The given expression is
[tex]\frac{1}{b}+\frac{1}{9}=\frac{1}{t}[/tex]First, we multiply the equation by t
[tex]\begin{gathered} (\frac{1}{b}+\frac{1}{9})\cdot t=\frac{1}{t}\cdot t \\ (\frac{1}{b}+\frac{1}{9})\cdot t=1 \end{gathered}[/tex]Now, we divide the equation by 1/b + 1/9
[tex]\begin{gathered} \frac{(\frac{1}{b}+\frac{1}{9})\cdot t}{(\frac{1}{b}+\frac{1}{9})}=\frac{1}{(\frac{1}{b}+\frac{1}{9})} \\ t=\frac{1}{(\frac{1}{b}+\frac{1}{9})} \end{gathered}[/tex]Now, we sum fractions
[tex]t=\frac{1}{\frac{9+b}{9b}}[/tex]Then, we solve this combined fraction
[tex]t=\frac{9b\cdot1}{9+b}=\frac{9b}{9+b}[/tex]Therefore, the final expression is
[tex]t=\frac{9b}{9+b}[/tex]An ordinary (Pair) die is a cube with the numbers 1 through 6 on the sides (represented by painted spots). Imagine that such a die is rolled twice in successionand that the face values of the two rolls are added together. This sum is recorded as the outcome of a single trial of andereCompute the probability of each of the following svents.Event A: The sum is greater than 7.Event B: The sum is divisible by 3 or 6 (or both).Write your answers as fractions
1) We are going to tackle this question starting with the total outcomes of dice rolled twice in succession.
(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)
(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)
(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)
(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)
(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)
So we can see that there are 36 possibilities.
2) Let's examine the events.
a) P (>7)
Let's bold the combinations of outcomes whose sum is greater than 7
(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)
(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)
(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)
(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)
(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)
So, we can see that there are 15 favorable outcomes.
Now, we can find the Probability of rolling the dice twice and get a sum greater than 7:
[tex]P(A)=\frac{15}{36}=\frac{5}{12}[/tex]b) Now, for the other event: The sum is divisible by 3 or 6, or both:
(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)
(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)
(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)
(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)
(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)
Hence, the favorable outcomes are: 12
So now, let's find the probability of getting a sum that way:
[tex]P(B)=\frac{12}{36}=\frac{1}{3}[/tex]Determine whether the equation represents an exponential growth function, anexponential decay function, and give the percent growth or decay.17. y = 18(1.3)^t
A exponential growth or decay function has the next general form:
[tex]y=a(1\pm r)^t[/tex]If it is :
(1+r) , (>1) the function growth
(1-r) , (<1) the function decay
------
The given equation:
[tex]y=18(1.3)^t[/tex]As the (1+r) is equal to 1.3 (> 1) then it is a exponential growth function.In (1+r) the r is the percent of growth, then for the given equation you have:
[tex]\begin{gathered} 1+r=1.3 \\ r=1.3-1 \\ \\ r=0.3 \end{gathered}[/tex]The percent of decay is 0.3 or 30%solve the following system of inequalities graphically on the set of axes below?witch of the coordinates points would be in the solution set
Solving triangles using the law of cosines . Find m
The law of cosines is defined as follows:
[tex]a^2=b^2+c^2-2bc\cos A[/tex]For the given triangle
a=AC=8
b=AB=14
c=BC=11
∠A=∠B=?
-Replace the lengths of the sides on the expression
[tex]8^2=14^2+11^2-2\cdot14\cdot11\cdot\cos B[/tex]-Solve the exponents and the multiplication
[tex]\begin{gathered} 64=196+121-308\cos B \\ 64=317-308\cos B \end{gathered}[/tex]-Pass 317 to the left side of the expression by applying the opposite operation to both sides of it
[tex]\begin{gathered} 64-317=317-317-308\cos B \\ -253=-308\cos B \end{gathered}[/tex]-Divide both sides by -308
[tex]\begin{gathered} -\frac{253}{-308}=-\frac{308\cos B}{-308} \\ \frac{23}{28}=\cos B \end{gathered}[/tex]-Apply the inverse cosine to both sides of the expression to determine the measure of ∠B
[tex]\begin{gathered} \cos ^{-1}\frac{23}{28}=\cos ^{-1}(\cos B) \\ 34.77º=B \end{gathered}[/tex]The measure of ∠B is 34.77º
As cashier, you need to record all over times you worked in hours. If you worked 330 mnts of over time how many hours will you record ?
First, we need the next equivalence
1 hour = 60 min
we have 330 min in order to know the number of hours we need to divide the 330 min between 60
[tex]\frac{330}{60}=5.5[/tex]He will record 5.5 hours
solve the equation by completing the square. Show all solutions8x^2 + 16x = 42
8x² + 16x = 42
x² + 16/8x = 42/8 dividing by 8 at both sides
x² + 2x = 5.25
x² + 2x - 5.25 = 0
If we compute (x + 1)², we get:
(x + 1)² = x² + 2*x*1 + 1² = x² + 2x + 1
Then,
x² + 2x - 5.25 + 1 - 1 = 0
(x² + 2x + 1) + (-5.25 - 1) = 0
(x + 1)² - 6.25 = 0
(x + 1)² = 6.25
x + 1 = √6.25
This has 2 solutions,
x + 1 = 2.5 or x + 1 = -2.5
x = 2.5 - 1 x = -2.5 - 1
x = 1.5 x = -3.5
8.1 km to miles and feet
Given
[tex]8.1\operatorname{km}[/tex]It should be noted that
[tex]\begin{gathered} 1\operatorname{km}=0.621371miles \\ 1\text{mile}=5280\text{feet} \end{gathered}[/tex][tex]\begin{gathered} \text{convert 8.1km to miles} \\ 1\operatorname{km}=0.621371\text{miles} \\ 8.1\operatorname{km}=8.1\times0.621371 \\ 8.1\operatorname{km}=5.0331051\text{miles} \end{gathered}[/tex][tex]\begin{gathered} 8.1\operatorname{km}=5\text{miles}+0.0331051\text{miles} \\ \text{convert 0.0331051miles to fe}et \\ 1\text{miles}=5280ft \\ 0.0331051\text{miles}=0.0331051\times5280feet \\ 0.0331051\text{miles}=174.79feet \end{gathered}[/tex]Hence, 8.1km is 5 miles and 174.79 feet
Using a graphing calculator to find local extrema of a polynomial function
The given function is:
[tex]f(x)=3x^4-5x^3-4x^2+5x-2[/tex]By using a graphing calculator, we found that the local maximum is located at:
x=0.41, then f(0.41)=-0.88
The answer is (0.41, -0.88)
3/4 square foot in 1/2 hour what is the unit rate as mixed number
Answer:
[tex]\text{1 }\frac{1}{2}[/tex]Explanation:
The unit rate is:
3/4 divided by 1/2
[tex]\begin{gathered} \frac{3}{4}\times\frac{2}{1} \\ \\ =\frac{3}{2} \end{gathered}[/tex]As a mixed fraction, it is
[tex]\text{1 }\frac{1}{2}[/tex]can some one clarify this question, i think ik the answer but i need some elses opinion Find m
hello
to solve this question, we simply need to add two quadrants that make up mto get m[tex]\begin{gathered} m<\text{WYV}=60^0 \\ m<\text{VYU}=85^0 \end{gathered}[/tex][tex]\begin{gathered} m<\text{WYU}=<\text{WYV}+m<\text{VYU} \\ m<\text{WYU}=60^0+85^0 \\ m<\text{WYU}=145^0 \end{gathered}[/tex]from the calculations above, the value of m
The graph of polynomial f is shown. Select all the true statements about the polynomial.aThe degree of the polynomial is even.bThe degree of the polynomial is odd.cThe leading coefficient is positive.dThe leading coefficient is negative.eThe constant term of the polynomial is positive.fThe constant term of the polynomial is negative.
Explanation:
From the graph,
we can see that the graph is symmetric about the y axis
Hence,
We can say that the Polynomial is even
Also, Because th opwning of the function is downwards,
Hence the leading coefficient is negative
Also we can see that the y-intercept is positive
That is when x=0, y=3
Hence,
The constant term of the polynomial is positive.
Therefore,
The final answers are OPTION A,OPTION D,OPTION E
Find the indicated function given f(x)=2x^2+1 and g(x)=3x-5. When typing your answer if you have an exponent then use the carrot key ^ by pressing SHIFT and 6. Type your simplified answers in descending powers of x an do not include any spaces between your characters.f(g(2))=Answerf(g(x))=Answerg(f(x))=Answer (g \circ g)(x) =Answer (f \circ f)(-2) =Answer
Given the functions
[tex]\begin{gathered} f(x)=2x^2+1 \\ g(x)=3x-5 \end{gathered}[/tex]1) To find f(g(2))
[tex]\begin{gathered} f(g(x))=2(3x-5)^2+1 \\ f(g(x))=2(9x^2-15x-15x+25)+1=2(9x^2-30x+25)+1 \\ f(g(x))=18x^2-60x+50+1=18x^2-60x+51 \\ f(g(2))=18(2)^2-60(2)+51=18(4)-120+51 \\ f(g(2))=72-120+51=3 \\ f(g(2))=3 \end{gathered}[/tex]Hence, f(g(2)) = 3
2) To find f(g(x))
[tex]\begin{gathered} f(g(x))=2(3x-5)^2+1 \\ f(g(x))=2(9x^2-15x-15x+25)+1=2(9x^2-30x+25)+1 \\ f(g(x))=18x^2-60x+50+1=18x^2-60x+51 \\ f(g(x))=18x^2-60x+51 \end{gathered}[/tex]Hence, f(g(x)) = 18x²-60x+51
3) To find g(f(x))
[tex]\begin{gathered} g(f(x))=3(2x^2+1)-5 \\ g(f(x))=6x^2+3-5=6x^2-2 \\ g(f(x))=6x^2-2 \end{gathered}[/tex]Hence, g(f(x)) = 6x²-2
4) To find (gog)(x)
[tex]\begin{gathered} (g\circ g)(x)=3(3x-5)-5=9x-15-5=9x-20 \\ (g\circ g)(x)=9x-20 \end{gathered}[/tex]Jo-o/checkpoint scatter plotsA2018161412Paw size (centimeters)10642X1b2030405066708090100Height (centimeters)Does this scatter plot show a positive association, a negative association, or no association?positive associationnegative associationno association
A scatter plot shows the association between two variables.
If the variables tend to increase and decrease together, the association is positive. If one variable tends to increase as the other decreases, the association is negative. If there is no pattern, the association is zero.
From the graph we notice that in this case both variables increcase together, therefore the scatter plot has a positive association.
Calculate the amount of money that was loaned at 4.00% per annum for 2 years if the simple interest charged was $1,240.00.
Given:-
Simple intrest is $1240. Rate is 4.00%. Time is 2 years.
To find:-
The principal amount.
The formula which relates Simple intrest, Rate, Time and Principal amount is,
[tex]I=prt[/tex]So from this the formula for p is,
[tex]p=\frac{I}{rt}[/tex]Subsituting the known values. we get,
[tex]\begin{gathered} p=\frac{I}{rt} \\ p=\frac{1240}{0.04\times2} \\ p=\frac{1240}{0.08} \\ p=\frac{124000}{8} \end{gathered}[/tex]By simplifying the above equation. we get the value of p,
[tex]\begin{gathered} p=\frac{124000}{8} \\ p=\frac{31000}{2} \\ p=15500 \end{gathered}[/tex]So the principle amount value is 15500.
Jan and her brother mel go to different schools. Jan goes 6 kilometer east from home. Mel goes 8 kilometer north. How many kilometer apart are their schools.
Jan goes 6 km east from her home, and Mel goes 8 km north from the same home. So we need to find the distance between both schools, and we do such using the Pithagorean theorem, since we are in the presence of a right angle triangle for which we know the two legs, and need to find the measure of the hypotenuse.
I am going to represent the problem with a diagram below, so you see the right angle triangle I am talking about.
So the two legs are represented by the distances each student travels, and the segment in red is the distance between the schools which appears as the HYPOTENUSE of the right angle triangle.
Therefore, we use the Pythagoras theorem for the hypotenuse:
[tex]\begin{gathered} \text{Hypotenuse}=\sqrt[]{leg1^2+\text{leg}2^2} \\ \text{hypotenuse}=\sqrt[]{6^2+8^2} \\ \text{Hypotenuse}=\sqrt[]{36+64} \\ \text{Hypotenuse}=\sqrt[]{100}=10 \end{gathered}[/tex]Therefore, the distance between the schools is 10 km
My name is nessalovetrillo i am prepping and studying to test out of my algebra class this is for a study guide Please see attached picture
Given:
S={(5,6),(-2,-9),(-9,6)}
To find the domain and range:
The domain is,
{-9, -2, 5}
The range is,
{-9, 6}
A 5p coin weighs 4.2g. Approximately, how much will one million pounds worth of 5p pieces
weigh?
Answer:
It would weight 840,000g
Step-by-step explanation:
1,000,000 ÷ 5
= 200,000
= 200,000 × 4.2
= 840,000
Please help I need by today only questions 5 and 6 need to show work
Part a: Pot the points X, Y and Z are obtained on graph.
Part b: Distances; XY = 3, YZ = 5 and XZ = √34 units.
Part c: Measure of angles; X = 59.04 degrees and Z = 30.96 degrees.
What is termed as the Pythagorean theorem?The Pythagorean theorem states that the sum of a squares just on legs of a right triangle equals the square just on hypotenuse.For the given question, Triangle XYZ with the vertexes are given.
Part a: Pot the points.
X = (6, 6)
Y = (6, 3)
Z = (1, 3)
The points on the graph are plotted.
Part b: Distances;
XY = 6 - 3 = 3 units
YZ = 6 - 1 = 5 units
XZ , use Pythagorean theorem.
XZ² = XY² + YZ²
Put the values.
XZ² = 3² + 5²
XZ² = 9 + 25
XZ² = 34
XZ = √34 units.
Part c: Measure of angles.
In right triangle XYZ
cos X = XY/XZ
cos X = 3/ √34
X = 59.04 degrees.
cos Z = ZY/XZ
cos Z = 5/ √34
Z = 30.96 degrees.
Thus, the value of the triangle are obtained.
To know more about the Pythagorean theorem., here
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1. Identify the vertex (locator point) of the above parabola2 po(1,2)(3,0)(3,0)(2,1)2. Identify the vertex from the quadratic function y=-5(x-6) 2+82 point
Answer:
(2,1)
Step-by-step explanation:
The vertex of a parabola is it's highest point(if it is concave down), or it's lowest point, if it's concave up.
In this question:
It's concave down, so the vertex is the highest point.
It happens when x = 2, at which y = 1.
So the vertex is the point (2,1)
review the rental and purchase property information to answer the question: calculate the difference in total move-in cost between the two properties. $31,497.35 $35,842.95$39,285.45$4,976.55
Let us calculate the move-in costs of both properties.
Rental Property
The monthly rent is $1,350.
The move-in costs are:
First month = $1,350
Last month = $1,350
Security deposit = 55% of one month's rent
[tex]\Rightarrow\frac{55}{100}\times1350=742.5[/tex]Therefore, the move-in cost is:
[tex]\Rightarrow1350+1350+742.5=3442.5[/tex]Purchase Property
The purchase price is $195,450.
The move-in costs are:
Down payment of 18% of purchase price:
[tex]\Rightarrow\frac{18}{100}\times195450=35181[/tex]Closing costs of 2.1% of purchase price:
[tex]\Rightarrow\frac{2.1}{100}\times195450=4104.45[/tex]Therefore, the move-in cost is:
[tex]\Rightarrow35181+4104.45=39285.45[/tex]Difference in Total Move-In Cost
This is calculated to be:
[tex]\Rightarrow39285.45-3442.5=35842.95[/tex]ANSWER
The difference in total move-in cost is $35,842.95
According to Debt.org the average household has $7,281 in credit card debt. Estimate how much interest the average household accumulates over the course of 1 year. We are going to assume the APR is 16.99%.
In order to estimate the interest the average househould accumulates in 1 year, you use the following formula:
A = Prt
where P is the initial credit card debt ($7,281), r is the interest rate per period (16.99%) and t is the number of time periods. In this case the value of r is given by the APR, then, there is one period of 1 year.
To use the formula it is necessary to express 16.99% as 0.1699. Thus, you have:
I = 7,281 x 0.1699 x 1
I = 1,237.04
Hence, the interest accumulated is of $1,234.04
Tony is a hiring director at a large tech company in Chicago, and he gets hundreds of resumes each week. How long does Tony MOST likely spend looking over each resume?30 seconds50 seconds3 minutes30 minutes
The time needed to look over the resumes depends on how many papers is the resume
But it is convenient to have a speed looking on each one
so, the answe will be 50 seconds
P(x) =x and q(x) = x-1Given:minimum x and Maximum x: -9.4 and 9.4minimum y and maximum y: -6.2 and 6.2Using the rational function [y=P(x)/q(x)], draw a graph and answer the following: a) what are the zeroes?b) are there any asymptotes? c) what is the domain and range for this function?d) it it a continuous function?e) are there any values of y= f(x)/g(x) that are undefined? Explain
we have the following function
[tex]\frac{p(x)}{g(x)}=\frac{x}{x\text{ -1}}[/tex]where x is between -9.4 and 9.4 and y is between -6.2 and 6.2.
We will first draw the function
from the graph, we can see that the zeroes are all values of x for which the graph crosses the x -axis
In this case, we see that that the only zero is at x=0.
Now, we have that the asymptotes are lines to which the graph of the function get really close to. On one side, we can see that as x goes to infinity or minus infinity, the values of the function get really close to 1. So the graph has a horizontal asymptote at y=1. Also, we can see that as x gets really close to 1, the graph gets really close to the vertical line x=1. So the graph has a vertical asymptote at x=1.
Recall that the domain of a function is the set of values of x for which the function is defined. From our graph, we can see that graph is not defined when x=1. So the domain of the function is the set of real numbers except x=1. Now, recall that the range of the function is the set of y values of the graph. From the picture we can see that the graph has a y coordinate for every value of y except for y=1. So, this means that the range of the function is the set of real numbers except y=1.
From the graph, we can see that we cannot draw the graph having a continous drawing. That is, imagine we take a pencil and start on one point on the graph on the left side. We can draw the whole graph on the left side, but we cannot draw the graph on the right side without lifting the pencil up. As we have to "lift the pencil up" this means that the graph is not continous
Finally note that as we have a vertical asymptote at x=1 and horizontal asymptote at y=1 we have that when y is 1 or x is 1, the function y=f(x)/g(x) is undefined
Determine (Freshman) Small Cafeteria). Interpret this answer in the context of the situation.
Step 1:
[tex]\text{Probability = }\frac{N\text{umber of required outcomes}}{N\text{umber of total possible outcome}}[/tex]Step 2:
a)
Total possible outcome = 2640
Total number of freshman = 625
[tex]\begin{gathered} P(\text{Freshman) = }\frac{625}{2640} \\ \text{= }\frac{125}{528} \\ \text{= 0.237} \end{gathered}[/tex]Step 3:
b)
Total number of senior and large cafeteria = 350
[tex]\begin{gathered} P(\text{senior and large cafeteria) = }\frac{350}{2640} \\ =\text{ }\frac{70}{528} \\ =\text{ }\frac{35}{264} \\ =\text{ 0.132} \end{gathered}[/tex]Step 4:
c)
Number of Sophomore or student center = 650 + 595 - 125 = 1120
[tex]\begin{gathered} P(\text{Sophomore or student center) = }\frac{1120}{2640} \\ =\text{ }\frac{112}{264} \\ =\text{ 0}.424 \end{gathered}[/tex]Step 5:
d)
[tex]\begin{gathered} p(\text{freshman}|\text{small cafeteria) = }\frac{n(freahman\text{ and small cafeteria)}}{n(small\text{cafeteria)}} \\ =\frac{435}{860}\text{ } \\ =\text{ }\frac{87}{172} \\ =\text{ 0.506} \end{gathered}[/tex]Use slope to determine if lines AB and CD are parallel, perpendicular, or neither 6. A(-3, 8), B(3, 2), C(7,1), D(5,-1)m(AB) m(CD) Types of Lines
what is the image of 2,10 after a dilation by a scale factor of 1/2 centered at the origin
A dilation is given by:
[tex](x,y)\rightarrow(kx.ky)[/tex]where k is the scale factor.
In this case we have:
[tex](2,10)\rightarrow(\frac{1}{2}\cdot2,\frac{1}{2}\cdot10)=(1,5)[/tex]Therefore the image is the point:
[tex](1,5)[/tex]Which angles are adjacent to <2? Select all that apply.
What is the value of x? A pair of intersecting lines is shown. The angle above the point of intersection is labeled left parenthesis 7 x minus 8 right parenthesis degrees. The angle directly opposite below the point of intersection is labeled left parenthesis 6 x plus 11 right parenthesis degrees. (1 point)
A –19
B 125
C 19
D 55
The value of x in the angles is 19.
How to find angles in intersecting lines?When lines intersect, angle relationships are formed such as vertically opposite angles, adjacent angles etc.
Therefore, let's find the value of x in the intersecting lines.
Hence,
7x - 8 = 6x + 11 (vertically opposite angles)
Vertically opposite angles are congruent and they share the same vertex point.
Hence,
7x - 8 = 6x + 11
subtract 6x from both sides of the equation
7x - 8 = 6x + 11
7x - 6x - 8 = 6x - 6x + 11
x - 8 = 11
add 8 to both sides of the equation
x - 8 + 8 = 11 + 8
x = 19
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A box of a granola contains 16.8 ounces . It cost $5.19 . What is the cost , to the nearest cent , of the granola per ounce ? A . $0.12 B . $0.31 C . $3.24
The cost per unit ounce is obtained by computing the quotient:
[tex]c=\frac{C}{N}.[/tex]Where:
• c is the cost per unit ounce,
,• C is the cost,
,• N is the number of ounces that you get for C.
In this problem we have:
• C = $5.19,
,• N = 16.8 ounces.
Computing the quotient, we get:
[tex]c=\frac{5.19}{16.8}\cong0.31[/tex]dollars per ounce.
Answer: B. $0.31
For an outdoor concert by the city orchestra, concert organizers estimate that 11,000 people will attend if it is not raining. If it is raining, concert organizers estimatethat 7000 people will attend. On the day of the concert, meteorologists predict a 60% chance of rain. Determine the expected number of people who will attend thisconcert
Step 1
Given;
For an outdoor concert by the city orchestra, concert organizers estimate that 11,000 people will attend if it's not raining.
If it is raining, concert organizers estimate 7000 people will attend.
On the day of the concert, meteorologists predict a 60% chance of rain.
Step 2
Given that the probability of having rain is 60%
[tex]Pr(rain)=\frac{60}{100}=0.6[/tex]So the probability of not having rain is;
[tex]\begin{gathered} Pr(rain)+Pr(no\text{ rain\rparen=1} \\ Pr(no\text{ rain\rparen=1-Pr\lparen rain\rparen} \\ Pr(no\text{ rain\rparen=1-0.6=0.4} \end{gathered}[/tex]Step 3
Now, the expected number of people who will attend the concert will be:
=(probability of not having rain x number of expected guests when it does not rain) + (probability of having rain x number of expected guests when rains)
[tex]\begin{gathered} Pr(expected\text{ number of peope\rparen=\lparen0.4}\times11000)+(0.6\times7000) \\ Pr(expected\text{ number of peope\rparen=4400+4200=8600} \end{gathered}[/tex]Answer; So, the expected number of people who will attend the concert is 8600