In order to find the percentage of students within 2 standard deviations, let's look at the z-table for the percentages when z = -2 and z = 2.
From the z-table, we have that the percentage for z = -2 is 0.0228 and for z = 2 is 0.9772.
The percentage between z = -2 and z = 2 is given by:
[tex]0.9772-0.0228=0.9544[/tex]Therefore the percentage is 95.44%.
Now, calculating the number of students within this percentage, we have:
[tex]500\cdot0.9544=477.2[/tex]Rounding to the nearest whole, we have 477 students.
i have to use interval notation and i’m stuck on it
Given two sets of real numbers:
[tex]\begin{gathered} D=\mleft\lbrace w\mright|w\ge4\} \\ E=\mleft\lbrace w\mright|w<8\} \end{gathered}[/tex]we will write the given sets as intervals
so,
[tex]\begin{gathered} D=\lbrack4,\infty) \\ E=(-\infty,8) \end{gathered}[/tex]The intersections and the union of the sets will be as follows:
[tex]\begin{gathered} D\cap E=\lbrack4,8) \\ \\ D\cup E=(-\infty,\infty) \end{gathered}[/tex]Select the correct choice below and fill in the answer
Step 1:
Write the function
[tex]g(x)=x^5-16x^3[/tex]Step 2:
Write an inequality equation where g(x) > 0
[tex]\begin{gathered} x^5-16x^3\text{ > 0} \\ \text{Factorize the left hand side of the equation} \\ x^3(x^2\text{ - 16) > 0} \\ x^3(x\text{ - 4)(x + 4) > 0} \end{gathered}[/tex]Step 3:
Identify the intervals
- 4 < x < 0 or x > 4
[tex]\text{Answer in interval notation: }(\text{ - 4 , 0 ) }\cup\text{ ( 4 , }\infty\text{ )}[/tex]Select the correct answer.What are the asymptote and the y-intercept of the function shown in the graph?
Answer:
Explanation:
Here, we want to get the y-intercept and the asymptote of the shown function
The y-intercept is simply the point at which the curve crosses the y-axis
We can see this at the point y = 5 which is coordinate form is (0,5)
The asymptote is the point on the y-axis where the curve almost flattens out but will never touch
We have this at the point y = 2
For z1 = 9cis 5pi/6 and z2=3cis pi/3, find z1/z2 in rectangular form
We have the following:
are the complex number
[tex]\begin{gathered} z_1=9cis\frac{5\pi}{6}_{} \\ z_2=3\text{cis}\frac{\pi}{3} \\ \frac{z_1}{z_2} \end{gathered}[/tex]So magnitudes are r₁ = 9, and r₂ = 3 and arguments are ∅₁ = 5π/6, and ∅₂ = π/3
[tex]\frac{z_1}{z_1}=\frac{r_1}{r_2}\cdot\text{cis(}\emptyset_1\cdot\emptyset_{2})[/tex]replacing:
[tex]\begin{gathered} \frac{z_1}{z_2}=\frac{9}{3}\cdot\text{cis}(\frac{5\pi}{6}-\frac{\pi}{3}) \\ \frac{z_1}{z_2}=3\cdot\text{cis}(\frac{5\pi}{6}-\frac{2\pi}{6}) \\ \frac{z_1}{z_2}=3\cdot\text{cis}(\frac{3\pi}{6}) \\ \frac{z_1}{z_2}=3\cdot\text{cis}(\frac{\pi}{2})\rightarrow\text{cis}(\frac{\pi}{2})=\cos \mleft(\frac{\pi}{2}\mright)+3i\sin \mleft(\frac{\pi}{2}\mright) \\ \frac{z_1}{z_2}=3\cdot\lbrack\cos (\frac{\pi}{2})+i\sin (\frac{\pi}{2})\rbrack \\ \frac{z_1}{z_2}=3\cdot\lbrack0+i\cdot1)\rbrack \\ \frac{z_1}{z_2}=3\cdot0+3\cdot i \\ \frac{z_1}{z_2}=3i \end{gathered}[/tex]Therefore, the answer is option D 3i
Fallington Fair charges an entrance fee of $10 and $1.00 per ticket for the rides. Levittown Fair charges $5 entrance fee and $2 per ticket. Write an equation/inequality to show when Fallington Fair and Levittown Fair will cost the same.
Information given
Fallington Fair charges an entrance fee of $10 and $1.00 per ticket for the rides. Levittown Fair charges $5 entrance fee and $2 per ticket. Write an equation/inequality to show when Fallington Fair and Levittown Fair will cost the same.
Solution
Let's put some notation for this case, let x the number of rides and we can set up the following equation:
[tex]\text{Fallington}=\text{Levitown}[/tex][tex]10+x=5+2x[/tex]And now we can solve for x on the following way:
10-5= 2x-x
5=x
So then Fallington Fair and Levittown Fair will cost the same at 5 rides
Given the points A(-8,-7) and B(8,5) find the coordinates of point P on directed line segment AB that partitions AB into the ratio 3:1
Given the points A(-8,-7) and B(8,5) find the coordinates of point P on directed line segment AB that partitions AB into the ratio 3:1
step 1
Find the distance in the x-coordinate between A and B
dABx=(8-(-8)=8+8=16 units
Find the distance in the y-coordinate between A and B
dABy=5-(-7)=5+7=12 units
step 2
we know that
point P on directed line segment AB that partitions AB into the ratio 3:1
so
AP/AB=3/(3+1)
AP/AB=3/4
Find the x coordinate of point P
APx/ABx=3/4
substitute
APx/16=3/4
APx=16*(3/4)
APx=12 units
The x-coordinate of P is
Px=Ax+APx
where
Ax is the x-coordinate of P
Px=-8+12=4
step 3
Find the y-coordinate of P
we have that
APy/ABy=3/4
substitute
APy/12=3/4
APy=12*(3/4)
APy=9
The y coordinate of P is
Py=APy+Ay
where
Ay is the y-coordinate of P
Py=9+(-7)=2
therefore
the answer is
The coordinate of P are (4,2)You deposit $ 1,821 in an account earning 3 % interest compounded monthly. How much will you have in the account in 1 years?$__________ (Give your answer accurate to 2 decimal places)
Using the compound interest formula:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Where:
A = Amount
P = Principal = $1821
r = Interest rate = 3% = 0.03
n = Number of times interest is compounded per year = 12
t = Time = 1
So:
[tex]\begin{gathered} A=1821(1+\frac{0.03}{12})^{12\cdot1} \\ A\approx1876.39 \end{gathered}[/tex]Answer:
$1876.39
Which equation is true when the value of x is -12
We are told to check for the correct equation that satisfies when the value of x = -12.
Let us resolve that by picking one of the options and testing it to confirm if it satisfies the value of x = -12.
Starting with OPTION B
[tex]15-\frac{1}{2}x=21[/tex]Solve for x
Subtract 12 from both sides
[tex]\begin{gathered} 15-15-\frac{1}{2}x=21-15 \\ -\frac{1}{2}x=6 \end{gathered}[/tex]Multiply both sides by 2
[tex]\begin{gathered} 2\times-\frac{1}{2}x=2\times6 \\ -1x=12 \end{gathered}[/tex]Divide both sides by -1
[tex]\begin{gathered} \frac{-1x}{-1}=\frac{12}{-1} \\ x=-12 \end{gathered}[/tex]From the solution, we can conclude that the above equation is true when the value of x = -12.
The correct option is Option B.
Find the formula for an exponential equation that passes through the points, (0,5) and (1,2). The exponential equation should be of the form y = ab^x
Answer:
[tex]y=5\cdot(\frac{2}{5})^x[/tex]Explanation:
The exponential equation has the form
[tex]y=a\cdot b^x[/tex]Since it passes through the point (0, 5). Let's replace (x, y) by (0, 5) to find the value of a
[tex]\begin{gathered} 5=a\cdot b^0 \\ 5=a\cdot1 \\ 5=a \end{gathered}[/tex]Then, the equation is
[tex]y=5\cdot b^x[/tex]To find the value of b, we will use the point (1, 2), so replacing x = 1 and y = 2, we get:
[tex]\begin{gathered} 2=5\cdot b^1 \\ 2=5\cdot b \\ \frac{2}{5}=\frac{5\cdot b}{5} \\ \frac{2}{5}=b \end{gathered}[/tex]Then, the exponential equation is:
[tex]a=5\cdot(\frac{2}{5})^x[/tex]Answer:
Step-by-step explanation: the answer is a= 5(2/5)^x
Each vertical cross-section of the triangular prism shown below is an isosceles triangle.4What is the slant height, s, of the triangular prism?Round your answer to the nearest tenth.The slant height isunits
The length of the diagonal of a cube can be calculated by the formula
[tex]\begin{gathered} d=a\sqrt[]{3} \\ \text{where a is one side of the cube} \\ a=60 \end{gathered}[/tex]Hence,
[tex]\begin{gathered} d=60\sqrt[]{3}\text{ units} \\ d=103.92\text{ units (2 decimal place)} \end{gathered}[/tex]x^2+x^2=11.3^2 solve using the pathogen theorem
The value of x in the given expression is 8.
What is Pythagoras theorem?Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (a² + b² = c²).
Given an expression, x²+x² = 11.3²
2x² = 11.3²
[tex]\sqrt{2}[/tex]x = 11.3
x = 7.99 = 8
Hence, The value of x in the given expression is 8.
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2x^3 - 4x^2 - 50x + 100 factoring completely
The factor is 2(x−2)(x+5)(x−5).
From the question, we have
2x³−4x²−50x+100
=2(x−2)(x+5)(x−5)
Factors :
The positive integers that can divide a number evenly are known as factors in mathematics. Let's say we multiply two numbers to produce a result. The product's factors are the number that is multiplied. Each number has a self-referential element. There are several examples of factors in everyday life, such putting candies in a box, arranging numbers in a certain pattern, giving chocolates to kids, etc. We must apply the multiplication or division method in order to determine a number's factors.The numbers that can divide a number exactly are called factors. There is therefore no residual after division. The numbers you multiply together to obtain another number are called factors. A factor is therefore another number's divisor.
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The time spent waiting in the line is approximately normally distributed. The mean waiting time is 6 minutes and the variance of the waiting time is 9. Find the probability that a person will wait for between 10 and 12 minutes. Round your answer to four decimal places.
The probability that a person will wait for between 10 and 12 minutes is 0.069.
What is meant by z score?z-score is defined as the number of standard deviations by which the value of a raw score is above or below the mean value of what is being measured or observed. It tells where the score lies on a normal distribution curve. It is a numerical measurement that describes a values relationship to the mean of a group of values.
z = (raw score - mean) / standard deviation
Given,
The mean waiting time is 6 minutes and variance waiting time is 9 minutes.
Standard deviation = √variance = √9 = 3minutes
For between 10 and 12 minutes, the probability is
z = (10- 6)/3 = 1.333 and z=(12-6)/3=2
p(z≤1.3333)=0.982
p(z≤2)=0.9772
Probability that a person will wait for between 10 and 12 minutes is,
|0.9082-0.9772|= 0.069
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Simplify each expression by using The Distributive Property and combine like terms to simplify the expression.4(3х - 2)
The given expression is
[tex]undefined[/tex]what is the value of 6n-2whenn=3
To find the value of an expression we only need to plug the value of the variable in said expression.
In this case we have:
[tex]6n-2[/tex]If, n=3, then:
[tex]6(3)-2=18-2=16[/tex]Therefore, the value of the expression when n=3 is 16.
3 3/10 divied by 1 4/7 in lowest terms
Answer:
Step-by-step explanation:
The answer is [tex]\frac{21}{10}[/tex] or 2 [tex]\frac{1}{10}[/tex] or 2.1.
Depending on what form your answer needs to be in, it can be one of those.
Explanation:
Turn both the mixed numbers into improper fractions. To do this, take the outside number and multiply it by the denominator. Then, add that number to the numerator. For this specific question, you would take 3×10 (because 10 is the denominator) and add it to the numerator, 3, giving the improper fraction [tex]\frac{33}{10}[/tex]. Doing the same to the divisor, you would get [tex]\frac{11}{4}[/tex].Next, take the divisor ([tex]\frac{11}{7}[/tex]) and turn it into the reciprocal ("flip" the fraction), making it [tex]\frac{7}{11}[/tex].Now, simply multiply the dividend ([tex]\frac{33}{10}[/tex]) to the reciprocal of the divisor ([tex]\frac{4}{11}[/tex]).So, your new equation is a much easier [tex]\frac{33}{10}[/tex]×[tex]\frac{7}{11}[/tex]=[tex]\frac{231}{110}[/tex]. These both are reducable by 11, therefore giving you the final answer of [tex]\frac{21}{10}[/tex].
Note: Upon reaching this step, you can simplify 33 into 3×11, then divide out the 11 from the numerator and the denominator making it a much easier problem to simplify. Hope this helps!
a figure has vertices (-13,13), (26,52), (39,39) what would the new coordinates of the vertices to the nearest tenth if the image were reduced by a scale factor of 0.77 with the origin as the center of dilation
Explanation
Given that the figure has vertices (-13,13), (26,52), (39,39), to reduce the image by a scale factor of 0.77 with the origin as the center of dilation, we will multiply the x and y coordinates by the scale factors.
is the least common denominator of two fractions always greater than the denominators of the fractions
The least common denominator of two fractions is not always greater than the denominators of each fraction because sometimes the least common denominator is equal to the greater denominator. For example, if we have the fractions
[tex]\frac{4}{5}-\frac{1}{5}[/tex]In this case, since you have equal denominators, the least common factor would be 5, not greater than 5.
Another example could be
[tex]4+\frac{2}{9}[/tex]In this case, the least common denominator is 9, not greater than 9.
Therefore, the least common denominator is not always greater than the denominator of the fractions.Find the minimum or maximum value of the function f(x)=10x^2+x−5. Give your answer as a fraction.
In order to find the minimum or maximum value of the function f(x),
[tex]f\mleft(x\mright)=10x^2+x-5[/tex]First, we have to find out at which value of x the function takes it. For example:
In order to find the value of x when it takes the maximum of minimum, we are going to analyze the derivative of the function. Then we are going to be following the next step-by-step:
STEP 1: finding the derivative of the function
STEP 2: analysis of the derivative of the function.
STEP 3: minimum or maximum value of the function
STEP 1: finding the derivative of the functionWe have that the derivative of the function is given by f'(x):
[tex]\begin{gathered} f\mleft(x\mright)=10x^2+x^1-5 \\ \downarrow \\ f^{\prime}(x)=2\cdot10x^{2-1}+1\cdot x^{1-1} \\ f^{\prime}(x)=20x^{2-1}+1\cdot x^0 \\ f^{\prime}(x)=20x^1+1\cdot1 \\ f^{\prime}(x)=20x^{}+1 \end{gathered}[/tex]Then, the derivative of f(x) is:
f'(x) = 20x + 1
STEP 2: analysis of the derivative of the function.We have that the function has a maximum or a minimum when its derivative takes a value of 0:
[tex]\begin{gathered} f^{\prime}\mleft(x\mright)=0 \\ 0=20x+1 \end{gathered}[/tex]when this happens, then, x has a value of:
[tex]\begin{gathered} 0=20x+1 \\ \downarrow\text{ taking -1 and 20 to the left side} \\ -1=20x \\ -\frac{1}{20}=x \end{gathered}[/tex]When x=-1/20, the function takes its minimum or maximum
STEP 3: minimum or maximum value of the functionNow, we can replace in the equation of f(x), to see what is the value of the function when x= -1/20:
[tex]\begin{gathered} f\mleft(x\mright)=10x^2+x-5 \\ \downarrow\text{ when x=}-\frac{1}{20} \\ f(-\frac{1}{20})=10(-\frac{1}{20})^2+(-\frac{1}{20})-5 \end{gathered}[/tex]Solving f(-1/20):
[tex]\begin{gathered} f(-\frac{1}{20})=10(-\frac{1}{20})^2+(-\frac{1}{20})-5 \\ \downarrow\sin ce(-\frac{1}{20})^2=\frac{1}{400} \\ =10(\frac{1}{400})-\frac{1}{20}-5 \\ =-\frac{201}{40} \end{gathered}[/tex]Then, the minimum value of the function is
[tex]f\mleft(x\mright)=\frac{-201}{40}[/tex]Answer: -201/40Use the drawing tool(s) to form the correct answer on the provided graph.
Graph the solution to this system of inequalities in the coordinate plane.
3y>2x + 122x + y ≤ -5Having trouble rewriting in form. Graphing once in form okay.
Explanation
We are given the following system of inequalities:
[tex]\begin{gathered} 3y>2x+12 \\ 2x+y\leqslant-5 \end{gathered}[/tex]We are required to graph the given system of inequalities.
This is achieved thus:
- First, we determine two coordinates from the given inequalities:
[tex]\begin{gathered} 3y>2x+12 \\ \text{ Suppose }3y=2x+12 \\ \text{ Let x = 0} \\ 3y=12 \\ y=4 \\ Coordinate:(0,4) \\ \\ \text{Suppose }3y=2x+12 \\ \text{ Let y = 0} \\ 0=2x+12 \\ 2x=-12 \\ x=-6 \\ Coordinate:(-6,0) \end{gathered}[/tex]- Now, we plot the points on a graph. Since the inequality is "strictly greater than", the line drawn will be broken. The graph is shown below:
- Using the second inequality, we have:
[tex]\begin{gathered} 2x+y\leqslant-5 \\ \text{ Suppose }2x+y=-5 \\ \text{ Let y = 0} \\ 2x=-5 \\ x=-2.5 \\ Coordinate:(-2.5,0) \\ \\ \text{Suppose }2x+y=-5 \\ \text{ Let x = 0} \\ y=-5 \\ Coordinate:(0,-5) \end{gathered}[/tex]The graph becomes:
Combining both graphs, we have the solution to be:
The solution is the intersection of both graphs as indicated above.
1. find the sum of the first 7 terms of the following sequence round to the nearest hundredth if necessary 18,-6,22. Find the sum of the first 6 terms of the following sequence to the nearest hundredth:324, 54, 9
You can find the sum of the first n terms of a geometric sequence using the formula:
[tex]S_n=\frac{a_1(1-r^n)}{1-r}[/tex]1. First, let's calculate r:
[tex]\begin{gathered} r_1=18-(-6)=24 \\ r_2=-6-2=-8 \\ r=-\frac{8}{24}=-\frac{1}{3} \end{gathered}[/tex]Replacing the values in the formula, (n=7 , r=-1/3) we get that:
[tex]S_n=13.51[/tex]2. Let's calculate r:
[tex]\begin{gathered} r_1=324-54=270 \\ r_2=54-9=45 \\ r=\frac{r_2}{r_1}=\frac{45}{270}=\frac{1}{6} \end{gathered}[/tex]Using the formula with the data we have, (n=6 , r=1/6) we get that
[tex]S_n=388.79[/tex]8+7i/4-6iI need the answer and how to solve asap!
ANSWER
[tex]\frac{1}{52}(-10\text{ + 76i) or }\frac{1}{26}(-5\text{ + 38i)}[/tex]EXPLANATION
We are given the fraction of complex numbers:
[tex]\frac{\text{8 + 7i}}{4\text{ - 6i}}[/tex]To simplify this, we will find the conjugate of the denominator and then multiply that with the numerator and denomiator.
The conjugate is gotten by changing the sign of the denominator. That is:
4 + 6i
So, we have:
[tex]\begin{gathered} \frac{\text{8 + 7i}}{4\text{ - 6i}}\cdot\text{ }\frac{4\text{ + 6i}}{4\text{ + 6i}} \\ =\text{ }\frac{(8\text{ + 7i) (4 + 6i)}}{(4\text{ - 6i) (4 + 6i)}} \\ =\frac{(8\cdot\text{ 4) + (8 }\cdot\text{ 6i) + (7i }\cdot\text{ 4) + (7i }\cdot\text{ 6i)}}{(4\cdot\text{ 4) + (6i }\cdot\text{ 4) - (6i }\cdot\text{ 4) - (6i }\cdot\text{ 6i)}} \\ We\text{ know that i = }\sqrt{i},\text{ so i }\cdot\text{ i = -1:} \\ \Rightarrow\text{ }\frac{\text{ }32\text{ + 48i + 28i - 42}}{16\text{ + 24i - 24i + 36}} \\ =\text{ }\frac{-10\text{ + 76i}}{16\text{ + 36}}\text{ = }\frac{-10\text{ + 76i}}{52} \\ =\text{ }\frac{1}{52}(-10\text{ + 76i) or }\frac{1}{26}(-5\text{ + 38i)} \end{gathered}[/tex]That is the answer.
Given: CD⎯⎯⎯⎯⎯⎯ is an altitude of △ABC.Prove: a2=b2+c2−2bccosAFigure shows triangle A B C. Segment A B is the base and contains point D. Segment C D is shown forming a right angle. Segment C D is labeled h. Segment A B is labeled c. Segment B C is labeled a. Segment A C is labeled b. Segment A D is labeled x. Segment D B is labeled c minus x. Select from the drop-down menus to correctly complete the proof.Statement ReasonCD⎯⎯⎯⎯⎯⎯ is an altitude of △ABC. Given△ACD and △BCD are right triangles. Definition of right trianglea2=(c−x)2+h2a2=c2−2cx+x2+h2Square the binomial.b2=x2+h2cosA=xbbcosA=xMultiplication Property of Equalitya2=c2−2c(bcosA)+b2a2=b2+c2−2bccosA Commutative Properties of Addition and Multiplication
Solution:
The equation below is given as
[tex]a^2=(c-x)^2+h^2[/tex]This represents the
PYTHAGOREAN THEOREM
The second equation is given below as
[tex]b^2=x^2+h^2[/tex]This represents the
PYTHAGOREAN THEOREM
The third expression is given below as
[tex]\cos A=\frac{x}{b}[/tex]This represents
Definition of cosine
The fourth expression is given below as
[tex]a^2=c^2-2c(bcosA)+b^2[/tex]This represents
Substitution property of equality
A bag of fertilizer covers 2,000 square feet of lawn. Find how many bags of fertilizer should be purchased to cover a rectangular lawn that is 29400 square feet.
Okay, here we have this:
Considering the provided information, we are going to calculate how many bags of fertilizer should be purchased to cover a rectangular lawn that is 29400 square feet, so we obtain the following:
Number of bags=Total space / Space per bag
Number of bags=29400ft² / 2000ft²
Number of bags=14.7
Number of bags≈15 bags of fertilizer.
Finally we obtain that rounded to the nearest unit, 15 bags of fertilizer are needed.
Select three points: one above the line, one below it, and one on it. Substitute each into the inequality and show the results.Select the words from the drop-down lists to correctly complete the sentences.The point (−5, 5) is on, below, above the line and is, is not a solution to the inequality. The point (0, 10) is on, below, above the line and is, is not a solution to the inequality. The point (0, 0) is on, below, above the line and is not, is a solution to the inequality.(0, 0) is on, below, above the line and is now, is a solution to the inequality.
EXPLANATION
Since we have the given graph, the points that we can use are the following:
The points (-5,5) is above the line and is not a solution to the inequality.
The point (0,10) is on the line and is not a solution to the inequality.
The point (0,0) is below the line and is a solution to the inequality.
find each measure 113° 23°x=?
We have that a vertex outside a circle is just the half of the difference of the angles:
Then, in this case:
[tex]x=\frac{113-23}{2}=\frac{90}{2}=45[/tex]Answer: x = 45º
Determine the number of solutions for the following system of linear equations. If there is only onesolution, find the solution.x + 3y – 2z = 6- 4x - 7y + 3z = 3- 7x – 4y - 3z = -5AnswerKeypadKeyboard ShortcutsSelecting an option will enable input for any required text boxes. If the selected option does not have anyassociated text boxes, then no further input is required.O No SolutionO Only One SolutionX =y =Z=Infinitely Many Solutions
First, let's clear z from equation 1:
[tex]\begin{gathered} x+3y-2z=6\rightarrow x+3y-6=2z \\ \rightarrow z=\frac{1}{2}x+\frac{3}{2}y-3 \end{gathered}[/tex]Now, let's plug it in equations 2 and 3, respectively:
[tex]\begin{gathered} -4x-7y+3z=3 \\ \rightarrow-4x-7y+3(\frac{1}{2}x+\frac{3}{2}y-3)=3 \\ \\ \rightarrow-4x-7y+\frac{3}{2}x+\frac{9}{2}y-9=3 \\ \\ \rightarrow-\frac{5}{2}x-\frac{5}{2}y=12_{} \\ \end{gathered}[/tex][tex]\begin{gathered} -7x-4y-3z=-5 \\ \rightarrow-7x-4y-3(\frac{1}{2}x+\frac{3}{2}y-3)=-5 \\ \\ \rightarrow-7x-4y-\frac{3}{2}x-\frac{9}{2}y+3=-5 \\ \\ \rightarrow-\frac{17}{2}x-\frac{17}{2}y=-8 \end{gathered}[/tex]We'll have a new system of equations:
[tex]\begin{gathered} -\frac{5}{2}x-\frac{5}{2}y=12_{} \\ \\ -\frac{17}{2}x-\frac{17}{2}y=-8 \end{gathered}[/tex]Now, let's simplify each equation. To do so, we'll multiply the first one by -2/5 and the second one by -2/17. We'll get:
[tex]\begin{gathered} x+y=-\frac{24}{5} \\ \\ x+y=\frac{16}{17} \end{gathered}[/tex]Now, let's solve each equation for y to see them as a pair of line equations:
[tex]\begin{gathered} y=-x-\frac{24}{5}_{} \\ \\ y=-x+\frac{16}{17} \end{gathered}[/tex]Notice that this lines have the same slope. Therefore, they're parallel and do not intercept.
This way, we can conlcude that the original system has no solution.
The model shows the expression 21 + 9. Which expression is equivalent to this sum? O 317+3) 0 31+ 3 0 3+7+3 O 763+3)
Given data:
The given expression is (21+9).
The given expression can be written as,
[tex](21+9)=3(7+3)[/tex]Thus, the first option is correct.
There is a bag full of 30 different colored and/or patterned balls. How many different three ball combinations can you have if you pull three balls out of the bag?Part 2: Write down (in factorial form) the total number of possible combinations there are if you draw all the balls out of the bag one at a time.I am really stuck on part 2
a) 4060 different combinations
b) 30!
Explanation:Given:
Total balls of different patterns = 30
To find:
a) the different three-ball combinations one can have if 3 balls are pulled out of the bag
b) the total number of possible combinations there are if you draw all the balls out of the bag one at a time in factorial form
a) To determine the 3-ball combinations, we will apply combination as the order they are picked doesnot matter
[tex]\begin{gathered} for^^^\text{ the 3 ball comination = }^nC_r \\ where\text{ n = 30, r = 3} \\ \\ ^{30}C_3\text{ = }\frac{30!}{(30-3)!3!} \\ ^{30}C_3\text{ = }\frac{30!}{27!3!}\text{= }\frac{30\times29\times28\times27!}{27!\times3\times2\times1} \\ \\ ^{30}C_3\text{ = 4060 different combinations} \end{gathered}[/tex]b) if you are to draw all the balls one at a time, then for the 1st it will be 30 possibilities, the next will reduce by 1 to 29 possibilities, followed by 28 possibilities, etc to the last number 1
The possible combination = 30 × 29 × 28 × 27 × 26 × 25 ......5 × 4 × 3 × 2 ×1
The above is an expansion of a number factorial. the number is 30
30! = 30 × 29 × 28 × 27 × 26 × 25 ......5 × 4 × 3 × 2 ×1
Hence, the total number of possible combinations when you draw all the balls out of the bag one at a time in factorial form is 30!
Graph the equation after plotting at least three points. Y= -2/3x+4
Given the function:
[tex]y=-\frac{2}{3}x+4[/tex]It's required to graph the function by joining at least 3 points.
Let's select the points x = -3, x = 3, and x = 9.
Substituting x = -3:
[tex]y=-\frac{2}{3}\cdot(-3)+4[/tex]Operating:
[tex]\begin{gathered} y=-\frac{-6}{3}+4 \\ y=2+4 \\ y=6 \end{gathered}[/tex]The first point is (-3,6)
Substitute x = 3:
[tex]y=-\frac{2}{3}\cdot3+4[/tex]Calculating:
[tex]\begin{gathered} y=-\frac{6}{3}+4 \\ y=-2+4 \\ y=2 \end{gathered}[/tex]The second point is (3,2)
Now for x = 9:
[tex]\begin{gathered} y=-\frac{2}{3}\cdot9+4 \\ y=-\frac{18}{3}+4 \\ y=-6+4 \\ y=-2 \end{gathered}[/tex]The third point is (9,-2).
Plotting the three points and joining them with a line, we get the following graph: