To simplify this expression:
1. Remove the parenthesis: To remove parenthesis you need to know that the symbol outside parenthesis affects all the terms inside parenthesis.
[tex]\begin{gathered} +(-)=- \\ -(+)=- \\ -(-)=+ \\ +(+)=+ \end{gathered}[/tex]The given expression after remove the parenthesis is:
[tex]6.2n-8.3-9.1+1.4n[/tex]2. Add or substract similar terms: similar terms have the same variable in this case n, or don't have any variable:
[tex]7.6n-17.4[/tex]Then, the given expression simplified is 7.6n - 17.4identify at least one Hamilton path and at least one how much in circuit
Hamilton path, is a path that exists between two vertices of a graph that visits each vertex exactly once
ABCDE is an Hamilton path
Suppose you wish to retire at the age of 60 with $80,000 in savings. Determine your monthly paymentinto an IRA if the APR is 5.5% compounded monthly and you begin making payments at 30 years old.Round your answer to the nearest cent, if necessary
how do I do ratios? please tell me by 8:30
we obtain the ratios dividing one value by another
1.
[tex]\frac{\text{Vowels}}{\text{consonants}}[/tex]the number of vowels are 5 and the consonants are 21
so the ratio is
[tex]\frac{5}{21}\longrightarrow5\colon21[/tex]the unit ratio is
[tex]\frac{\frac{5}{21}}{1}=\frac{0.238}{1}=0.238[/tex]2.
to determine if two ratios are equivalent we must simplify the fractions
[tex]\frac{12}{16}=\frac{6}{8}=\frac{3}{4}[/tex][tex]\frac{72}{96}=\frac{36}{48}=\frac{18}{24}=\frac{9}{12}=\frac{3}{4}[/tex]the ratios are equivalent because the two represent 3/4
the unit ratio of 3/4 is
[tex]\frac{\frac{3}{4}}{1}=\frac{0.75}{1}=0.75[/tex]25. A group of students were asked how many movies they had watched the previous week. The results are shown below. Number of Movies Frequency 0 8 1 8 2 5 3 5 4 7 Find the mean and median for the number of movies watched per student. Round your answers to the nearest hundredth. Mean = Median =
mean = 1.85
median = 2.00
Explanation:To find the mean of a data that has frequency:
[tex]\text{mean = }\frac{\sum ^{}_{}fx}{\sum ^{}_{}f}[/tex][tex]\begin{gathered} \sum ^{}_{}fx\text{ = product of the numbers and their frequency} \\ \sum ^{}_{}fx\text{ = (0}\times8)\text{ + (1}\times8)\text{ + (2}\times5)\text{ + (3}\times5)\text{ + (4}\times7) \\ \sum ^{}_{}fx\text{ =}0\text{ + 8 + 10 + 15 + 28} \\ \sum ^{}_{}fx\text{ = 61} \end{gathered}[/tex][tex]\begin{gathered} \sum ^{}_{}f\text{ = sum of frequency} \\ \sum ^{}_{}f=\text{ 8 + 5 + 5 + 5 + 7} \\ \sum ^{}_{}f=\text{ }33 \\ \operatorname{mean}\text{ = }\frac{61}{33} \\ \operatorname{mean}\text{ = }1.85 \end{gathered}[/tex]To get the median, we need the numbers in ascending order. Since the number is in ascending order in the table, we find the middle of the frequency:
frequency = 33
middle of 33 numbers = 16.5
8 + 8 = 16 (so it can't fall under 0 or 1). it has to be the next number
Frequency of 16.5 will fall under the 2 as it is the number next in line
To the nearest hundredth, median = 2.00
A family has two cars. During one particular week, the first car consumed 20 gallons of gas and the second consumed 40 gallons of gas. The two cars drove a combined total of 1200 miles, and the sum of their fuel efficiencies was 45 miles per gallon. What were the fuel efficiencies of each of the cars that week? Note that the ALEKS graphing calculator can be used to make computations easier. First car: miles per gallon Second car: miles per gallon ?
Solution:
Let the car efficiency of first car be x
Let the car efficiency of the second car be y
Given that the first car consumed 20 gallons of gas and the second consumed 40 gallons of gas. The two cars drove a combined total of 1200 miles
This can be represented as
[tex]20x+40y=1200-----(1)[/tex]Given that the sum of their fuel efficiencies was 45 miles per gallon
This can be represented as
[tex]x+y=45----------(11)[/tex]Solve both equations simultaneously
[tex]\begin{gathered} 20x+40y=1200 \\ x+y=45 \\ x=45-y \\ thus,\text{ } \\ 20(45-y)+40y=1200 \\ 900-20y+40y=1200 \\ 900+20y=1200 \\ 20y=1200-900 \\ y=\frac{300}{20} \\ y=15 \\ \end{gathered}[/tex][tex]\begin{gathered} x+y=45 \\ x=45-y \\ x=45-15 \\ x=30 \end{gathered}[/tex]Thus,
First car: 30 miles per gallon
Second car: 15 miles per gallon
Could you please help me and my grandson with this problem? Thank you.
SOLUTION:
Case: Simple linear equations
Given: x + 14 = -28
Initial method:
[tex]\begin{gathered} x+14=-28 \\ (x+14)-14=-28-14 \\ x=-14 \end{gathered}[/tex]Spotting the mistake:
[tex]-28-14\ne-14[/tex]Correcting the mistake:
[tex]\begin{gathered} x+14=-28 \\ Subtracting\text{ 14 from both sides} \\ (x+14)-14=-28-14 \\ x+14-14=-28-14 \\ x=-42 \end{gathered}[/tex]Final answer:
x= -42
Find the reference angle. St 47 23 to
Given the angle
[tex]-\frac{5\pi}{4}[/tex]Add 2π to the angle to find the corresponding positive angle
so, the angle will be:
[tex]-\frac{5\pi}{4}+2\pi=\frac{3\pi}{4}[/tex]So, the angle Lies in the second quadrant
so, the reference angle will be:
[tex]\pi-\frac{3\pi}{4}=\frac{\pi}{4}[/tex]so, the answer will be the reference angle = π/4
quadratic, list the center and radius, then graph each circle lah (b) x2 + y2 - 4x = 0 (d) x2 + y2 - 2x - 8y = 8 (f) 4x2 + 4y2 - 16x + (h) x2 + y2 - 7y = 0 (1) x2 + y2 - 2ax + 2by = c 4y2 - 16x + 24y = -27
Given the equation of circle b;
[tex]x^2+y^2-4x=0[/tex]We need to express the above equation in the form;
[tex](x-h)^2+(y-k)^2=r^2[/tex]where;
[tex]\begin{gathered} r=\text{radius of the circle} \\ (h,k)=\text{ coordinate of the center of the circle} \end{gathered}[/tex]Solving for h,k and r;
[tex]\begin{gathered} x^2+y^2-4x=0 \\ x^2-4x+y^2=0 \\ \text{add 4 to both sides;} \\ x^2-4x+4+y^2=0+4 \\ (x-2)^2+(y-0)^2=4 \\ (x-2)^2+(y-0)^2=2^2 \\ So; \\ h=2 \\ k=0 \\ r=2 \end{gathered}[/tex]A farmer has a 25 ft by 100 ft rectangular field that he wants to reduce to 16% of its original size. How wideof a strip should he cut around the edge of his field to do this?
10feet
Given:
A farmer has a 25 ft by 100 ft rectangular field that he wants to reduce to 16% of its original size.
To find how wideof a strip he can cut around the edge of his field to do this.
Let w be the width of a strip should he cut around the edge to reduce to 16%
Original area = 25 x 100 = 2500 ft²
Hence;
(25 - 2w)(100 - 2w)= 16% of 2500
(25 - 2w)(100 - 2w) = 0.16 x 2500
(25 - 2w)(100 - 2w) =400
Open the parenthesis.
2500 - 50w - 200w + 4w² = 400
Rearrange in the form of quadratic equation.
2500 - 250w + 4w² - 400 = 0
2100 - 250 w + 4w² = 0
4w² - 250w + 2100 = 0
Divide through by 2
2w² - 125w + 1050 = 0
We can now solve the above using using the quadratic formula.
a = 2 b=-125 c=1050
[tex]w=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex][tex]w=\frac{125\pm\sqrt[]{15625-8400}}{4}[/tex][tex]=\frac{125\pm\sqrt[]{7225}}{4}[/tex][tex]=\frac{125\pm85}{4}[/tex][tex]\begin{gathered} \text{Either } \\ w=\frac{125+85}{4}=\frac{210}{4}=52.5 \\ \\ or \\ \\ w=\frac{125-85}{4}=\frac{40}{4}=10 \end{gathered}[/tex]Let's check for the reasonable solution.
(25 - 2w)(100 - 2w) = 400
w=10
(25 - 20)(100 - 20) = (5)(80) = 400
The only reasonable solution is w= 10
Therefore, the widthof the strip should be 10 feet.
I need someone to help me answer 1 and 2
Solution
The sum of angles in a triangle needs to be 180
For this case we can find the arclenght with the following formula:
The angle < RPQ = 180 -60- 50= 70°
Then the answer is:
C 70°
Solve the proportion to determine the total size of Iran.11.2 7 million miles squared/33.81 million miles squared= 0.636 million miles squared/1.908 million miles squared
Answer:
0.3333 million square miles.
Explanation:
[tex]\begin{gathered} \frac{11.27}{33.81}=\frac{0.636}{1.908}=\frac{1}{3} \\ =0.3333\text{ million square miles} \end{gathered}[/tex]The total size of Iran is 0.3333 million square miles.
Find the equation of the linear function represented by the table below in slope-intercept form.xy112-13-34-5
Given:
Two points
[tex](1,1)\text{ and (2,-1)}[/tex]To find: The equation of the linear function
Explanation:
Using the two-point formula,
[tex]\frac{y-y_1}{y_2-y_1}=\frac{x-x_1}{x_2-x_1}[/tex]Here,
[tex]\begin{gathered} x_1=1 \\ y_1=1 \\ x_2=2 \\ y_2=-1 \end{gathered}[/tex]Substituting we get,
[tex]\begin{gathered} \frac{y-1}{-1-1}=\frac{x-1}{2-1} \\ \frac{y-1}{-2}=\frac{x-1}{1} \\ y-1=-2(x-1) \\ y=-2x+2+1 \\ y=-2x+3 \end{gathered}[/tex]Final answer: The equation of the linear function is,
[tex]y=-2x+3[/tex]Two boats, 70m apart and on opposite sides of a light-house are in straight line with the light house. The angles of elevation of the top of the light-house from the two boats are 70° and 42°. Find the height of the light-house.
A diagram of the problem will be:
Where h is the height of the light-house.
We can apply tangent to find the height.
Let's start:
[tex]\begin{gathered} \tan42=\frac{h}{70-x} \\ \\ h=\tan42*(70-x)\text{ Equation 1} \\ \\ \tan70=\frac{h}{x} \\ \\ h=\tan70*x\text{ Equation 2} \end{gathered}[/tex]Now, find h in terms of x from equation 2, and replace it into equation 1, to find x:
[tex]\begin{gathered} h=2.75x \\ 2.75x=tan42(70-x) \\ 2.75x=0.9(70-x) \\ 2.75x=0.9*70-0.9x \\ 2.75x=63-0.9x \\ 2.75x+0.9x=63 \\ 3.65x=63 \\ x=\frac{63}{3.65} \\ x=17.26m \end{gathered}[/tex]Now, replace x into equation 2 and solve for h:
[tex]\begin{gathered} h=tan70*x \\ h=2.75*17.26m \\ h=47.42m \end{gathered}[/tex]The height of the light-house is 47.42 m.
Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint. (Hint: Let (x,y) be the unknown endpoint. Apply the midpoint formula,and solve the two equations for x and y.)midpoint (3,20), endpoint (10,13)The other endpoint is ___.(Type an ordered pair.)
The midpoint is (3,20) and the other endpoint is (10,13);
Since the midpoint formula is;
[tex](x_m,y_m)=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]Thus;
[tex]\begin{gathered} x_m=\frac{x_1+x_2}{2} \\ 3=\frac{x_1+10}{2} \\ x_1+10=6 \\ x_1=-4 \end{gathered}[/tex]and;
[tex]\begin{gathered} y_m=\frac{y_1+y_2}{2} \\ 20=\frac{y_1+13}{2} \\ y_1+13=40 \\ y_1=27 \end{gathered}[/tex]Thus, the other endpoint is;
[tex](-4,27)[/tex]The perimeter of square F is 3 meter less than the perimeter of square G. The side lengths of square F are each f meters, and the 2 side lengths of square G are each 4 3 meters. Which expression also represents the side lengths of square G?
Answer: 1/4f - 1/6
Each length side of Perimeter G is given as
[tex]\frac{1}{4}\text{ (f - }\frac{2}{3})[/tex]Open the parenthesis by multiplying through by 1/4
1/4 x f - 1/4 x 2/3
1/4f - 2/12
1/4f - 1/6
The answer is 1/4f - 1/6
Find the standard form for the equation of the line that contains the point (-5, -12) and that is perpendicular to 2x + 3y = 12.
Answer:
The equation of the line perpendicular to the given line is
[tex]y=\frac{3}{2}x-\frac{9}{2}[/tex]Explanation:
Given the equation:
2x + 3y = 12
Let us rewrite it in standard form to have the slope and y-intercept.
Subtract 2x from both sides
3y = 12 - 2x
Divide both sides by 3
[tex]y=\frac{12}{3}-\frac{2}{3}x[/tex]or
[tex]y=-\frac{2}{3}x+4[/tex]Here, the slope is -2/3, and the y-intercept is 4
An line perpendicular to this line has it's slope as the negative reciprocal of the slope -2/3
The negative reciprocal of -2/3 is 3/2
The perpendicular line is in the form:
[tex]y=\frac{3}{2}x+b[/tex]Where b is the y-intercept.
Since the line contains the point (-5, -12), -5 and -12 are the coordinates of the x and y axes respectively, using them, we can obtain a value for b, the y-intercept.
[tex]\begin{gathered} -12=\frac{3}{2}(-5)+b \\ \\ -12=-\frac{15}{2}+b \\ \\ \text{Add 15/2 to both sides} \\ -12+\frac{15}{2}=b \\ \\ b=-\frac{9}{2} \end{gathered}[/tex]Therefore, the equation of the line perpendicular to the given line is
[tex]y=\frac{3}{2}x-\frac{9}{2}[/tex]Fill in the blanks below with the correct units. (a) The mass of the baseball was about 145 ? (b) Jose drank about 300? (c) A two story house is about 12 ? of juice with lunch. tall.
Given
(a) The mass of the baseball was about 145____.
(b) Jose drank about 300___ of juice with lunch.
(c) A two story house is about 12__ tall.
To fill in the blanks with the correct units.
Explanation:
It is given that,
(a) The mass of the baseball was about 145____.
(b) Jose drank about 300___ of juice with lunch.
(c) A two story house is about 12__ tall.
That implies,
(a) The mass of the baseball was about 145 grams.
(b) Jose drank about 300 milliliters of juice with lunch.
(c) A two story house is about 12 meters tall.
Look at the factors of 50 and 75.Factors of 50: 1, 2, 5, 10, 25, 50Factors of 75: 1, 3, 5, 15, 25, 75The GCF of 50 and 75 is .
the greatest common factor of 50 and 75 is 25
Isabelle has $5250 in her bank account and makes automatic $750 monthly payments on a home loan. Ifshe stops making deposits to that account, when would the automatic payments make the value of theaccount zero?The value of the account would be zero inmonths.
Let's define
x: months
If she stops making deposits and makes automatic $750 monthly, her account would have 5250 - 750x dollars after x months.
To find when the value of the account will be zero, we have to solve:
5250 - 750x = 0
5250 = 750x
5250/750 = x
7 = x
The value of the account would be zero in 7 months.
6x²y²-3xy³factor out the gcf
we have
6x²y²-3xy³
so
Remember that
6x²y²=(2)(3)(x)(x)(y)(y)
3xy³=(3)(x)(y)(y)(y)
therefore
GCF=(3)(x)(y)(y)=3xy²
3xy²(2x-y)Write the function or evaluate for each of the below
Answer:
[tex]\begin{gathered} (e)2x^3-10x^2 \\ \text{ }(f)\frac{2x^2}{x-5},x\neq5\; \; \; \mleft(g\mright)5\text{ } \\ (h)(f\circ g)(x)=2x^2-5 \\ (I).(g\circ f)(x)=2x^2-20x+50 \\ (J).\text{ }(f\circ g)(3)=13 \end{gathered}[/tex]Explanation:
Given the functions f(x) and g(x) below:
[tex]\begin{gathered} f(x)=x-5 \\ g(x)=2x^2 \end{gathered}[/tex]Part E (f * g(x)
[tex]\begin{gathered} (f\cdot g)(x)=f(x)\cdot g(x) \\ =\lbrack x-5\rbrack\lbrack2x^2\rbrack \\ =2x^3-10x^2 \end{gathered}[/tex]Part F (g ÷ f)(x)
[tex]\begin{gathered} (g\div f)(x)=\frac{g(x)}{f(x)} \\ =\frac{2x^2}{x-5} \end{gathered}[/tex]Part G
When the denominator of a rational function is 0, the function is Undefined.
The denominator of (g ÷ f)(x) = x-5
[tex]\begin{gathered} x-5=0 \\ \implies x=5 \end{gathered}[/tex]The value of x that cannot be inputed into (g ÷ f)(x) is 5.
Part H (f o g)(x)
[tex]\begin{gathered} (f\circ g)(x)=f\lbrack g(x)\rbrack \\ f(x)=x-5 \\ \implies f\lbrack g(x)\rbrack=g(x)_{}-5=2x^2-5 \\ Therefore\colon \\ (f\circ g)(x)=2x^2-5 \end{gathered}[/tex]Part I (g o f)(x)
[tex]\begin{gathered} (g\circ f)(x)=g\lbrack f(x)\rbrack \\ g(x)_{}=2x^2 \\ \implies g\lbrack f(x)\rbrack=2\lbrack f(x)\rbrack^2_{}=2(x-5)^2 \\ =2\mleft(x-5\mright)\mleft(x-5\mright) \\ =2\mleft(x^2-10x+25\mright) \\ Therefore\colon \\ (g\circ f)(x)=2x^2-20x+50 \end{gathered}[/tex]Part J
From part H:
[tex](f\circ g)(x)=2x^2-5[/tex]Substitute 3 for x to get (f o g)(3).
[tex]\begin{gathered} (f\circ g)(3)=2(3)^2-5 \\ =2(9)^{}-5 \\ =18-5 \\ (f\circ g)(3)=13 \end{gathered}[/tex]The value of (f o g)(3) is 13.
What is the constant of proportionality? у 3 2 (2, 2) 1 -3 -2 1 2 3x 2 (-3, -3) Cannou Solve NT 2/3
Explanation:
The constant of proportionality can be calculated as:
[tex]\frac{y}{x}[/tex]For every point (x,y) in the line.
So, if we replace (x, y) by point (2,2) or by point (-3,-3), we are going to get:
[tex]\begin{gathered} \frac{x}{y}=\frac{2}{2}=1 \\ or \\ \frac{x}{y}=\frac{-3}{-3}=1 \end{gathered}[/tex]So, the constant of proportionality is 1.
Answer: 1
SOS can’t figure this one out I need a little help
• Let n be number of student who responded = 145
• Let x be number of student who attended basketball = 22
,• P = sample proportion = x/n = 22/145 = 0.15
,• The 95% confidence interval forstudent who attended basketball game can be estimated as below :
[tex]\begin{gathered} P^{\text{ }}-EInterpretation of the above : we have 95 % confidence that the population percentage of women who attended the basket ball game will lie between 0.09 and 0.21.
What is your equation? Re-watch thelast section if you're not sure how todo it.1 2 3 4 5 6 7 8 9 10Years Since 1998Note: Your equation doesn't have to beperfect ... just give it your best effortand then watch the explanation thatfollows.
Part a.
We are asked to type an equation that could represent the line of best fit shown in the following image:
So, we need just two points on the line that can be used to find the slope and finally the complete equation of the line.
We select two particular points: (1, 61) and (8, 71) whcu seem to be two points where the line goes through.
Then we use the formula for the slope of a line through two points on the plane:
slope = (y2 - y1) / (x2 - x1)
in our case: (71 - 61) / (8 - 1) = 10 / 7
Then the slope-intercept form ofthe equation should look like:
y = 10/7 x + b
we can determine "b" by using one of the points (for example (1, 61)):
61 = (10/7) (1) + b
61 - (10/7) = b
b = 417/7
The final form of the equation is:
y = 10/7 x + 417/7
In approximate decimal form it becomas:
y = 1.43 x + 59.8
Part b:
Interpretation of the slope and y-intercept:
The slope represents the change in percent of graduates per year. so every year there is an increase of about 1.43 % of graduates relative to the previous year.
The y-intercept represents the graduation rate (about 59.8%) when this study started (year 0 zero corresponding to 1998)
Part c:
In order to estimate the prediction of percent of graduates in the year 2020, we first calculate the number of years between 2020 and 1998:
2020 - 1998 =
Solve log11 (y + 8) + log11 4 = log11 60.
SOLUTION
We want to solve
[tex]log_{11}(y+8)+log_{11}4=log_{11}60[/tex]Collecting like terms we have
[tex]\begin{gathered} log_{11}(y+8)=log_{11}60-\log _{11}4 \\ log_{11}(y+8)=log_{11}(\frac{60}{4}) \\ log_{11}(y+8)=log_{11}15 \\ \text{cancelling }log_{11}\text{ from both sides, we have } \\ y+8=15 \\ y=15-8 \\ y=7 \end{gathered}[/tex]Hence the answer is y = 7
If you reflect the triangle below over the x-axis, what quadrant would it be in?
The correct answer is Quadrant 4, that is, the last option.
18) Determine if the number is rational (R) or irrational (I) 7÷54
By definition, a rational number is any number that can be written as a fraction, where both the numerator and the denominator are integers.
Now, consider the following number:
[tex]\frac{7}{54}[/tex]notice that the numerator and the denominator are both integers. Thus, by definition, the number 7/54 is a rational number.
We can conclude that the correct answer is:
Answer:Rational number (R).
Im going to send the full problem it asked me to crop the problem
Given that BD = 3 x+ 5,
AE = 5 x + 19
( 5 x + 19 ) / ( 3 x+ 5 ) = 2
cross- multiply, we have :
5 x + 1 9 = 2 ( 3 x+ 5 )
5 x + 19 = 6x + 10
collecting like terms , we have :
19 - 10 = 6 x - 5 x
x= 9
Which set of systems of equations represents the solution to the graph?an upward opening parabola decreasing from negative 3 comma 8 to a minimum at negative 1 comma 4 and then increasing to 1 comma 8 and a downward opening parabola increasing from negative 2 comma 1 to a maximum at 0 comma 5 and then decreasing through the point 1 comma 4A. f(x) = –x2 + 2x + 5g(x) = x2 + 5B. f(x) = –x2 + 2x – 5g(x) = x2 + 5C. f(x) = x2 + 2x – 5g(x) = –x2 + 5D. f(x) = x2 + 2x + 5g(x) = –x2 + 5
Looking at the graph we can identify both functions have a y-intercept of y = 5. This would be the independent term of both parabolas, so choices B and C are discarded because one of the functions in each choice has a y-intercept of -5.
This gives only two valid choices: A and D.
We can also see the parabola that is symmetrical with respect to the y-axis (the red one) is concave down, so its leading coefficient must be negative.
The condition above only occurs in choice D, so it's our correct answer:
D
Jan and 4 of her friends plan to spend a day at the zoo seeing as many animals they can They each purchase a ticket for admission, and they split a pizza for lunch. The pizza costs $20. The total amount of money that was spent on their zoo day was $80. Create an equation to represent the situation. What is the cost for each ticket? 16 12
Jan and 4 of her friends plan to spend a day at the zoo seeing as many animals they can They each purchase a ticket for admission, and they split a pizza for lunch. The pizza costs $20. The total amount of money that was spent on their zoo day was $80. Create an equation to represent the situation. What is the cost for each ticket?
Let
x ------> the cost for each ticket
we have that
Jan and 4 of her friends--------> 5 persons
so
5x+20=80 ------> equation that represent the situation
solve for x
5x=80-20
5x=60
x=$12
therefore
the cost of each ticket is $12