The teacher being most pleased with the period 1 class suggests they had the highest median score, indicating a better overall performance by the majority in this class.
Explanation:The statement that would make the teacher most pleased with the exam scores in his period 1 class would be B. The scores for period 1 had the highest median.
This is because the median represents the middle score in a set of scores. If period 1 had the highest median, it means that at least half of the students in this class scored higher than those in his other classes.
In essence, it shows better overall performance by the majority of the class in period 1, which would make a teacher pleased with the results.
This conclusion may not necessarily hold if we choose other options; for example, low Standard Deviation or Interquartile Range (IQR) mainly speak to the consistency of scores, and lowest median would imply most of the class did not perform very well. Hence, the highest median would generally reflect the most favor on the class performance.
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The statement that would lead us to believe that the teacher was most pleased with the exam scores in his period 1 class is C. The scores for period 1 had the lowest standard deviation.
Explanation:The statement that would lead us to believe that the teacher was most pleased with the exam scores in his period 1 class is C. The scores for period 1 had the lowest standard deviation.
The standard deviation measures the spread of data around the mean. A lower standard deviation indicates that the scores in period 1 are closer to the average score, suggesting more consistency and potentially higher performance.
The other options, such as the median or IQR, do not directly relate to the teacher's satisfaction with the scores, as they focus on different aspects of the distribution.
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what is the surface area of the rectangular prism please explain i failed my last session and im just trying to get through this without any mistakes
Answer:
B. 250 ft²Step-by-step explanation:
We have two squares S × S and four rectangles S × L.
S = 5 ft and L = 10 ft.
The area of a square:
[tex]A_s=(5)(5)=25\ ft^2[/tex]
The area of a rectangle:
[tex]A_r=(5)(10)=50\ ft^2[/tex]
The Surface Area:
[tex]S.A.=2A_s+4A_r[/tex]
Substitute:
[tex]S.A.=2(25)+4(50)=50+200=250\ ft^2[/tex]
Marie is making a recipe that calls for 1 1/4 cups of oil. How many fluid ounces of oil should she use?
A. 5 fl oz
B. 20 fl oz
C. 9 fl oz
D. 10 fl oz
Answer:
D
Step-by-step explanation:
1 cup = 8 fluid ounces.
1.25 cups = 8 fluid ounces + 1/4 of 8.
1/4 of 8 = 2
8 + 2 = 10.
10 fluid ounces should be used.
Answer:
d
Step-by-step explanation:
i had the question
What is the scale factor of triangle ABC to triangle DEF?
The scale factor of triangle ABC to triangle DEF is 1/6.
Compare corresponding side lengths:
I observed that a side length of triangle ABC (2 units) is 6 times smaller than the corresponding side length of triangle DEF (12 units).
This initial comparison hinted at a scale factor of 1/6.
Checked other side lengths:
To confirm, I verified that the other side lengths also have a ratio of 1/6.
AB = 2 units, DE = 12 units (2/12 = 1/6)
AC = 4 units, DF = 24 units (4/24 = 1/6)
BC = 2 units, EF = 12 units (2/12 = 1/6)
Since all corresponding side lengths have a ratio of 1/6, this confirms that triangle ABC is a scaled-down version of triangle DEF with a scale factor of 1/6.
Complete question:
The coordinates of PQR are P(1, 1), Q(2, 2), and R(3, 1). If PQR is rotated 90° about the origin, what are the vertices of P'Q'R'?
Answer:
(-1, 1), (-2, 2), and (-1, 3)
Step-by-step explanation:
The formula for rotation of a point (x,y) by an angle θ about the origin is
x' = xcosθ - ysinθ
y' = ycosθ + xsinθ
If θ = 90°, sinθ = 1 and cosθ = 0, and the formula becomes
x' = -y
y' = x
P: (1, 1) ⟶ (-1, 1)
Q:(2, 2) ⟶ (-2, 2)
R: (3, 1) ⟶ (-1, 3)
The vertices of P'Q'R' are (-1, 1), (-2, 2), and (-1, 3).
The Figure below shows the triangle before and after the rotation.
A librarian put 33 books back on the shelves before lunch. Of the books, 11 were non-fiction. What is the ratio of the number of non-fiction books to the total number of books the librarian put away before lunch?
A.
3 to 1
B.
1 to 3
C.
1 to 2
D.
2 to 1
The answer is A, there are 3 books to every 1 non fiction book.
Answer:
I think it's B but I'm not sure hope this helped. <3
Step-by-step explanation:
Solve for z:
-4.75 = z/2
z = ?
Answer:
-9.5
Step-by-step explanation:
To solve for z, use inverse operations by multiplying both sides by 2.
-4.75 = z/2
-9.5 = z
To solve the equation -4.75 = z/2, multiply both sides by 2 to isolate z, which gives you the solution z = -9.5.
To solve for z in the equation -4.75 = z/2, you need to isolate z on one side of the equation. This can be achieved by multiplying both sides of the equation by 2 (the reciprocal of 1/2, which is the current coefficient of z) to cancel out the division.
Here's the calculation step by step:
Multiply both sides by 2 to get: 2 × -4.75 = (z/2) × 2.Simplify the equation to get: -9.5 = z.Therefore, the solution to the equation is z = -9.5.
Which of the below statements is false?
Answer:
A and C
Step-by-step explanation:
The area formulas for the shapes area as follows:
Triangle, Kite, Rhombus A = 1/2 bhTrapezoid A = 1/2(b1 + b2)hParallelogram, rectangle and square A = bhKnowing this, you can see that rhombus and trapezoids have different formulas then other quadrilaterals. This means A and C can be considered false.
Please help !! Asap Study island explanation please
What is the inverse of the statement below?
[if the perimeter of a square is 20cm, then its area is 25cm2.]
A) if the perimeter of a square is not 20cm, then its area is not 25cm2
B) if the perimeter of a square is not 20cm, then its area is 25cm2.
C) if the area of a square is not 25cm2, then its perimeter is not 20cm.
D) if the area of a square is 25cm2, then its perimeter is 20cm.
Answer:
A
Step-by-step explanation:
The inverse of a statement is the negation of both the hypothesis and conclusion. This means that both parts of the statement gets a not.
If the perimeter of a square is NOT 20cm, then its area is NOT 25cm2.
help me please asap!
Answer: [tex]\bold{\dfrac{3}{2}}[/tex]
Step-by-step explanation:
[tex]\dfrac{12z^2}{2y^2}\\\\\\y = -2\quad z=-1\\\dfrac{12(-1)^2}{2(-2)^2}=\dfrac{12(1)}{2(4)}=\dfrac{12}{8}\\\\\\\dfrac{12}{8}\div \dfrac{4}{4}=\boxed{\dfrac{3}{2}}[/tex]
2x-y=4
3y-3x=6
How do I graph this
Step-by-step explanation:
Put y's on the one side and divided by what they have in the front so it would be
y=2x-4
and
y=x+2
and they y intercept for first one is -4
and slope is 2 which it goes up twice and goes right once because its positive
second one, y intercept is 2
and slope is 1 goes one up and one right because it is positive
Answer:
See the attached image
Step-by-step explanation:
You must graph the system of equations. To do so, find the intersection points of each line with the axes.
2x-y=4 intersection with the x axis. -----y=0
2x = 4
x = 2.
2x-y=4 intersection with the y axis. -----x=0
-y = 4
y = -4.
Now we have
3y-3x=6 intersection with the x axis. -----y=0
-3x = 6
x = -2
3y-3x=6 intersection with the y axis. -----x=0
3y = 6
y = 2.
Now you can graph both lines. The solution the system will be the intersection of both lines
what is a reasonable estimate for the problem?
-3/2 * (-5 1/4)
See the image attached for solution
how do i find the area of this shape and you tell me step by step it says find the area of the shaded region
First, you need to find out the are of the whole rectangle, which as you probably know, you just need to multiply base by height.
Then, you need to substract the are of the two little squares, which luckily are both the same size. To find out the are of a square you multiply a side twice.
Therefore,
Whole rectangle area:
(32+8) * (8+8) = 40 * 16 = 640 sq. ft.
Two small squares:
2 * (8 * 8) = 2 * 64 = 128 sq. ft.
We substract:
640 - 128 = 512 sq. ft.
Answer:
512
Step-by-step explanation:
i fond the area of the whole big rectangle , so to do this i did 32+8 because i needed to find length. then i found the width, which was 8+8, 16. to find area , i need to multiply with times height so i did 40 x 16. this gets me to 640, but now i need to take out the two smaller cubes since i included them when i found the are of the rectangle. since the sides of both squares are 8 by 8, we can do 8 x 8 x 2 to find the area of both of them. now we taake 128(the product of 8 x 8 x 2) and subtract it from the big rectangle with the area of 640. 640-128 is 512.
which object has a weight of approximately 1 ounce?
A slice of bread weighs approximately 1 ounce.
The probability that the first color is violet and the second is orange, if the first is replaced is?
If the crayons are replaced after they are drawn, the probability of drawing any particular color is 1/7.Also the result of each draw is independent of any previous result. Therefore the solution to the first part of the question is found from:P(violet\ then\ orange)=\frac{1}{7}\times\frac{1}{7}=\frac{1}{49}
If the crayons are not replaced after they are drawn, the probability of drawing violet on the first pick is 1/7. Then there are only six crayons left, so the probability of drawing orange is 1/6. The solution to the second part of the question is found from:
P(violet\ then\ orange)=\frac{1}{7}\times\frac{1}{6}=\frac{1}{42}
Does this help
What Is The Missing Angle Measure of This Irregular Quadrilateral
Answer:
the sum of the angles in a quadrilateral is 360 degrees
Step-by-step explanation:
360 - (60 + 150 + 70) = 360 - 280 = 80 degrees
A circle has a circumference of 7,850 units. What is the radius of the circle
Answer: Radius = 1,250
Step-by-step explanation: The circumference of a circle equals the 2 x radius x π.
The formula to solve the radius is 2r x 3.14 = 7,850
Divide both sides by 3.14 = 2r = 2,500
Divide both sides by 2 = r = 1,250.
The radius = 1,250
Answer: 1,250 units
Step-by-step explanation:
Can someone help and show the work please
Answer:
A = 75 in²Step-by-step explanation:
We have the rectangle and the right triangle.
The formula of an area of a rectangle:
A = lw
l - length
w - width
We have l = 10 in and w = 5 in. Substitute:
A = (10)(5) = 50 in²
The formula of an area of a triangle:
A = 1/2 bh
b - base
h - height
We have b = 5 in and h = 5 in + 5 in = 10 in. Substitute:
A = 1/2(5)(10)=1/2(50)=25 in²
The area of figure:
A = 50 in² + 25 in² = 75 in²factorization for the monomial
[tex]48x^{10}[/tex]
Answer:
Some of the possible factorizations of the monomial given are:
[tex](16x^5)(3x^5)[/tex]
[tex](48x)(x^9)\\\\(4x^5)(12x^5)\\\\(16x^2)(3x^8)\\\\(2x^2)(4x^7)(6x)[/tex]
Step-by-step explanation:
To factorize the monomia you need to express it as a product of two or more monomials. Therefore, you must apply the proccedure shown below:
- Descompose into prime numbers:
[tex]48x^{10}=2*2*2*2*3*x*x*x*x*x*x*x*x*x*x[/tex]
- Then, keeping on mind that, according to the Product of powers property, when you have two powers with equal base you must add the exponents, you can make several factorizations. Below are shown some of the possible factorizations of the monomial given:
[tex](2^4x^5)(3x^5)[/tex]
[tex](48x)(x^9)\\\\(4x^5)(12x^5)\\\\(16x^2)(3x^8)\\\\(2x^2)(4x^7)(6x)[/tex]
Answer with step-by-step explanation:
We are given the following monomial and we are to factorize it:
[tex] 4 8 x ^ { 10 } [/tex]
We have a number of options that we can opt for in order to factorize the given monomial:
[tex] ( 16 x ^ 2 ) ( 3 x ^ 8 ) [/tex]
or
[tex] ( 12 x ^ 5 ) ( 4 x ^ 5 ) [/tex]
or
[tex] ( 24 x ^ 3 ) ( 2 x ^ 7 ) [/tex]
So basically it depends how do you want to break the coefficient and the exponent in order to get a product of [tex] 4 8 x ^ { 10 } [/tex].
A fast typist can type 120 words in 100 seconds. At that rate, how many seconds would it take to type 258 words?
Answer: 215 seconds
Step-by-step explanation:
This is a ratio problem so you can set up the ratio like this:
120 words : 100 second.
If you divide both sides of the ratio by 120 you get:
1 word: 0.8333 seconds
Multiply both sides of the ratio by 258 and you get:
258 words: 215 seconds.
Therefore typing 258 will take them 215 seconds.
This will take 215 seconds to type 258 words.
This problem is solved by the concept of unitary method.
Given that Typist types 120 words in 100 seconds
so in one second he types 120/100 words = 1.2 Words per second
let us suppose he types 258 words in 'x' seconds
so in one second he types 258/x words
258/x = 1.2
x = 258/1.2
x = 215 seconds
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In the diagram, what is the value of x?
A. 78°
B. 108°
C. 98°
D. 82°
The unknown measure of the angle x is (c) 98 degrees
Finding the unknown measure of the angle xFrom the question, we have the following parameters that can be used in our computation:
The lines (see attachment)
By definition, the sum of angles on a line is 180
using the above as a guide, we have the following:
x + 82 = 180
So, we have
x = 180 - 82
Evaluate
x = 98
Hence, the solution is (c) 98 degrees
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when $82.00 is increased by 5%, what is the new amount?
Answer:
The new amount is $86.10
Step-by-step explanation:
First we find the increase
82*5%
82 *.05
4.1
Next we add the increase to the original amount
82+4.1
86.10
The new amount is $86.10
♫ - - - - - - - - - - - - - - - ~Hello There!~ - - - - - - - - - - - - - - - ♫
➷ First, you need to find what 5% of 82 is.
82*5%=4.1
Now, you need to add 4.1 to 82:
82+4.1= $86.10 is the new amount.
✽
➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
↬ TROLLER (don't worry, I didn't troll you)
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. The graph of a linear equation passes through three of these points: (0, 5), (2, 2), (3, 1), and (4, -1). The point that the graph does not pass through is
Answer:
(3,1)
Step-by-step explanation:
Calculate the rise-over-run ratio to find the slope between the points.
r/r between 0,5 and 2,2 was -3/2
r/r between 2,2 and 4,-1 was -3/2
r/r between 0,5 and 4,-1 was -6/4 = -3/2
r/r between 0,5 and 3,1 was -4/3
r/r between 2,2 and 3,1 was -1/1
as you can see the r/r for the points involving 3,1 was inconsistent with the rest, therefore it is not part of the linear system.
The point that the graph does not pass through is (3 ,1)
What is an equation?
An equation is a mathematical statement which equate two algebraic expressions. An equation has an equal to (=) sign in between the expression.
What is a linear equation?An equation in which the slope is constant is called a linear equation.
What is slope?Slope is the measure of the line's inclination towards horizontal.Slope of a line joining points (a,b) and (c,d) can be found with the formula: [tex]\frac{d - b}{b-a}[/tex] How to find point through which the graph does not pass ?The graph is linear. So the slope should be constant.Slope of the graph between points (0, 5), (2, 2) = [tex]\frac{2-5}{2-0} = -\frac{3}{2}[/tex]
Slope of the graph between points (2, 2) , (4, -1) = [tex]\frac{-1-2}{4-2} = - \frac{3}{2}[/tex]
Slope of the graph between points (0, 5), (4, -1) = [tex]\frac{-1-5}{4-0} = -\frac{-6}{4} = - \frac{3}{2}[/tex]
Slope of the graph between points (3, 1) , (0, 5) = [tex]\frac{5-1}{0-3} = - \frac{4}{3}[/tex]
Slope of the graph between points (3, 1) , (2, 2) = - 1
Slope of the graph between points (3, 1) , (4, -1) = -2
We can see that the slope is constant for the points (0, 5), (2, 2), (4, -1), and inconsistent for the point (3 , 1) with every other points.So, we can say the graph is not passing through the point (3 , 1).
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write the expression without radicals, using only positive exponents
Answer:
[tex]\sqrt[3]{a^{2}+b^{2}}=(a^{2}+b^{2})^{\frac{1}{3}}[/tex]
Step-by-step explanation:
∵∛x = (x)^1/3
∴ [tex]\sqrt[3]{a^{2}+b^{2}}=(a^{2}+b^{2})^{\frac{1}{3}}[/tex]
So you can replace the radicals by fractional exponents
Answer:
The required expression is: [tex]\sqrt[3]{a^2+b^2}=(a^2+b^2)^{\frac{1}{3}[/tex].
Step-by-step explanation:
Consider the provided expression.
[tex]\sqrt[3]{a^2+b^2}[/tex]
Now use the property: [tex]\sqrt[n]{x+y}=(x+y)^{\frac{1}{n}}[/tex]
By using the above property the provided expression can be written as:
[tex]\sqrt[3]{a^2+b^2}=(a^2+b^2)^{\frac{1}{3}[/tex]
Therefore, the required expression is: [tex]\sqrt[3]{a^2+b^2}=(a^2+b^2)^{\frac{1}{3}[/tex].
x is 110% of 10, y% of 50 is 3.5
Step-by-step explanation:
Set up a proportion.
x/10=110/100
x=11
Set up a proportion.
3.5/50=y/100
y=7
A parking lot is 20 yards wide and 30 yards long. If the college increases the length and width by the same amount to handle and increasing number of cars, then what polynomial represents the area of the new lot?
Answer:
x² + 50x + 600
Step-by-step explanation:
The length changes from 20 yards to 20 + x. The width changes from 30 to 30+x.
The area will be A = l*w = (20+x)(30+x).
Use the distributive property to find the polynomial simplified.
A = (20+x)(30+x) = 600 + 30x + 20x + x² = 600 + 50x + x²
Write the polynomial in descending order by writing the exponents first.
x² + 50x + 600
The polynomial representing the area of the new parking lot would be 600 + 50x + x^2 square yards, where x is the amount by which both the length and width are increased.
Explanation:The area of the initial parking lot can be computed using the formula for the area of a rectangle, which is length times width. In this case, the area would be 20 yards times 30 yards, or 600 square yards.
If we let x be the amount by which both the length and the width are increased, the new length becomes 30 + x yards, and the new width becomes 20 + x yards.
Therefore, the polynomial representing the area of the new parking lot would be (30+x)(20+x), which equals 600 + 50x + x^2 square yards.
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what are the solutions of the quadratic function 49x2=9
Answer:
49x^2 - 9 = 0As there is no x term, we can pretty much guess we have a situation where we factlrise by something known aa difference of two squares, so to factorise it:49 = 7^29 = 3^2x^2 = (x)^2so...(7x - 3)(7x + 3) = 07x - 3 = 0 7x + 3 = 0x = 3/7 x = -3/7
Step-by-step explanation:
49x² = 9
Divide both sides by 49:
x² = 9/49
Take the square root of both sides:
x = +/- √9/49
Simplify:
x = -3/7 and 3/7
assume f(x)= -2x+8 and g(x)=3x what is the value of (gof)(3)
a. x+8
b. 23
c. -10
d. 6
ANSWER
d. 6
EXPLANATION
The given functions are
[tex]f(x) = - 2x + 8[/tex]
and
[tex]g(x) = 3x[/tex]
We find
[tex](g \circ f)(x) = g(f(x))[/tex]
[tex](g \circ f)(x) = g( - 2x + 8)[/tex]
[tex](g \circ f)(x) = 3( - 2x + 8)[/tex]
[tex](g \circ f)(x) = - 6x + 24[/tex]
We now substitute x=3
[tex](g \circ f)(3) = - 6(3) + 24[/tex]
This gives us
[tex](g \circ f)(x) = - 18 + 24[/tex]
[tex](g \circ f)(3) = 6[/tex]
The correct choice is D.
Answer:
Step-by-step explanation:
6
There are 884 students enrolled at a certain college. The number of students from Indiana is exactly three times the number of students from the rest of the country and abroad. Write a pair of linear equations to represent the information. Be sure to state what the variables represent. Find the number of students who are from from Indiana. Show your work.
Answer:
Let the no. Of students from Indiana be x
Let the no. Of students from the rest of the country and abroad be y
x = 3y (Given) (i)
x + y = 884 (Given) (ii)
Subtract equation (ii) from 1
x -3y = 0
-(x+y = 884)
-4y = -884
Therefore y = 221
Therefore no. Of students from the rest of the country and abroad is 221
Substituting the value of y in (i)
x = 3 x 221
Therefore x = 663
Therefore no. Of students from Indiana is 663
Hope this helps!
Can someone please help me with this thank you!!
Given: m
EL=(2x)°, m
LG=(3x)°, m
GF=(4x−8)°, m
FE=(x−12)°
Find: m∠LTE
Answer:
1. add up all of the arcs.
2x+3x+4x-8+x-12
2. all of the arcs equal 360
2x+3x+4x-8+x-12=360
3. Find x
10x-20=360, x=38
4. angle LTE is equal to half of the sum of the intercepted arcs.
.5(arc LE +GF)
5. plug in LE +GF with x
.5(76+144)
LTE=110
Applying the angles of intersecting chords theorem, m∠LTE = 110°.
What is the Angles of Intersecting Chords Theorem?When two chords intersect inside a circle, according to the angles of intersecting chords theorem, the vertical angle formed equals the half the sum of the measures of the intercepted arcs.
Given the following:
EL=(2x)°LG=(3x)°GF=(4x−8)°FE=(x−12)°A full circle = 360°
Therefore we would have:
2x + 3x + 4x - 8 + x - 12 = 360
Add like terms
10x - 20 = 360
10x = 360 + 20
10x = 380
x = 38
Based on the angles of intersecting chords theorem, we have:
m∠LTE = 1/2(EL + GF)
Substitute
m∠LTE = 1/2(2x + 4x - 8)
m∠LTE = 1/2(6x - 8)
Plug in the value of x
m∠LTE = 1/2(6(38) - 8)
m∠LTE = 1/2(220)
m∠LTE = 110°
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if cos^2(6x)-sin^2(6x)=cos(B)
then B=?
Answer:
[tex]B=12x[/tex]
Step-by-step explanation:
Given: [tex]cos^2(6x)-sin^2(6x)=cos(B)[/tex]
Let's simplify the left part of the equation:
[tex]cos(12x)=cos(B)[/tex]
Solve for B:
[tex]B=12x[/tex]
Final answer:
To find the value of B for the given equation, we employ the cosine double angle identity, which leads us to determine that B equals 12x or 12x ± 2kπ, considering the periodic nature of the cosine function.
Explanation:
The question asks us to find the value of B given that cos2(6x) - sin2(6x) = cos(B). This expression can be rewritten using a trigonometric identity, the cosine difference identity, which states that cos(A) - cos(B) = -2sin((A+B)/2)sin((A-B)/2). However, in our case, we use the cosine double angle identity, which states that cos(2θ) = cos2(θ) - sin2(θ). Applying this identity to the given expression gives us cos(12x) = cos(B). Therefore, B = 12x or B = 12x ± 2kπ, where k is an integer, because the cosine function is periodic with a period of 2π.