Number of weeks required before Jacob and Diego will be tied in the race to complete community service hours for scouting is equal to 50 weeks.
As given in the question,
Let number of weeks be represented by a variable x.
Jacob plans to devote 5 hours per week from now onwards. Hence his volunteer hours will cumulate to 5x+50 as he has already completed 50 weeks.
Diego plans to devote 6 hours per week from now onwards. Hence his volunteer hours will cumulate to 6x.
For Jacob and Diego to tie in the race, their volunteer hours should be equal. Translating this into a linear algebraic equation,
6x = 5x+50
=> 6x-5x = 50
=> x = 50
Therefore, number of weeks required before Jacob and Diego will be tied in the race to complete community service hours for scouting is equal to 50 weeks.
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Zoe is making a rectangular box with measurements as shown below 5 inches 3 inches 3 inches what is the surface area of the box
Surface area of rectangular box is 78 inches².
What is surface area?The surface area of an object is the sum of the areas of all of its faces, or the exterior surfaces of its three dimensions. It is calculated in square units. The total area of all faces (or surfaces) on a 3D form is the surface area. The six rectangular faces of a cuboid. Add the areas of each of the cuboid's six faces to determine its surface area. Additionally, we can label the prism's length (l), width (w), and height (h), and then calculate its surface area using the formula SA=2lw+2lh+2hw.
Given Data
rectangular box with measurements as shown below 5 inches 3 inches 3 inches
Length = 5 inches
Width = 3 inches
Height = 3 inches
Surface area formula
2lw + 2lh+2hw
Equating values
2(5)(3) + 2(5)(3) +2(3)(3)
30 + 30 + 18
78
Surface area of rectangular box is 78 inches².
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(5+6) + what = 5 + (6+2)
Answer:
total is 13. so 5+6 = 11 and total is 13 so 13 - 11 = 2
f(-3) = -1, f(-2) = 4
Answer:
1(-3) = -3, 1f(-2) = -2
Step-by-step explanation:
help meeeeee
8 Answer:
Evaluate the expression (2y)3 when y = 3.
9 Answer:
Evaluate the expression x2 + y when x = 4 and y = 3.
10 Answer:
Evaluate the expression (a + b)3 when a = 3 and b = 5.
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textsf{Equation \#1.}[/tex]
[tex]\mathsf{(2y)^3}\\\mathsf{= (2(3)^3}\\\mathsf{= (6)^3}\\\mathsf{= 6^3}\\\mathsf{= 6\times6\times6}\\\mathsf{= 36\times6}\\\mathsf{= 216}\\\huge\text{Therefore, your answer should be: \boxed{\mathsf{216}}}\huge\checkmark[/tex]
[tex]\huge\textsf{Equation \#2.}[/tex]
[tex]\mathsf{x^2 + y}\\\mathsf{= 4^2 + 3}\\\mathsf{= 4\times 4 + 3}\\\mathsf{= 16 + 3}\\\mathsf{= 19}\\\huge\text{Therefore, your answer should be: \boxed{\mathsf{19}}}}}\huge\checkmark[/tex]
[tex]\huge\textsf{Equation \#3.}[/tex]
[tex]\mathsf{(a + b)^3}\\\mathsf{= (3 + 5)^3}\\\mathsf{= (8)^3}\\\mathsf{= 8^3}\\\mathsf{= 8\times 8 \times 8}\\\mathsf{= 64\times8}\\\mathsf{= 512}\\\huge\text{Therefore, your answer should be: \boxed{\mathsf{512}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
A cement walkway is to be poured .it is consists of the two rectangles with dimensions and a circle with radius 1.5 yards use 3.14 as an approximate value.how many square yards will the walkway be?If a painter it for 3.75 per square yard,how much will the painting cost?
The area of the walkway in square yards is 22.77 yards²
The cost of painting the walkway will be $85.37.
What is the area of the walkway?The square yards of the walkway can be determined by adding the areas of the two rectangles and the area of the quarter of a circle together.
Area of a rectangle = length x width
Area of the first rectangle = 9.5 x 1.5 = 14.25 yards²
Area of the second rectangle = 4.5 x 1.5 = 6.75 yards²
Area of a circle = πr²
Area of quarter of a circle = 1/4 × πr²
Where:
π = pi = 3.14
r = radius
1/4 x (3.14 x 1.5²) = 1.77 yards²
Area of the walkway = 1.77 yards² + 6.75 yards² + 14.25 yards² = 22.77 yards²
The cost of the painting can be determined by multiplying the area of the walkway by the cost per square yard.
Total cost = 22.77 yards² x 3.75 = $85.37
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Show your work here. Use the pen as needed. North High School is selling game tickets for one of their football games. Adult tickets (x) cost $7 each and student tickets (y) cost $4 each. Write and graph an inequality to represent the combination of tickets sold, assuming they estimate to make at most $280 in ticket sales for this game.graph it
Adult tickets cost $7 each
Student tickets cost
8 ÷ 2(2 + 2)
what is the answer
Answer: 16
Step-by-step explanation: 8 ÷ 2(2 + 2)
At American High School, there is a 25.5% probability a randomlyselected student is an honor roll student, while there is a 37%probability that a randomly selected student is a varsity athlete.The probability that a student is an honor roll student and avarsity athlete is 6%.
Given,
probability of randomly selected student is an honor roll student,
[tex]\frac{25\cdot5}{100}=0\cdot255[/tex]probability of randomly selected student is a varsity athlete,
[tex]\frac{37}{100}=0\cdot37[/tex]The probability of the student is an honor roll student and a
varsity athlete,
[tex]\frac{6}{100}=0\cdot06[/tex]The probability of multiple events is,
[tex]0.255\times0.37\times0.06=0.005661[/tex]0.005661
Find the measure of each angle indicated
Answer:
68°
Step-by-step explanation:
Alternate exterior angles have the same measurement.
Two shops rent pairs of skis for a rental fee plus a fee per hour. Write and solve an equation to
find how many hours must a pair of skis be rented for the total costs to be the same?
Shop A Equation:
Shop B Equation:
Solution:
Rental Fee
Hourly Fee
Shop A
$3
$9
Shop B
$9
$6
For the total costs to be the same a pair of skis must be rented for 3 hours.
Two shops rent pairs of skis for a rental fee plus a fee per hour.
Let, the number of hours must a pair of skis be rented = x
Equation for Shop A,
3 + 9x equation 1
Equation for Shop B,
9 + 6x equation 2
Total cost for Shop A and Shop B is same so we can equate equation 1 and equation 2 as mentioned below:
3 + 9x = 9 + 6x
3x = 6
x = 3
Thus we can write, for the total costs to be the same a pair of skis be rented for 3 hours.
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Arielle is hiking down into the canyon. She starts at the rim and hikes down 55 feet in 2 3/4 minutes. If she continues at this rate, where will Arielle be in relation to the rim after 15 minutes
First, determine the speed of Arielle by calculating the quotient in between 55 ft and 2 3/4 minutes. To find the quotient, convert the mixed number to a normal fraction before:
[tex]2\frac{3}{4}=2+\frac{3}{4}=\frac{8+3}{4}=\frac{11}{3}[/tex]then, calculate the speed:
[tex]v=\frac{55}{\frac{11}{3}}=\frac{\frac{55}{1}}{\frac{11}{3}}=\frac{55\cdot3}{11\cdot1}=\frac{165}{11}=15[/tex]then, the Arielle's speed is 15 ft/min
next, find the distance traveled by Arielle in 15 min, by using the previous result:
[tex]d=v\cdot t=(15ft/\min )(15\min )=225ft[/tex]Hence, in relation to the rim, Arielle will be at 225 ft
Movie theaters keep track of how many tickets they sell. For the 5:30 showing, the theater
sold a total of 272 adult and student tickets and took in a total of 1694 dollars. If adults
tickets sold or 7 dollars and students sold for 4 dollars each how many of each type were sold
for the 5:30 show.
As a result, we deduce that 101 tickets were sold to adults and 171 to students after solving the algebraic equations.
What are Algebraic equations ?The term "algebraic equation" refers to a formulation of the equality of two expressions using the algebraic operations of addition, subtraction, multiplication, division, raising to a power, and extraction of a root on a set of variables.
A mathematical statement in which two expressions are rendered equal to one another is known as an algebraic equation.
So on the information provided to us:
we know that the total amount of the tickets sold =1694$
total no. of people = 272
Lets assume the no. of kids to be y and the adults to be x
So the first equation we get for the total no. of people is:
x+y=272...(i)
the next equation we get for the total amount of tickets sold will be equal to the no. of adults and children multiplied by the cost of each adult and child respectively :
7x+4y=1694....(ii)
Two solve both equations simultaneously , we multiply equation i with 4
we get:
4x+4y=1088
7x+4y=1694
on solving both the equations simultaneously we get
3x=606
x=101
putting value of x in equation (i) we get
y=171
Therefore, we conclude that the no. of tickets sold to adults were 101 and to students were 171.
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Write an equation to represent the word problem. Then solve it.
←
Dinh has 3 more patients to care for than Juan. If Dinh has 17 patients to ca
The equation is
(Type an equation using x as the variable. Do not evaluate.)
Juan has to care for
patients.
0
We get that Juan has 14 patients to care for.
What is an equation?
A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.
Let Juan has x patient to care for.
Therefore according to the question Dinh has x + 3 patients to care for.
Therefore,
The equation is x + 3= 17
=> x = 17 -3
=> x = 14
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Find MK.
08
04
O 14
06
L
4x-2
O
x+2
K
Il
Answer:
14
Step-by-step explanation:
well, the logic is simply that the sum of the parts must be the same as the whole.
so,
8 + (x + 2) = 4x - 2
10 + x = 4x - 2
12 = 3x
x = 4
therefore,
MK = 4x - 2 = 4×4 - 2 = 16 - 2 = 14
I need help with the following question
The values of the trigonometry formulas are sin(240) = -sin(60), cos(225) = -cos(45) and tan(225) = tan(45)
How to determine the values of the trigonometry formulas?The trigonometry ratios are given as
sin(180 - ∅) = sin(∅)
cos(180 - ∅) = -cos(∅)
tan(180 - ∅) = -tan(∅)
Also, we have the following trigonometry ratios are given as
sin(180 + ∅) = -sin(∅)
cos(180 + ∅) = -cos(∅)
tan(180 + ∅) = tan(∅)
Using the above trigonometry ratios, we have
sin(240) = sin(180 + 60)
By comparison, we have
sin(240) = sin(180 + 60)
sin(180 + ∅) = -sin(∅)
This gives
∅ = 60
So, we have
sin(180 + 60) = -sin(60)
Evaluate
sin(240) = -sin(60)
Using the above trigonometry ratios, we have
cos(225) = cos(180 + 45)
By comparison, we have
cos(225) = cos(180 + 45)
cos(180 + ∅) = -cos(∅)
This gives
∅ = 45
So, we have
cos(180 + 45) = -cos(45)
Evaluate
cos(225) = -cos(45)
Using the above trigonometry ratios, we have
tan(225) = tan(180 + 45)
By comparison, we have
tan(225) = tan(180 + 45)
tan(180 + ∅) = tan(∅)
This gives
∅ = 45
So, we have
tan(180 + 45) = tan(45)
Evaluate
tan(225) = tan(45)
Hence, the value is tan(225) = tan(45)
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Question
A golden retriever weighing 85 lb was prescribed a medication. If the dosage is 1 mg for every 5 lb, how much medicine was
the dog given?
3) A clock is set correctly at 1pm. If it loses 3 minutes every hour, what will the clock show
when the correct time is 10 am the next day?
Based on the time the clock is set to, and the minutes lost every hour, the time the clock would show the next day at 10 am is 8:57 am
How to find the time shown?To find the time that the clock would show the next day, first find the difference between the 1 pm and 10 am the next day:
This difference is:
= 10 am the next day - 1 pm
= 10 + (12 - 1)
= 10 + 11
= 21 hours
The number of minutes lost is:
= 21 x 3 minutes per hour
= 63 minutes
The time the clock would be showing is:
= 10 am - 63 minutes
= 8:57 am
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evaluate 4.141414 as a rational number
we'll start by moving the recurring part to the left of the decimal point hmmm so the recurring part is 0.14 so if we just multiply that by 100, that'll give us 14.141414...., now let's make the recurring part a variable
[tex]x=0.\overline{14}\hspace{5em} \begin{array}{llll} 100x&=&14.\overline{14141414}\\\\ &&14+0.\overline{14141414}\\\\ &&14+x \end{array} \\\\[-0.35em] ~\dotfill\\\\ 100x=14+x\implies 99x=14\implies x=\cfrac{14}{99}[/tex]
Answer:
2070707/500000
Step-by-step explanation:
rational no. simply means a fraction.
i need help will give points
x = -16
Explanation:The given equation is:
[tex]3+\frac{x}{-8}=5[/tex]Multiply through by -8 (Equality property of multiplication)
[tex]\begin{gathered} -8(3)+(-8)\frac{x}{-8}=-8(5) \\ -24+x=-40 \end{gathered}[/tex]Add 24 to both sides of the equation (Equality property of addition)
-24 + 24 + x = -40 + 24
x = -40 + 24
x = -16
Therefore, the solution to the equation is x = -16
Identify Linear Function from Points Which table of Values REPRESENTS a linear Functions?draw the problems on the table Please.
Linear functions from tables
I'll draw the calculations directly on the tables as required. The table that has the same slope represents a linear function.
Table A has different values for the slope, this table is not a linear function.
Table C is not a linear function since the slope is not constant
Table B does not have a constant slope, so it's not a linear function
Table D has a constant slope of 1/3, thus this table represents a linear function
please help !!!!!!!!! THANK YOU
For the give question;
The given line is; -2x + 3y = 6
Write the equation in slope intercept form; y = mx + c.
-2x + 3y = 6
3y = 2x + 6
y = (2/3)x + 2
Slope m₁ = 2/3 and y intercept is 2.
For the relation of slope;
Parallel line : m₁ = m₂Perpendicular line: m₁×m₂ = -1Part a: -3x - 2y = 4
Write the equation in slope intercept form;
-2y = 3x + 4
y = (-3/2)x - 2
m₂ = -3/2
m₁ ≠ m₂ as 2/3 ≠ -3/2
m₁×m₂ = 2/3 × -3/2 = -1
Thus, the both lines are perpendicular.
Part b: -2x + 3 y = -6
Write the equation in slope intercept form;
3y = 2x - 6
y = (2/3)x - 2
m₂ = (2/3)
m₁ = m₂
Thus, both lines are parallel.
Part c: 2x + 3y = 6
Write the equation in slope intercept form;
3y = -2x + 6
y = (-2/3)x + 2
m₂ = -2/3
m₁ ≠ m₂ as 2/3 ≠ -2/3
And, m₁×m₂ = 2/3 × -2/3 ≠ 1
Thus, lines are neither parallel not perpendicular.
Part d: -2x + 3y = 0
Write the equation in slope intercept form;
3y = 2x
y = 2/3 x
m₂ = 2/3
m₁ = m₂
Thus, both lines are parallel.
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50÷2 and 5÷3solve the question and tell the remainder
Step-by-step explanation:
the perimeter of a triangle is 84 cm and its area is 36 CM square if one its side is 30 cm find the length of remaining two side
Please help me solve question
In this problem, we are looking for the doubling time of the wage of the Toyota automobile assembly line workers. Initially, their wage is $6.70 and by the end of 15 years, their salary is now $29.59.
What we can find here first is the rate of the increase of the salary of the workers. We can use the equation
[tex]y=y_0e^{rt}[/tex]We are looking for the value of r. We have to derive an equation solving for r. We have
[tex]\begin{gathered} \frac{y}{y_0^{}}=e^{rt} \\ rt=\ln \frac{y}{y_0} \\ r=\frac{1}{t}\ln \frac{y}{y_0} \end{gathered}[/tex]Now, we solve for the value of r given y = 29.59, y0 = 6.70, and t = 15 years. We get
[tex]\begin{gathered} r=\frac{1}{15}\ln (\frac{29.59}{6.70}) \\ r=0.099yr^{-1} \end{gathered}[/tex]The doubling time is computed as
[tex]d=\frac{\ln 2}{r}[/tex]Substitute the value of r on the equation above and solve, we get
[tex]d=\frac{\ln 2}{0.099}=7.00yr[/tex]Hence, the doubling time for this problem is equal to 7 years.
Answer: 7 years
Identify the correct description of the values in both the domain and range of the function
Domain is number of minutes water has been added .
Range is amount in the pond
What are domain and range ?The domain and range of a relation are, respectively, the sets of all the x-coordinates and all the y-coordinates of ordered pairs. For example, if the relationship is R = (1, 2), (2, 2), (3,), (4, 3), then
Domain is the set of all x-coordinates that is all with values of 1, 2, 3, and 4.
The set of all y-coordinates in the range is equal to 2, 3.
Domain : Let y = f(x) be a function with an independent variable x and a dependent variable y.
Range : a function represents a defined relationship between an independent variable (x) and a dependent variable (y). The formula to find the range of a function is y = f(x).
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How do we get our voice?
Answer: The lungs provide the airstream which powers human voice. As air is pushed up the windpipe from the lungs, the larynx, which is made up of two vocal folds, opens and closes to produce vibrations. These vibrations are carried through to the throat, nose, and mouth, which act as resonators- morphing the vibrations into distinct human sounds.
Step-by-step explanation:
Answer:
Our vocal cords gve us our voice.
Step-by-step explanation:
The vocal folds (cords) produce sound when they come together and then vibrate as air passes through them during exhalation of air from the lungs. This vibration produces the sound wave for your voice.
Find the slope and the y-intercept of the line with the equation 9y - 6x + 8 = 0.Select the correct choice below and fill in any answer boxes within your choice. A. The slope is(Type an integer or a simplified fraction.)B. The slope is undefined.Select the correct choice below and fill in any answer boxes within your choice.A. The y-intercept is(Type an integer or a simplified fraction. Type an ordered pair.)B. There is no y intercept
Rewrite the given equation in slope intercept form, y=mx+c. Where the slope is m and the y-intercept is c.
Rewrite the given equation as follows:
[tex]\begin{gathered} 9y-6x+8=0 \\ \text{Take x term and the constant to the right side and change their sign} \\ 9y=6x-8 \\ \text{Divide each term by 9:} \\ \frac{9y}{9}=\frac{6x}{9}-\frac{8}{9} \end{gathered}[/tex]Simplify the equation:
[tex]y=\frac{6}{9}x-\frac{8}{9}[/tex]Compare to the equation y=mx+c, to get:
[tex]\begin{gathered} m=\frac{6}{9} \\ c=-\frac{8}{9} \end{gathered}[/tex]Hence, the slope is 6/9 and the y-intercept is -8/9.
You can also write the y-intercept as an ordered pair (0,-8/9) since the x-value at the y-intercept is zero.
Assume the average test score from the last year's class was 85 points with a standard deviation of 9. By sketching a normal curve, which value below is the best estimate for the proportion of students earned a 70 points or higher?
The given information is:
- The average test score is 85 points
- The standard deviation is 9
- It is a normal distribution
We need to find the best estimate for the proportion of students earned a 70 points or higher.
First, we need to find the z-score for 70, by applying the following formula:
[tex]z=\frac{x-\mu}{\sigma},\text{ where }\mu=average,\sigma=standard\text{ }deviation,x=value[/tex]Then, as x=70, we replace the given values and find z:
[tex]z=\frac{70-85}{9}=\frac{-15}{9}=-1.67[/tex]Then, we can find the estimate as follows:
[tex]P(X\ge70)=P(z\ge-1.67)=1-P(z<-1.67)[/tex]Now, in a standard normal table, we search the cumulative probability of z<-1.67, and it is 0.0475:
Thus, replace this value to find P(X>=70):
[tex]P(X\ge70)=1-0.0475=0.9525[/tex]The probability is 0.9525, if we multiply it by 100%, we obtain: 95.25%
The best estimate is 95%.
Sara bought 7 red peppers for $5.60.
Find the unit rate. Then use the unit rate to write an equation relating the cost in dollars c to the number of red peppers p.
The unit rate of what Sarah bought is 0.8 dollars per pepper.
The equation relating cost in dollars, c to the number of red peppers is c = 0.8p
How to find unit rate?A unit rate describes the ratio of two different units for the quantity of one.
In other words, the unit rate can be defined as the ratio between two measurements with the second term as 1.
Therefore, the unit rate when Sara buys 7 red peppers for $5.60 can be calculated as follows
unit rate = cost of pepper / number of pepper
unit rate = 5.60 / 7
unit rate = 0.8 dollars per pepper
Let's use the unit rate to write an equation relating the cost in dollars c to the number of red peppers, p.
Therefore,
c = 0.8p
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I need help please
Step-by-step explanation:
To help, but not give the answer so you can learn to do this:
To find the slope, choose any two points on the graph (no really IT DOESN'T MATTER WHICH ONE). Use the equation y-y/x-x to get the slope.
Ex. 8-3/5-1=4/3
(NOTE: Always write your answer as either an improper fraction or a whole number!)
To find the distance, go across the x-axis, however many units away the closest point is to your chosen point. Then, go across the y-axis for the required # of units. Next, find the total number of the x and y units. You can also subtract the smallest coordinate from the greatest if the two ordered pairs are in the same quadrant. If not in the same quadrant, add the coordinates together. If the value of x or y happens to be the same as your chosen coordinate, find the sum of the two numbers that are equal, or subtract if in the same quadrant.
Also, in case you have another question relating to the same line, the given line is NOT proportional. Just in case, though!
I hope this helps you with your question!
(Happy Halloween! )
Evaluate the expression shown below and write your answer as a fraction in simplest form.
\frac{1}{10}+\frac{11}{20}
10
1
+
20
11
The addition of the fraction 1/10 + 11/20 based on the computation will be 13/20.
What is a fraction?In mathematics, a fraction is defined as a portion of the whole. If a pizza is cut into four equal pieces, each slice is represented by ¼.
It should be noted that a fraction simply means a part of a whole number. It should be noted that it's usually expressed as a/b where a is the numerator and b is the denominator.
In this case, we want to add 1/10 + 11/20. This will be illustrated thus:
= 1/10 + 11/20
= 2/20 + 11/20
= 13/20
Therefore the addition is 13/20.
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