Price after discount = $14
discount = 30%
x (1-30/100) = 14
x (1-0.3) = 14
x 0.7 = 14
Solve for x (original price )
x = 14/0.7
x = 20
The enrollment at a local college increased 3% over last year's enrollment of 500. Find the current enrollment.
Given:
Last year's enrollment is 500.
Enrollment increased percentage is 3%
[tex]\begin{gathered} \text{Increased enrollment=500}\times\frac{3}{100} \\ \text{Increased enrollment=}5\times3 \\ \text{Increased enrollment=}15 \end{gathered}[/tex][tex]\begin{gathered} \text{Current enrollment=500+15} \\ \text{Current enrollment=}515 \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
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
In the sketch below, A ABC is similar to AXY Z. Find the length of side x
From geometry, we know that if two triangles are similar, then their corresponding sides are in proportion.
From the statement, we know that ΔABC is similar to ΔXYZ.
From the diagram, we see that:
• AB = 15 is the corresponding side to XY = 10,
,• BC = 9 is the corresponding side to YZ = x.
So we must have the equality:
[tex]\begin{gathered} \frac{AB}{XY}=\frac{BC}{YZ}, \\ \frac{15}{10}=\frac{9}{x}, \\ 1.5=\frac{9}{x}. \end{gathered}[/tex]Solving for x, we get:
[tex]\begin{gathered} 1.5x=9, \\ x=\frac{9}{1.5}=6. \end{gathered}[/tex]Answerx = 6
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
determine if the following sequence is Arithmetic if so what is the common difference 77 44 16 -12
Answer:
The sequence is not an arithmetic sequence.
Explanation:
Given the sequence:
[tex]77,44,16,-12,\ldots[/tex]Calculate the difference between the terms below:
[tex]\begin{gathered} 44-77=-33 \\ 16-44=-28 \\ -12-16=-28 \end{gathered}[/tex]Observe that the differences between the terms are not the same all through.
Thus, there is no common difference which implies that the sequence is not an arithmetic sequence.
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.
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]if 1=1.50 then what are the next 4 terms of it?
If a line has slope a, what is the slope of its reflection across the line y=x?Question content area bottomPart 1The slope of its reflection across the line y=x will be
By definition, let m be the slope a line, then m can be calculated by the following equation:
[tex]m=\frac{y_2-y_1}{x_2-x_1}^{}[/tex]Given that (x1, y1) and (x2, y2) are known points of the line. By reflecting all the points of the line across the line y = x
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
b. What is the sample space if you spin the spinner TWO TIMES?RedYellowBlueRedYellowBluec. One spin, P(red)(fraction)d. Two spins, Pared then blue)(decimal to 2 places)e. Two spins, P(yellow or red)=% (percent to 1 decimal place)
Hanna, this is the solution:
As you can see there are three equal sectors colored yellow, blue, red, therefore, the sample space for spinning the spinner two time is:
{yellow-yellow, blue-yellow, red-yellow, red-blue, red-red, blue-blue}
Spin the spinner one time:
• Red = 1/3 or 0.33
,• Blue = 1/3 or 0.33
,• Yellow = 1/3 or 0.33
Spin the spinner a second time:
• Red - Red = 1/3 * 1/3 = 1/9 or 0.11
,• Red - Blue = 1/3 * 1/3 = 1/9 or 0.11
,• Red - Yellow = 1/3 * 1/3 = 1/9 or 0.11
,• Blue - Blue = 1/3 * 1/3 = 1/9 or 0.11
,• Blue - Red = 1/3 * 1/3 = 1/9 or 0.11
,• Blue - Yellow =1/3 * 1/3 = 1/9 or 0.11
,• Yellow - Yellow = 1/3 * 1/3 = 1/9 or 0.11
,• Yellow - Red = 1/3 * 1/3 = 1/9 or 0.11
,• Yellow - Blue = 1/3 * 1/3 = 1/9 or 0.11
,•
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
Write the coordinates of the vertices after a translation 2 units left and 1 unit up. 10 D E F -10 0 10 -10 D(-6, 4) → E(0,4) → Ell F(-4, 2) + FIC D
We need to subtract 2 from our x-coordinate and add 1 to our y-coodrinate. Doing this gives us
[tex]D(-6,4)\rightarrow D(-8,5)[/tex][tex]E(0,4)\rightarrow E(-2,5)[/tex][tex]F(-4,2)\rightarrow F(-6,3)[/tex]And hence, we have correctly given the coordinates of our translated points.
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.
Which polynomial function is graphed below?-10A. (x) = (x – 3yº (x + 2)B. f(x) = (x - 2y(x +3)C. (*) - (x - 2)(x+3)D. *(x) = (x-3)(x + 2y4
Every polynomial can be written in the form:
[tex]f(x)=(x-a_1)(x-a_2)\ldots_{}[/tex]The a_1, a_2.... are the roots of the polynomial, meaning that f(a_1) = f(a_2) = ... = 0. This happens wen the graph of the polynomial intersects or tangency the x-axis. Whe it only tangecy the x-axis, it means that you have two of the root.
In this case, we have the polynomial tangency the x-axis in x = -2 and intersect the x-axis in x = 3. This means that the polynomial has roots -2, -2 (again) and 3. So:
[tex]\begin{gathered} f(x)=(x-(-2))(x-(-2))(x-3) \\ f(x)=(x+2)(x+2)(x-2) \\ f(x)=(x+2)^2(x-3) \end{gathered}[/tex]Since the order doesn't metter, we can right in this way:
[tex]f(x)=(x-3)(x+2)^2[/tex]Which corresponds to alternative D.
If ƒ (7) = 22, thenf-¹(f(7)) = [?]
Remember the following property of invertible functions:
[tex]f(x)=y\qquad\Leftrightarrow\quad f^{-1}(y)=x[/tex]Then:
[tex]f^{-1}(f(x))=x\qquad\forall x[/tex]Then:
[tex]f^{-1}(f(7))=7[/tex]Therefore, the answer is: 7.
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
(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
https://brainly.com/question/27862246
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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).
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
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.
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.
{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]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]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
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 graphs to the probability that z-score is between 0 and 1?
The z-score of a measure is given by the following formula
[tex]z=\frac{x-\mu}{\sigma}[/tex]where x represents the measure, mu represents the mean of the distribution, and sigma represents the standard deviation.
If we have a z-score equal to zero, our measure will be
[tex]\begin{gathered} 0=\frac{x-\mu}{\sigma} \\ 0=x-\mu \\ x=\mu \end{gathered}[/tex]a z-score equal to zero represents the mean of the distribution.
For a z-score equal to 1, we have
[tex]\begin{gathered} 1=\frac{x-\mu}{\sigma} \\ \sigma=x-\mu \\ x=\mu+\sigma \end{gathered}[/tex]Then, the interval between z = 0 and z = 1 is the interval between the mean and one positive standard deviation.
[tex](\mu,\mu+\sigma)[/tex]The graph that represents this interval is the first graph.
2х +8y = 16 -3х +6y = 30determine the number of solutions
Given: The system of equation below
[tex]\begin{gathered} 2x+8y=16 \\ -3x+6y=30 \end{gathered}[/tex]To Determine: The number of solutions
Solution
Combine the two equations and solve
[tex]\begin{gathered} equation1:2x+8y=16 \\ equation2:-3x+6y=30 \end{gathered}[/tex]Multiply equation by 3 and equation 2 by 2
[tex]\begin{gathered} 3(2x+8y=16)=6x+24y=48==equation3 \\ 2(-3x+6y=30)=-6x+12y=60==equation4 \end{gathered}[/tex]Add equation 3 and 4
[tex]\begin{gathered} 6x-6x+24y+12y=48+60 \\ 36y=108 \\ y=\frac{108}{36} \\ y=3 \end{gathered}[/tex]Substitute y in equation 1
[tex]\begin{gathered} 2x+8y=16 \\ 2x+8(3)=16 \\ 2x+24=16 \\ 2x=16-24 \\ 2x=-8 \\ x=-\frac{8}{2} \\ x=-4 \end{gathered}[/tex]Hence, x = -4, y = 3
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)