Explanation
We are given the following:
• 13 balls numbered 1 through 13 placed in a bucket.
We are required to determine the probability of randomly drawing two balls numbered 12 and 2 without replacement, in that order.
This is achieved thus:
The probability of randomly selecting a ball numbered 12 from the bucket is:
[tex]Pr.(12)=\frac{1}{13}[/tex]The probability of randomly selecting 2 from the bucket after the first selection is:
[tex]Pr.(2)=\frac{1}{12}[/tex]Therefore, the probability of randomly selecting two balls numbered 12 and 2 is:
[tex]\begin{gathered} Pr.=\frac{1}{13}\times\frac{1}{12} \\ Pr.=\frac{1}{156} \end{gathered}[/tex]Hence, the answer is:
[tex]\frac{1}{156}[/tex]1. Draw a graph for the scenario below. Remember to label the axes.The level of water in a river rose rapidly during the storm then gradually decreased back to the originallevel.2. A student drew the dashed line on the graph shown and concluded
ANSWER and EXPLANATION
We want to draw a graph to describe the scenario given.
The x axis will be labelled as time spent by storm.
This is because the time of the storm is the independent variable. The level of water in the river depends on the time by spent by the storm.
The y axis will be laballed as level of water in the river.
This is because it is the dependent the variable.
Since the level of water rises rapidly initially, the graph will go from a low value to a high value in a short span of time.
Then it will gradually go down again since the water level dropped gradually.
The graph will look like that.
6. A hot air balloon rises from the ground. Does the height of the balloon vary directly with the time it has been in the air? How do you know? Time (minutes) 5 7 10 15 Height (feet) 70 98 140 210
yes, it vary directly with the time, because:
[tex]\begin{gathered} \text{let:} \\ h=\text{height} \\ t=\text{time} \\ h(t)=kt \\ \text{Where:} \\ k=\text{constant of proportionality} \end{gathered}[/tex]For t = 5 , h = 70
so:
[tex]\begin{gathered} 70=k\cdot5 \\ k=\frac{70}{5} \\ k=14 \end{gathered}[/tex]If:
[tex]\begin{gathered} t=7\colon \\ h(7)=14\cdot7=98 \\ t=10\colon \\ h(10)=14\cdot10=140 \\ t=15\colon \\ h(15)=14\cdot15=210 \end{gathered}[/tex]Since there is a constant of direct proportionality for each of the values, the function varies directly
I got 12/37 but I'm not sure I did it right
We are given the following triangle
We are interested in calculating the sine of angle B. Recall in a right triangle, the sine of angle is given by the expression
[tex]\sin (\text{angle)}=\frac{\text{length of the opposite side}}{length\text{ of the hypotenuse}}[/tex]Here, we have angle B as reference. With respect to angle B, the opposite side would be side AC. Also, in the triangle, the hypotenuse is side AB. So we have
[tex]\sin (B)=\frac{35}{37}[/tex]which of these shapes are a parallelogram but not a square
A parallelogram is a flat shape that has 4 sides. The two sets of opposite sides are parallel and have the same measure to each other.
A square is a figure with four equal sides.
Then, for the given shapes, those that are parallelogram but not a square are:
Expand the logarithm fully using the properties of logs. Express the final answer interms of log x, and log y. log x^3/y
Answer
3 log x - log y
Step-by-step explanation
Given the expression:
[tex]\log(\frac{x^3}{y})[/tex]Applying the quotient property:
[tex]\log(x^3)-\log y[/tex]Applying the power property to the first term:
[tex]3\log x-\log y[/tex]there are 12 rows of seats on a concert hall: 25 seats are in the first row, 27 seats are on the second row, 29 seats are on the third row, and so on. If the price per ticket is $28, how much will be the total sales for a one-night concert if all seats are taken?how many seats are in the 12 row? how many seats are there total? what is the total amount made on that night?
Based on the given information, you have that the number of seats on each row is:
25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47
then, by adding the previous number of seats, you obtain:
25 + 27 + 29 + 31 + 33 +35 + 37 + 39 + 41 + 45 + 47 = 389
- If each ticket costs $28 per seat, the total cost for all seats is:
$28 x 389 = $10,892
- In the 12th row there are 47 seats
- The total number of seat in the 12 rows are 389
- The total amoun made was $10,892
f(x) = 3x2 + 6x – 14g(x) = -2x + 12Find: (gºf)(x)
We are asked to find te composition of function g with f. (gof)(x)
and we are given the following expressions:
[tex]\begin{gathered} f(x)=3x^2+6x-14 \\ g(x)=-2x+12 \end{gathered}[/tex]So, we cecall that the composition of functions means that we need to use for the input of the one function (g), the other function (f):
(gof)(x) = g (f(x))
So we proceed to do such
[tex]\begin{gathered} g(f(x))=g(3x^2+6x-14)=-2(3x^2+6x-14)+12= \\ -6x^2-12x+28+12=-6x^2-12x+40 \end{gathered}[/tex]Therefore the composition gives: -6 x^2 - 12 x + 40
Ajay is on the swim team. he improves this time on the 50 yard freestyle from 32 seconds to 31 seconds. what's the percent decrease in his tim3
from 32 seconds to 31 seconds decrease in 1 second, therefore
32 seconds -----> 100%
1 second ---------> x
[tex]\begin{gathered} 32\times x=1\times100 \\ 32x=100 \\ \frac{32x}{32}=\frac{100}{32} \\ x=3.125 \end{gathered}[/tex]answer: the percent decrease in 3.125%
Gabby worked 60 hours in 7 days. Determine the rate for a ratio of the two different quantities.
As per the data, Gabby worked 60 hours in 7 days , the required rate for a ratio of the two different quantities is equal to (60 /7) hours per day.
As given in the question,
Number of days Gabby worked = 7 days
Number of hours Gabby worked = 60 hours
Then the required rate for a ratio of the two different quantities that is hours and days is equal to
60 hours in 7 days
In worked done in 1 day is equal to
7 days = 60 hours
1 day = ( 60 / 7 ) hours per day
Therefore, as per the data, Gabby worked 60 hours in 7 days , the required rate for a ratio of the two different quantities is equal to
(60 /7) hours per day.
Learn more about ratio here
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for the polynomial below, what is the coefficient of the term with the power of 3[tex] {x}^{2} + \frac{1}{3} {x}^{4} + 6x + 5[/tex]
We have the polynomial:
[tex]x^3+\frac{1}{3}x^4+6x+5[/tex]The coeficient of the term with the power of 3 is 1, because we have:
[tex]x^3=1\cdot x^3[/tex]The correct answer is B.
Ravi’s chocolate bar is 62% cocoa. if the weight of the chocolate bar is 61 grams, how many grams of cocoa does it contain? Round your answer to the nearest tenth.
Recall that the x% of y can be computed using the following expression:
[tex]y\cdot\frac{x}{100}\text{.}[/tex]Now, since Ravi's chocolate bar is 62% cocoa, and the weight of the chocolate bar is 61 gr, then the chocolate bar contains:
[tex]61\cdot\frac{62}{100}[/tex]grams of cocoa.
Simplifying the above result we get:
[tex]61\cdot0.62=37.82\approx37.8.[/tex]Answer: Ravi's chocolate bar contains 37.8 grams.
for a circle there is a segment fm=8, mg=7 and pm=14. what is the measure of chord pq. see attached.
Hello there. To solve this question, we'll need to remember some properties about chords in a circle.
For this question specifically, we'll need chord-chord power theorem:
If two chords in a circle intersect at a point P, the product of the measures of one chord is equal to the product of the measures of the second chord, as in the drawing below:
The theorem says that A * B = C * D
In the case of the question, the chords FG and PQ intersects at the point M.
The measures of FM, MG and PM are given: 8, 7 and 14, respectively.
By the theorem above, we know that:
FM * MG = PM * MQ
We want to find the measure of PQ
In this case, know that PQ = PM + MQ (2)
Solving for MQ, we have:
8 * 7 = 14 * MQ
56 = 14 MQ
Divide both sides of the equation by a factor of 14
MQ = 4
By (2), we have that:
PQ = 14 + 4 = 18.
This is the measure of the chord PQ.
Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.A librarian is expanding some sections of the city library. He buys books at a special price from a dealer who charges one price for any hardback book and another price for any paperback book. For the children's section, Mr. Whitaker purchased 78 new hardcover books and 46 new paperback books, which cost a total of $840. He also purchased 78 new hardcover books and 14 new paperback books for the adult fiction section, spending a total of $744. What is the special price for each type of book?
Ans
Explanation:
Let's call x the price for the hardcover books and y the price for the paperback book.
If he purchased 78 hardcover books and 46 new paperback books for $840, we can write the following equation
78x + 46y = 840
In the same way, if he purchased 78 hardcover books and 14 paperback books for $744, we get:
78x + 14y = 744
So, the system of equations is
78x + 46y = 840
78x + 14y = 744
To solve the system, we need to multiply the second equation by -1
-78x - 14y = -744
And then add this to the first equation
78x + 46y = 840
-78x - 14y = -744
32y = 96
Solving for y, we get:
32y/32 = 96/32
y = 3
Finally, we can replace y by 3 and solve for x
78x + 46y = 840
78x + 46(3) = 840
78x + 138 = 840
78x + 138 - 138 = 840 - 138
78x = 702
78x/78 = 702/78
x = 9
Therefore, the price for the hardcover books is $9 and the price for the paperback books is $3
-15•monomial•other polynomial•binomial•trinomial
Answer
The polynomial given is a monomial.
Explanation
The term used to describe any polynomial depends on how many terms are in the polynomial.
•monomial
A polynomial with only one term.
•other polynomial
A polynomial with more than three terms.
•binomial
A polynomial with only two terms.
•trinomial
A polynomial with only three terms.
For this question,
The polynomial = -15
The polynomial has only one term, hence, this is a monmial.
Hope this Helps!!!
Solve each equation Show steps for credit 6.6=n-47.r-2=58.6=m+6
Answer:
• n=10
,• r=7
Explanation:
No 6
Given the equation:
[tex]6=n-4[/tex]To solve for n, add 4 to both sides of the equation:
[tex]\begin{gathered} 6+4=n-4+4 \\ 10=n \end{gathered}[/tex]The value of n is 10.
No 7
Given the equation:
[tex]r-2=5[/tex]To solve for r, add 2 to both sides of the equation:
[tex]\begin{gathered} r-2+2=5+2 \\ r=7 \end{gathered}[/tex]The value of r is 7.
I’m confused I’ve tried doing the equation and get x = 1.75
Solution:
Given:
A parallelogram with;
[tex]\begin{gathered} \angle M=8x+1 \\ \angle K=16x-13 \end{gathered}[/tex]In a parallelogram, the angles on the same side of the transversal are supplementary, which means they add up to 180 degrees.
Hence,
[tex]\angle M+\angle K=180^0[/tex]Thus,
[tex]\begin{gathered} 8x+1+16x-13=180^0 \\ \text{Collecting the like terms,} \\ 8x+16x+1-13=180^0 \\ 24x-12=180 \\ 24x=180+12 \\ 24x=192 \\ \text{Dividing both sides by 24 to get the value of x,} \\ x=\frac{192}{24} \\ x=8 \end{gathered}[/tex]To get the measure of angle K, we substitute the value of x gotten.
[tex]\begin{gathered} \angle K=16x-13 \\ \text{Hence,} \\ m\angle K=16x-13 \\ m\angle K=16(8)-13 \\ m\angle K=128-13 \\ m\angle K=115^0 \end{gathered}[/tex]Therefore, the measure of angle K in the parallelogram is 115 degrees.
Use algebra to rewrite the following identity in 2 different forms. tan^2(θ) + 1 = sec^2(θ)
Let's rewrite the identity in two different forms conserving the functions given:
[tex]\tan ^2\theta-\sec ^2\theta=-1[/tex]and
[tex]\tan ^2\theta=\sec ^2\theta-1[/tex]Now, let's find two different identities from this one. To do this let's remember that:
[tex]\begin{gathered} \tan \theta=\frac{\sin \theta}{\cos \theta} \\ \sec \theta=\frac{1}{\cos \theta} \end{gathered}[/tex]Then we have:
[tex]\begin{gathered} \tan ^2\theta+1=\sec ^2\theta \\ \tan ^2\theta-\sec ^2\theta=-1 \\ \frac{\sin^2\theta}{\cos^2\theta}-\frac{1}{\cos^2\theta}=-1 \\ \frac{\sin^2\theta-1}{\cos^2\theta}=-1 \\ \sin ^2\theta-1=-\cos ^2\theta \\ \sin ^2\theta+\cos ^2\theta=1 \end{gathered}[/tex]Therefore, we can write the identity given as:
[tex]\sin ^2\theta+\cos ^2\theta=1[/tex]Let's find a second identity from the one given, to do this we will mutiply it by the cotangent squared of the angle:
[tex]\begin{gathered} \tan ^2\theta+1=\sec ^2\theta \\ \tan ^2\theta\cdot\cot ^2\theta+\cot ^2\theta=\sec ^2\theta\cdot\cot ^2\theta \\ \frac{\sin^2\theta}{\cos^2\theta}\cdot\frac{\cos^2\theta}{\sin^2\theta}+\cot ^2\theta=\frac{1}{\cos^2\theta}\cdot\frac{\cos ^2\theta}{\sin ^2\theta} \\ 1+\cot ^2\theta=\frac{1}{\sin ^2\theta} \\ 1+\cot ^2\theta=\csc ^2\theta \end{gathered}[/tex]Therefore, we can write the identity given as:
[tex]1+\cot ^2\theta=\csc ^2\theta[/tex]I don't understand how to find the quotient of 2.8√68.32
Answer:
The quotient is;
[tex]24.4[/tex]Explanation:
We want to find the quotient;
[tex]\frac{68.32}{2.8}[/tex]Solving, we have;
Therefore, the quotient is;
[tex]\frac{68.32}{2.8}=24.4[/tex]find the volume of a cube? 8 inches
A cube has all it sides equal.
The volume of a cube is given by Length x Length x Length
[tex]\begin{gathered} Volume=8X8X8inches^3 \\ \text{Volume = 512 inches }^3 \end{gathered}[/tex]1. Max had $36.06. He spent $14.60 on a new shirt and $4.95 on a pack of socks. How much money did Max have left? type
$16.51
Explanation
to solve this we can use a subtraction
make
Max had $36.06 (positive)
He spent $14.60 on a new shir(negative)
$4.95 on a pack of socks(negative)
so, the money he left is
Money he left0 money he had- money he spent
Step 1
add to final the total money he spent
[tex]\begin{gathered} \text{money spent=new shirt+a pack of socks} \\ \text{replace} \\ \text{money spent=14.60+4.95=19.55} \end{gathered}[/tex]Step 2
find the money left
money left=money he had-money he spent
replace
[tex]\text{money left}=36.06-19.55=16.51[/tex]so, the answer is $16.51
I hope this helps you
y = f(x)The graph of the linear function f is shown in thexy-plane above. The graph of the linear function g(not shown) is perpendicular to the graph offand passes throu the point (1,3). What is thevalue of g(0)?
Answer:
g(0) = 5/2
Step-by-step explanation:
The equation of a line is given by:
y = ax + b
In which a is the slope, which is given by the variation in y divided by the variation in x.
If two lines are perpendicular, the multiplication of their slopes is -1.
Line f:
Passes through the points (0,3) and (1,1).
Variation in y: 1 - 3 = -2
Variation in x: 1 - 0 = 1
Slope = -2/1 = -2.
Line g:
Perpendicular to g, so the slope is:
-2*a = -1
2a = 1
a = 1/2
So the line g has an equation given by:
y = (1/2)*x + b
Passes through the point (1,3).
This means that when x = 1, y = 3. We use this to find b.
3 = (1/2)*1 + b
b = 3 - 1/2
b = 5/2
So:
g = y(x) = (1/2)*x + 5/2
g(0) = (1/2)*0 + 5/2 = 5/2
g(0) = 5/2
Answer : its c
Explanation
Write the word sentence as an equation. Then solve the equation.A number multiplied by 2/5 is3/20Equation:Solution: x=
Answer: x=0.375
Explanation:
The sentence we have is:
"A number multiplied by 2/5 is 3/20"
We can call that number x, and we get the following equation:
[tex]\frac{2}{5}x=\frac{3}{20}[/tex]that is the first part.
Now we need to solve that equation for x.
Step 1: Multiply the left side and right side by 20 (to cancel the 20 in the right side)
[tex]20(\frac{2}{5}x)=3[/tex]Step 2: Solve the operations on the left
[tex]\begin{gathered} \frac{40x}{5}=3 \\ 8x=3 \end{gathered}[/tex]Step 3: Divide both sides of the equation by 8
[tex]\begin{gathered} x=\frac{3}{8} \\ x=0.375 \end{gathered}[/tex]Answer: x=0.375
if g(x) =2x-3 and fog (x)=4x -9 ,find f(x)
To answer this, we need to ask, what did f do to "2x-3" to turn it into 4x-9.
Well, we can multiply 2x-3 by 2 to give us the 4x in 4x-9.
But 2(2x-3) = 4x-6, so we're not quite there. We need to also subtract 3 to turn -6 into -9.
So f(x) = 2x-3 would give (f o g)(x) = 4x-9.
Oh, f(x) = g(x). Weird.
Given the unit circle what is the value of x
The equation of the unit circle is
[tex]x^2+y^2=1[/tex][tex]\text{ The point (x,}\frac{3}{4})\text{ lies on the given unit circle.}[/tex]Replace x=x and y=3/4 in the equation, we get
[tex]x^2+(\frac{3}{4})^2=1[/tex][tex]x^2+\frac{9}{16}=1[/tex]Subtracting 9/4 from both sides, we get
[tex]x^2+\frac{9}{16}-\frac{9}{16}=1-\frac{9}{16}[/tex][tex]x^2=\frac{16}{16}-\frac{9}{16}[/tex][tex]x^2=\frac{16-9}{16}[/tex][tex]x^2=\frac{7}{16}[/tex]Taking square root on both sides, we get
[tex]x=\pm\sqrt[]{\frac{7}{16}}[/tex][tex]x=\pm\frac{\sqrt[]{7}}{4}[/tex][tex]x=\frac{\sqrt[]{7}}{4}\text{ or }x=-\frac{\sqrt[]{7}}{4}\text{ }[/tex]Hence the required value of x is
[tex]\text{ }x=-\frac{\sqrt[]{7}}{4}\text{ }[/tex]how do I find the following answer to parts A ?
Given that DE is the midsegment of ΔABC, then:
[tex]\frac{1}{2}BC\text{ = }DE[/tex]BD = DA
AE = EC
Option A is true because:
AC = AE + EC
AC - AE = EC
Option B is true because:
AD + DB = AB
AD + AD = AB (BD = DA)
2AD = AB
AD = 1/2AB
Option C is true because:
1/2BC = DE
BC = 2DE
Given that ΔABC is scalene, then AB ≠ AC ≠ BC, in consequence, AD ≠ AE. Then option D is the correct option
Translate point A 9units right and 3 units up.Drag and place the BLUE dot to show the location of A where is the location of A'?
we have that
Part 1
Point A(-7,-7)
The rule to translate point A is
(x,y) -------> (x+9, y+3)
so
A(-7,-7) -------> A'(-7+9,-7+3)
A'(2, -4)
Part 2
The rule to translate point B is
(x,y) ------> (x-5, y+6)
we have
B(7,-3)
so
B(7,-3) ------- B'(7-5,-3+6)
B'(2,3)
Edwin deposited money into a savings account that pays a simple annual interestrate of 1.2%. He earned $27 in interest after 3 years. How much did he deposit?
SOLUTION:
Step 1:
In this question, we are given the following:
Edwin deposited money into a savings account that pays a simple annual interest rate of 1.2%.
He earned $27 in interest after 3 years.
How much did he deposit?
Step 2:
The details of the solution are as follows:
[tex]\begin{gathered} Simple\text{ Interest = }\frac{Principa\text{l x Rate x Time}}{100} \\ Interest\text{ = \$ 27} \\ Time\text{ = 3 years} \\ Principal\text{ = P} \\ Rate\text{ = 1.2 \%} \end{gathered}[/tex]Making P the subject of the formulae, we have that:
[tex]\begin{gathered} P\text{ =}\frac{100\text{ x Simple Interest}}{Rate\text{ X Time}} \\ P\text{ = }\frac{100\text{ x 27}}{1.\text{ 2 x 3}} \\ P\text{ = }\frac{2700}{3.6} \\ P=\text{ \$ 750} \end{gathered}[/tex]CONCLUSION:
He deposited $ 750
span. The following ordered pairs shows the population and the year over the ten-year span, (population, year) for specific recorded years:(2500,2000),(2650,2001),(3000,2003),(3500,2006),(4200,2010)Using this tool we find the linear regression line to be y=Answer Type your answer without spaces or commas and rounded to the nearest hundredth.The population will hit 8,000 in the year Answer Using this tool we find the r-value to be Answer
Given the ordered pairs:
(2500, 2000), (2650, 2001), (3000, 2003), (3500, 2006), (4200, 2010)
Let's find the linear regression line.
Apply the formula:
y = mx + b
Where m si the slope and b is the y-intercept.
To find the slope, apply the formula:
[tex]m=\frac{n(\sum^{}_{}xy)-\sum^{}_{}x\sum^{}_{}y}{n(\sum^{}_{}x^2)-(\sum^{}_{}x)^2}[/tex]Where:
∑x = 2500 + 2650 + 3000 + 3500 + 4200 = 15850
∑y = 2000 + 2001 + 2003 + 2006 + 2010 = 10020
∑xy = (2500 * 2000) + (2650 * 2001) + (3000 * 2003) + (3500 * 2006) +(4200 * 2010) = 31774650
∑x² = 2500² + 2650² + 3000² + 3500² + 4200² = 52162500
∑y² = 2000² + 2001² + 2003² + 2006² + 2010² = 20080146
n = number of ordered pairs = 5
Thus, we have:
[tex]\begin{gathered} m=\frac{5(31774650)-15850\ast10020}{5(52162500)-(15850)^2} \\ \\ m=0.00587 \end{gathered}[/tex]The slope of the regression line is 0.00587
To find the y-intercept, apply the formula:
[tex]b=\frac{(\sum ^{}_{}y)(\sum ^{}_{}x^2)-\sum ^{}_{}x\sum ^{}_{}xy}{n(\sum ^{}_{}x^2)-(\sum ^{}_{}x)^2}[/tex]Thus, we have:
[tex]\begin{gathered} b=\frac{(10020)(52162500)-15850\ast10020}{5(52162500)-(15850)^2} \\ \\ b=1985.41 \end{gathered}[/tex]Therefore, the regression line is:
[tex]y=0.00587x+1985.41[/tex]To determine the year the population will hit 8000, substitute 8000 for x and solve for y:
[tex]\begin{gathered} y=0.00587(8000)+1985.41 \\ \\ y=46.92+1985.41 \\ \\ x=2032.33 \end{gathered}[/tex]Therefore, the population will hit 8000 in the year 2032.
To find the R-value, apply the formula:
[tex]R=\frac{n(\sum ^{}_{}xy)-\sum ^{}_{}x\sum ^{}_{}y}{(n(\sum ^{}_{}x^2)-(\sum ^{}_{}x)^2)-(n(\sum ^{}_{}y^2^{})-(\sum ^{}_{}y)^2}[/tex]Thus, we have:
[tex]\begin{gathered} R=\frac{5(31774650)-15850\ast10020}{\sqrt{5(52162500)-(15850)^2)-(5(20080146)-(10020)^2}} \\ \\ R=18.16 \end{gathered}[/tex]The R value is
1 The median____ of the algebraClass is____ the interquartile range is______ Part A what is the median of the algebra classPart b Determine the interquartile range
We are given a box plot.
From the box plot, we can tell the median to be 12 because the interquartile line division is also split at 12.
The interquartile range is the difference between the 1st and 3rd quartile.
[tex]16-6=10[/tex]ANSWERS
Median = 12
IQR = 10
A band is receiving $650.00 for playing at a festival. Their manager takes 15% of the money received for each show, and the band pays their sound technician 10% of all profit. How much money is left for the band to split?
We have the following:
To find the answer we must subtract the percentages as follows
[tex]\begin{gathered} 650-\frac{15}{100}\cdot650-\frac{10}{100}\cdot650 \\ 650-97.5-65=487.5 \end{gathered}[/tex]Therefore to distribute among the band $487.5