar bills, and no change.
That means the total cash amount is in the form of $1 and $5.
So, we can frame the above sentence in equation form as;
[tex]1\times x+5\times y=231\\\\x+5y=231[/tex]⇒ equation 2
Now substituting the value of x in equation 2, we get;
[tex]6y+5y=231\\\\11y=231\\\\y=\frac{231}{11}=21[/tex]
So, [tex]x=6y=6\times 21=126[/tex]
Hence There are 126 $1 bills and 21 $5 bills.
A rectangle has a length of 6 and a width of y + 4. Use the distributive property to write an expression to represent the area of the rectangle.
Answer:
[tex]\large\boxed{A=6y+24}[/tex]
Step-by-step explanation:
[tex]\text{The formula of an area of a rectangle:}\\\\A=l\times w\\\\l-\text{length}\\w-\text{width}\\\\\text{We have:}\\\\l=6,\ w=y+4\\\\\text{Substitute:}\\\\A=6\times(y+4)\\\\\text{use the distributive property}:\ a(b+c)=ab+ac\\\\A=(6)(y)+(6)(4)\\\\A=6y+24[/tex]
Final answer:
To find the expression that represents the area of the rectangle, use the distributive property. The expression is 6y + 24.
Explanation:
To find the expression that represents the area of the rectangle, we can use the distributive property. The area of a rectangle is given by the formula A = length imes width. So, for this rectangle, the length is 6 and the width is y + 4. To distribute the 6, we multiply it by both terms inside the parentheses: A = 6(y) + 6(4). This simplifies to A = 6y + 24, which is the expression that represents the area of the rectangle.
A store sells notebooks for $3 each and does not charge sales tax. If x represents the number of notebooks Adele buys and y represents the total cost of the notebooks she buys, which best describes the values of x and y?
Answer:
The value of x will be an interger above or equal to 0. The value of y will be a interger equal or above 0.
Step-by-step explanation:
You can never buy a negative amount of books (x). You can only spend a positive amount of money. So even if she did not buy a book it would be 0, never under it.
Answer: it's the 2nd one
Step-by-step explanation: The value of x can be any real number greater than or equal to 0, and y will be a real number greater than or equal to 0
THE GRINCH FOUND THE STRENGTH OF
2x6x3) ÷4+1 GRINCH'S PLUS TWO
Answer: 2x6x3=36 divided by 4=9+1=10.
The expression (2x6x3) ÷ 4 + 1 Grinch's plus two is solved using the order of operations, giving a result of 10 plus two Grinch's, symbolized as 10 + 2G.
Explanation:The question is a basic arithmetic problem that involves both multiplication and addition within parentheses, followed by division and then more addition.
The order of operations, often abbreviated as PEMDAS - which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right) - must be followed to solve the expression correctly.
Let's solve the expression step by step:
First, handle the expression within the parentheses: (2x6x3), which is multiplication. So, 2 times 6 equals 12, and 12 times 3 equals 36.Now, divide the result by 4: 36 ÷ 4 equals 9.Finally, add 1 to the result of the division: 9 + 1 equals 10.Add the last element of the expression, which is two Grinch's. Since we're not given a numerical value for a Grinch, let's symbolize it as 'G'. Therefore, if one Grinch is 'G', two Grinch's would be '2G'.The final answer is 10 plus two Grinch's, which we write as 10 + 2G.
Solve the following triangle for all missing sides and angles.
Part I: What is the measure of angle A?
Part II: Use the law of sines to find the length of side a.
Part III: Use the law of cosines to find the length of side b.
Can someone please help?I'll give extra points and mark as brainliest.
PLEASEEEEEE!!!
Answer:
Part 1: 100
Part 2: 29.19 (Rounded)
Part 3: 20.96 (Rounded)
Step-by-step explanation:
Part 1: Triangle Sum Theorem (All angles of a triangle add up to 180 degrees)
45 + 35 + A = 180
80 + A = 180
Move the constant to the other side
80 + A = 180
-80 -80
A = 80°
Part 2: Law of sines
[tex]\frac{a}{sin(100)} = \frac{17}{sin(35)}[/tex]
Cross multiplication
sin(35)a = 16.7417318
Divide both sides by sin(35)
a = 29.18831866
Part 3: Law of cosines
[tex]b=29.19^{2}+17^{2}-2*29.19*17*cos(45)[/tex] = 439.2809039
Square root the answer
[tex]\sqrt{439.2809039}[/tex] =20.95902917
The value of angle A is 100 degrees and the measure of side a is 29.2 and b is 20.96.
What is a Triangle?A triangle is a polygon with three sides, angles, and vertices.
The triangle ABC, has AB = 17, angle ABC = 45 degree, angle ACB = 35 degree.
The measure of angle A can be determined by using the angle sum property.
45 + 35 + A = 180
80 + A = 180
A = 180-80
A = 100 degree.
Using the law of sines to find the length of side a,
a/ sin A = b/ sin B = c/sin C
a/ sin100 = 17/ sin 35
a = 17 * sin 100 / sin35
a = 29.2
Use the law of cosines to find the length of side b.
b² = c² +a² -2ac cos B
b² = (17)² + (29.2)² - 2* 17* 29.2 cos 45
b² = 439.23
b = 20.96
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