Hence the slope is 1/3
Suppose we interpret 20 ÷ 8. How many groups of 8 are in 20? Show how we think we could draw a diagram for this (optional)
To find number of groups of 8 are in 20
Divide 20 by 8 :
20 ÷ 8. = 2
Number of groups = 2
8. Mel's mean on 10 tests for the semester was 89. She complained to the teacher that she should be given an A because she missed the cutoff of 90 by only a single point. Explain whether it is clear that she really missed an A by only a single point if each test was based on 100 points. Explain how many points she actually missed.
Answer
Check Explanation
Explanation
The mean of a group of numbers is the average of these numbers.
Mathematically, the mean is the sum of variables divided by the number of variables.
Mean = (Σx)/N
x = each variable
Σx = Sum of the variables
N = number of variables
So, when Mel's mean is 89 for 10 tests, this means
Mean = 89
N = Number of variables = 10
So, we can calculate the sum of all of Mel's scores
Mean = (Σx)/N
Cross multiply,
Σx = N [Mean]
Σx = 10 (89) = 890
For Mel to have an average score of 90 from 10 tests,
Mean = 90
N = Number of variables = 10
So, we can calculate the sum of all of Mel's scores
Mean = (Σx)/N
Cross multiply,
Σx = N [Mean]
Σx = 10 (90) = 900
So, we can see that Mel does not actually need 1 point to score an A (90), Mel needs 10 extra points gathered from the 10 tests, to get the extra average 1 point.
Hope this Helps!!!
Hello my name is chayse may you please get straight to the point
Solve the inequality for v:
20 > v - 4
When the variable is at the right of the inequality, it's a good idea to flip the inequality, that is, swap the sides and (very important), swap the symbol:
v - 4 < 20
Now we add 4 to both sides:
v - 4 + 4 < 20 + 4
Operating:
v < 24
This is the answer
{57, 53, 53, 71, 73, 57, 61, 58, 78. 64, 54, 69, 56, 58, 49, 56, 53, 52, 82, 62, 61, 60, 71, 75, 60} Whats the mean?. and the iqr? what is the five number summary? what is Q3? The Median is 60.
Given the data set:
[tex]\lbrace57,53,53,71,73,57,61,58,78,64,54,69,56,58,49,56,53,52,82,62,61,60,71,75,60\rbrace[/tex]• You can find the Mean by adding all the values and dividing the sum by the number of values in the data set:
[tex]Mean=\frac{57+53+53+71+73+57+61+58+78+64+54+69+56+58+49+56+53+52+82+62+61+60+71+75+60}{25}[/tex][tex]Mean\approx61.72[/tex]• By definition the term for the third quartile can be found with this formula:
[tex]\frac{3}{4}(n+1)[/tex]Where "n" is the number of observations.
In this case:
[tex]n=25[/tex]Then:
[tex]\frac{3}{4}(25+1)\approx19.5[/tex]Since it is an integer, you get that the position of the terms is:
[tex]Q_3=\frac{69+71}{2}=70[/tex]Because, when you order the data set, 69 is the 19th value and 71 is the 20th value. Then, the third quartile is the average between them:
[tex]\lbrace49,52,53,53,53,54,56,56,57,57,58,58,60,60,61,61,62,64,69,71,71,73,75,78,82\rbrace[/tex]• By definition:
[tex]IQR=Q_3-Q_1[/tex]And the term position of the first quartile is found with:
[tex]\frac{n+1}{4}[/tex]You get:
[tex]\frac{25+1}{4}=6.5[/tex]Therefore, you can determine that:
[tex]Q_1=\frac{54+56}{2}=55[/tex]Then:
[tex]IQR=70-55=15[/tex]• By definition, the Five-Number Summary is:
- The minimum value:
[tex]Minimum=49[/tex]- The first quartile:
[tex]Q_1=55[/tex]- The median:
[tex]Median=60[/tex]- The third quartile:
[tex]Q_3=70[/tex]- The maximum value:
[tex]Maximum=82[/tex]Hence, the answers are:
• Mean:
[tex]Mean\approx61.72[/tex]• IQR:
[tex]IQR=15[/tex]• Five-Number Summary:
[tex]Minimum=49[/tex][tex]Q_1=55[/tex][tex]Median=60[/tex][tex]Q_3=70[/tex][tex]Maximum=82[/tex]• Third quartile:
[tex]Q_3=70[/tex]A bad contains 31 red blocks, 46 green blocks, 23 yellow blocks, and 25 purple blocks. You pick one block from the bag at random. Find the indicated theoretical probability. Pr(green or red) = ______
SOLUTION
The probability of the event is given by the formula
[tex]\text{Probability}=\frac{\text{required outcome }}{total\text{ oucome }}[/tex]From the question, we have
[tex]\begin{gathered} \text{Red}=31,\text{green}=46,\text{ yellow=23, Purple=25} \\ \text{Total blocks=31+46+23+25=125} \end{gathered}[/tex]The indicated probability is
[tex]P(\text{green or red )=Pr(gr}een)+Pr(red)[/tex]where
[tex]Pr(\text{green)}=\frac{\text{Number of gre}en}{total\text{ blocks }}=\frac{46}{125}[/tex]Also, we have
[tex]Pr(\text{red)}=\frac{\text{Number of red }}{total\text{ blocks }}=\frac{31}{125}[/tex]Hence
[tex]Pr(\text{green or red )=}\frac{31}{125}+\frac{46}{125}=\frac{31+46}{125}=\frac{77}{125}[/tex]Therefore
The Pr(green or red ) will be 77/125
what line is perpendicular to the line y = 2x+4 ? what line is parallel to the line y+2xt4? Options1) y=2x+12) y=1/2x+63) y=-1/2x+104) y=-2x+3
Given the line
[tex]y=2x+4[/tex]The line is expressed in slope-intercept form:
[tex]y=mx+b[/tex]Where
m is the slope
b is the y-intercept
1) Any line that has the same slope as this line will be parallel to it.
The slope of the line is m=2
From the given options, the only one that has the same slope as the given line is the first one
[tex]y=2x+1[/tex]2) For perpendicular lines, the slope of a line perpendicular to another is the inverse negative of the slope of the line.
So let
[tex]y=nx+c[/tex]Represent the equation of the line perpendicular to the given one. The relationship between their slopes can be expressed as:
[tex]n=-\frac{1}{m}[/tex]The slope of the line is m=2 so the slope of the perpendicular line is
[tex]n=-\frac{1}{2}[/tex]A line with slope -1/2 will be perpedicular to the given one. Looking at the options, the line that can be perpendicular to this one is
[tex]y=-\frac{1}{2}x+10[/tex]The correct option is the third one.
Expand binomial using binomial expansion (x-y)^3
The expression is,
[tex](x-y)^3[/tex]Expanding the expression we get,
[tex](x-y)^3=(x-y)(x-y)^2\ldots.(1)[/tex]We have,
[tex](x-y)^2=x^2-2xy+y^2\ldots..(2)[/tex]Substituting equation 2 in equation 1, we get,
[tex]\begin{gathered} (x-y)^3=(x-y)(x^2-2xy+y^2) \\ \text{ =}x(x^2-2xy+y^2)-y(x^2-2xy+y^2) \\ \text{ =}x^3-2x^2y+xy^2-yx^2+2xy^2-y^3 \\ \text{ =x}^3-y^3+3xy^2-3x^2y \end{gathered}[/tex]Which of the following is a quadraticfunction?F. f(x) = -x4 + x + 11G. f(x) = 5x2-8H. f(x) = x3 - 7x + 12J. f(x) = 47 - X
The qudratic function is the function that the x-variable has a power to the power of two
Hence, the quadratric function is G
f(x) = 5x²-8
In circle E with mZDEF 36 and DE = 15 units find area of sector DEF. Round to the nearest hundredth. E F D
Given:
m∠DEF = 36
DE = 15 units
Let's find the area of the sector.
To find the area of the sector, apply the formula:
[tex]A=\frac{\theta}{360}\ast\pi r^2[/tex]Where:
radius, r = DE = 15 units
θ = 36
Substitute values into the formula:
[tex]\begin{gathered} A=\frac{36}{360}\ast\pi\ast15^2 \\ \\ A=\frac{1}{10}\ast\pi\ast225 \end{gathered}[/tex]Solving further:
[tex]\begin{gathered} A=0.1\pi\ast225 \\ \\ A=70.69\text{ square units} \end{gathered}[/tex]Therefore, the area of the sector rounded to the nearest hundredth is 70.69 square units
ANSWER:
[tex]\begin{gathered} ^{} \\ \text{ 70.69 units}^2 \end{gathered}[/tex]Consider the arithmetic sequence:3,5,7,9,...If n is an integer, which of these functions generate the sequence?
Answer:
Tn = 2n+1
Explanation:
Gven tthe arithemetic sequence 3, 5, 7, 9...
The nth term of the sequence is expressed as;
Tn = a + (n-1)*d
Given
first term a = 3
Common difference d = 5 - 3 = 7 - 5 = 2
Substitute into the expression
Tn = 3 + (n-1) * 2
Tn = 3 + 2n - 2
Tn = 2n + 1
hence the function that gennerate the sequence is Tn = 2n+1
(9x10 to the 7th power) (7x10 to the 9th power) in scientific notation.
The value of the expression in scientific format is 6.3 x 10¹⁷
How to determine the expression in scientific format?From the question, we have the following parameters that can be used in our computation:
(9x10 to the 7th power) (7x10 to the 9th power)
To start with, we need to represent the above expression using numbers and mathematical operators
So, we have the following representation
(9 x 10⁷) (7 x 10⁹)
Next, we combine the brackets using a product sign
This gives
(9 x 10⁷) x (7 x 10⁹)
Next, we remove the brackets from the expression
This gives
9 x 10⁷ x 7 x 10⁹
Evaluate the products of 9 and 7
63 x 10⁷ x 10⁹
Apply the law of indices to evaluate the final products
63 x 10¹⁶
Rewrite as
6.3 x 10¹⁷
Hence, the solution is 6.3 x 10¹⁷
Read more about scientific notation at
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Which equation is perpendicular to y= 1/2x + 4
The equation is given as
[tex]y=\frac{1}{2}x+4[/tex]For finding the perpendicular line,
The product of slope is -1.
For the given equation , the slope is 1/2.
Now find the slope of perpendicular line.
[tex]\frac{1}{2}\times m=-1[/tex][tex]m=-2[/tex]Hence the slope of perpendicular line is -2.
Now the perpendicular equation to the given line can be
y=-2x+b.
Where assume b=1.
Then the equation perpendicular to the given line is
[tex]y=-2x+1[/tex]In the diagram of △△ADC below, EB∥∥DC, AE=2, AB=10, and BC=45. What is the length of AD?
Answer:
11 units
Explanation:
Given that lines EB and DC are parallel, we use the proportional division theorem:
[tex]\frac{AE}{ED}=\frac{AB}{BC}[/tex]Substitute the given values:
[tex]\begin{gathered} \frac{2}{ED}=\frac{10}{45} \\ \text{Cross multiply} \\ ED\times10=2\times45 \\ \text{Divide both sides by 10} \\ \frac{ED\times10}{10}=\frac{2\times45}{10} \\ ED=9 \end{gathered}[/tex]Next, find the length of AD:
[tex]\begin{gathered} AD=AE+ED \\ =2+9 \\ =11\text{ units} \end{gathered}[/tex]The length of AD is 11 units.
Alternate Method
[tex]ED=AD-2[/tex]So, we have that:
[tex]\frac{AE}{ED}=\frac{AB}{BC}\implies\frac{AE}{AD-2}=\frac{AB}{BC}[/tex]Substitute the given values:
[tex]\frac{2}{AD-2}=\frac{10}{45}[/tex]Cross multiply:
[tex]undefined[/tex]In a mini pharagh, how would I explain wether the rectangles are similar and explain how I know?
If they are similar then the ratio between RS and RQ has to be tha same to the ratio between WV and WX:
RS/RQ = WV/WX
8/5 = 24/15 = 3(8)/3(5) = 8/5
8/5 = 8/5
Answer:
Therefore both rectangles are similar because the ratio of their lenght to their widht is the same (8/5)
Find the value of an investment of $15,000 for 13 years at an annual interest rate of 3.15%
EXPLANATION:
We are given an investment of $15,000 invested for 13 years at an annual rate of 3.15%.
To calculate the Simple Interest on this investment, the formula given is;
[tex]I=PRT[/tex]Where the variables are;
[tex]\begin{gathered} P=15000 \\ R=3.15\% \\ T=13 \end{gathered}[/tex]We now have;
[tex]I=15000\times0.0315\times13[/tex][tex]I=6142.5[/tex]The value at the end of the investment period is now derived as;
[tex]A=P+I[/tex][tex]A=15000+6142.5[/tex][tex]A=21,142.5[/tex]To calculate value of this investment using the compound interest formula, we shall apply the formula which is;
[tex]A=P(1+r)^t[/tex]Given the same variables as earlier, we simply substitute and solve as shown below;
[tex]A=15000(1+0.0315)^{13}[/tex][tex]A=15000(1.0315)^{13}[/tex][tex]A=15000(1.49658028574)[/tex][tex]A=22448.7042861[/tex]We can round this to 2 decimal places and we'll have;
[tex]A=22,448.70[/tex]ANSWER:
Amount of the investment after 13 years will be $22,448.70
if 1=1.50 then what are the next 4 terms of it?
A surveyor measures the distance across a straight river by the following method: Starting directly across from a tree on the opposite bank, he walks x = 116 m along the riverbank to establish a baseline. Then he sights across to the tree. The angle from his baseline to the tree is = 29.2°. How wide is the river?
SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
The details of the solution are as follows:
The width of the river can see calculated thus:
[tex]\begin{gathered} \\ Using\text{ Trignometry, we have that:} \\ tan\text{ 29.2}^0\text{ =}\frac{opposite\text{ }}{adjacent}=\frac{y}{116} \end{gathered}[/tex][tex]\begin{gathered} cross-multiply,\text{ we have that:} \\ y\text{ = 116 x tan 29.2}^0 \\ Then,\text{ } \\ y\text{ = 116 x 0.5589} \\ y\text{ = 64.8324 m} \\ y\text{ }\approx\text{ 65 m \lparen to the nearest metre\rparen} \end{gathered}[/tex]CONCLUSION:
The width of the river is:
[tex]y=\text{ 65 m \lparen correct to the nearest metre\rparen}[/tex]Find the slope of the line passing through the points (-3, 5) and (-6, 4).13-13-3131
Step 1
Given; Find the slope of the line passing through the points (-3, 5) and (-6, 4).
Step 2
Slope is given as;
[tex]\begin{gathered} y_2=4 \\ y_1=5 \\ x_2=-6 \\ x_1=-3 \end{gathered}[/tex][tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{4-5}{-6-(-3)} \\ m=\frac{-1}{-3}=\frac{1}{3} \end{gathered}[/tex]Answer;
[tex]slope=\frac{1}{3}[/tex]statement if p then not q this is different statement than the one give in the notes
Solution:
Given:
The conditional statement;
[tex]\begin{gathered} \text{If p, then not q} \\ p\rightarrow\text{ \textasciitilde{}q} \end{gathered}[/tex]A converse statement is a result of reversing its two constituent statements.
[tex]\begin{gathered} \text{Conditional statement-If p, then not q} \\ \text{Converse statement-If not q, then p} \end{gathered}[/tex]Therefore, the converse statement is: If not q, then p
The inverse statement assumes the opposite of each of the original statements.
[tex]\begin{gathered} \text{Conditional statement-If p, then not q} \\ I\text{nverse statement-If not p, then q} \end{gathered}[/tex]Therefore, the inverse statement is: If not p, then q
To get the contrapositive statement, we interchange the conclusion of the inverse statement.
[tex]\begin{gathered} \text{Conditional statement-If p, then not q} \\ I\text{nverse statement-If not p, then q} \\ \\ \text{Hence, the contrapositive statement is gotten by reversing the conclusion of the inverse statement.} \\ \text{Contrapositive statement-If q, then not p} \end{gathered}[/tex]
Therefore, the contrapositive statement is: If q, then not p
I need help with this questions please. This is non graded.
Given that we have to write the quadratic equation and then we have to solve it and represent it graphically.
Then,
let the equation be
[tex]x^2+10x-24=0[/tex]To find the roots we will do the factorization then we have
[tex]\begin{gathered} x^2+10x-24=0 \\ x^2+12x-2x-24=0 \\ x(x+12)-2(x+12)=0 \\ (x+12)(x-2)=0 \\ x+12=0\text{ and x-2=0} \\ x=-12\text{ and x = 2} \end{gathered}[/tex]So the roots are -12 and 2.
Given BA=DCCB=ADWhich postulate/theorem will be sufficient to prove ∆ABC= ∆CDB
We are given two triangles and we are told that
[tex]\begin{gathered} BA=DC \\ CB=AD \end{gathered}[/tex]since the triangle share side BD this means that the triangles have the same side length, therefore, congruency can be proved by SSS (Side Side Side).
21/6 divided by 2/3.
Remember that to divide fractions we can use the following method:
First, multiply a times d and write the result in the numerator:
Next, multiply b times c and write the result in the denominator:
Then, by using this method:
[tex]\begin{gathered} \frac{21}{6}\div\frac{2}{3}=\frac{21\cdot3}{6\cdot2} \\ =\frac{21\cdot3}{3\cdot2\cdot2} \\ =\frac{21}{2\cdot2} \\ =\frac{21}{4} \end{gathered}[/tex]Therefore, 21/6 divided by 2/3 is equal to 21/4.
Step-by-step explanation:
21/6÷2/3=21.3/6.2
= 21.3/2.3.2
=21/2.2=21/4=5.25
Kate started with a piece of bubblegum that was 5/8 in wide . She later blew a bubble that was 2 7/8 in wide how much wider was Kate's bubble than the original piece of bubblegum
The answer is 23/5 or 4.6
how to solve this question?
Answer:
2+4+2= 8
Step-by-step explanation:
a dodecagon is a polygon with 12 sides. what's the sum of the interior angles of a dodecagon
Answer:
1800 degrees
Explanation:
The sum of the interior angles of a dodecagon can be calculated using the following equation:
Sum of the interior angles = ( n - 2 ) x 180
Where n is the number of sides of the polygon.
So, if we replace n by 12, we get:
Sum of the interior angles = ( 12 - 2 ) x 180
Sum of the interior angles = 10 x 180
Sum of the interior angles = 1800
Therefore, the sum of the interior angles of a dodecagon is 1800 degrees.
Use the diagram and problem below to find the missing anglemeasure.
Given:
BAC = 33 degrees
BDC = 35 degrees
Solution:
From the properties of an isosceles triangle:
The base angles of an isosceles triangle are equal. Hence from triangle BDC, we have:
[tex]\angle\text{BDC = }\angle\text{BCD = 35}^0[/tex]We can obtain angle DBC using the theorem that the sum of angles in a triangle is 180 degrees:
[tex]\begin{gathered} \angle DBC=180^0-35^0-35^0 \\ =110^0 \end{gathered}[/tex]To find angle ABD, we use the theorem of congruency. i.e
[tex]\Delta\text{ ABD }\cong\text{ }\Delta\text{ ABC}[/tex]Hence,
[tex]\angle\text{ ABD = }\angle\text{ ABC}[/tex]Since the angles ABD, ABC and DBC lie at a point, we have:
[tex]\begin{gathered} Let\text{ }\angle\text{ ABD = x} \\ x+x+110^0=360^0 \\ 2x=250^0 \\ x=125^0 \end{gathered}[/tex]Answer : angle ABD = 125 degrees
Put a T for a true or a F for false .and don't worry this is just a practice :)and let me know if you can see the picture !!
1)
Working with inequalities, when you draw them in a number line or a coordinate system. The Open circle, or "blank dot" indicates that the number itself is not included in the definition, while the closed circle or "blak dot" indicates the value is included.
For example:
The inequality marked in the number line can be expressed symbolically as:
[tex]x<2[/tex]So the first statement is True.
2)
When an inequality includes a variable (letter) this one can be writen in terms of said variable following almost the same rules as when you calculate the value of a variable in an equation.
The greatest exception is that when you divide by a negative number, the direction of the inequality changes.
So for the given inequality:
[tex]-10w>100[/tex]To determine one possible value of w you have to divide both sides of the expression by "-10" and when you do so, the direction of the inequality gets inverted from > to <
[tex]\begin{gathered} -10w>100 \\ w<\frac{100}{-10} \\ w<-10 \end{gathered}[/tex]So this statement is False.
3)
This statement is True, when the variable is "alone" the coefficient is 1. Since multiplying a number by one results in said number it is redundant to write it, but altough "invisible" one is the coefficient of any variable that is "alone" in any given expression.
4)
"At most" indicates that it is the maximum value possible for the determined inequality. So the inequality can be equal or less than the determined value.
For example, "The cell phone repair will cost at most $100" → You know that you will pay no more than $100 dollars for the repair, it can be less but not more.
Let "x" symbolize the repair cost, you can express this as:
[tex]x\leq100[/tex]So this statement is True
5)
"Minimum" indicates that is the lowest value of the inequality, it is the startpoint, from the determined value onwards.
Compute.-2.65 - 16.3 =23.5 + ( -62.74) =
Given:
There are given the expression:
[tex]\begin{gathered} -2.65-16.3\text{ and} \\ 23.5+(-62.74) \end{gathered}[/tex]Explanation:
To find the value of the expression, we need to subtract 16.3 from the -2.65.
Then,
[tex]-2.65-16.3=-18.95[/tex]And,
In the next expression, we need to add 23.5 with (-62.74).
So,
[tex]\begin{gathered} 23.5+(-62.74)=23.5-62.74 \\ =-39.24 \end{gathered}[/tex]Final answer:
Hence, the value of the expressions is shown below:
[tex]undefined[/tex]graph the following system of inequalities and the solution set.y>2x+1y
Problem
graph the following system of inequalities and the solution set.
y>2x+1
ySolution
For this case when we create the plot we got:
And we can see that the solution set in terms of x is given by:
[tex](-\infty,-3)[/tex]And for y:
[tex](-\infty,-5)[/tex]
3. The vertex of the graph of y = ax + b is at the ?, and the vertex of the graph of y = a + b is at the ?
3. The vertex of the function y=|ax+b| happens at y=0, where the function changes its direction.
Then, the value of x at that point is x=-b/a.
The vertex happens at (-b/a,0). This is the x-intercept
In the second function y=a|x|+b, the vertex happens when x=0 and y=b. This is the y-intercept.
Answer: Option B: x-intercept, y-intercept.