Equation that represents the total number of miles he runs after weeks is n * (n + 2).
The equation that represents the total number of miles Tripp runs after "n" weeks can be written as:
Total miles = 3 + 5 + 7 + ... + (2n + 1)
We can see that the first week Tripp runs 3 miles, and every week after that, he adds 2 more miles to the previous week's total. So, for the second week, he runs 3 + 2 = 5 miles, and for the third week, he runs 5 + 2 = 7 miles, and so on.
To simplify the equation, we can use the formula for the sum of an arithmetic series:
S = (n/2) * (a + l)
where S is the sum of the series, n is the number of terms in the series, a is the first term, and l is the last term.
In this case, the first term is 3, and the last term is (2n + 1), since Tripp is adding 2 miles each week. So, we have:
Total miles = (n/2) * (3 + 2n + 1)
Simplifying this equation, we get:
Total miles = (n/2) * (2n + 4)
Total miles = n * (n + 2)
Therefore, the equation that represents the total number of miles Tripp runs after "n" weeks is:
Total miles = n * (n + 2)
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A group of students is collecting 16 oz and 28 oz jars of peanut butter to donate to a food bank. At the end of the collection period, they donated 1,876 oz of peanut butter and a total of 82 jars of peanut butter to gre food bank.
a. Write a system of equations that represents the constraints in this situation. Be sure to specify the variables that you use.
b. How many 16 oz jars and how many 28 oz jars of peanut butter were donated to the food bank? Explain or show how you know.
35 16 oz jars and 47 28 oz jars of peanut butter were donated to the food bank by solving equation
Let x be the number of 16 oz jars of peanut butter collected, and y be the number of 28 oz jars of peanut butter collected.
The system of equations that represents the constraints in this situation is:
x + y = 82 (total number of jars collected)
16x + 28y = 1876 (total amount of peanut butter collected in ounces)
b. To solve for the number of 16 oz jars and 28 oz jars of peanut butter donated to the food bank
we need to solve the system of equations from part (a). One way to do this is to use elimination:
Multiplying the first equation by 16, we get:
16x + 16y = 1312
Subtracting this equation from the second equation, we get:
12y = 564
Dividing both sides by 12, we get:
y = 47
Substituting this value of y into the first equation, we get:
x + 47 = 82
Subtracting 47 from both sides, we get:
x = 35
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4. Chelsea determined that the value of x in the triangle at the right was 5.
a. Find the value of each angle by substituting 5 for x.
b. Was Chelsea's solution, x = 5, correct? How do you know?
15x
x
11x
(8x+5)
Z
a.) The value of each angle when 5 is substituted for X would be ;
Y = 55°
Y = 55°W = 75°
Y = 55°W = 75°Z = 45°
b). Chelsea is wrong in her calculation because the total internal angle of a triangle should be 180° and not 175°.
How to calculate the value of the various angles through substitution?For angle Y;
11x = 11(5) = 55°
For angle W;
15x = 15(5) = 75°
For angle Z;
(8x+5) = 8(5) +5
= 45°
The total angles = 55+75+45 = 175°
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Find y.
I will give Brainliest to correct answer !
Since the graph was obtained by transforming the graph of the square root function, an equation for the function the graph represent is: [tex]g(x) = -\sqrt{9(x - 1)} + 2[/tex]
What is a square root function?In Mathematics and Geometry, a square root function is a type of function that typically has this form f(x) = √x, which basically represent the parent square root function i.e f(x) = √x.
In Mathematics and Geometry, a horizontal translation to the right is modeled by this mathematical equation g(x) = f(x - N) while a vertical translation to the positive y-direction (upward) is modeled by this mathematical equation g(x) = f(x) + N.
Where:
N represents an integer.g(x) and f(x) represent functions.In this context, the required square root function can be obtained by applying a set of transformations to the parent square root function as follows;
f(x) = √x
g(x) = -√9(x - 1) + 2
[tex]g(x) = -\sqrt{9(x - 1)} + 2[/tex]
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Which set of ordered pairs represents a function?
O {(-5, -9), (-7,-9), (-5, -7), (-8,6)}
O {(-1,6), (0, -3), (5, -9), (-1,3)}
O {(1, 2), (-6, 2), (3,9), (5,3)}
O {(-3,9), (2, 7), (2, -4), (1,5)}
The set of ordered pairs which represents a function among the given answer choices is; {(1, 2), (-6, 2), (3,9), (5,3)}.
Which of.the answer choices represents a function?By definition, a function is a special kind of relation in which case, each input value is assigned not more than one output value.
On this note, by evaluation of the given sets of ordered pairs; the set {(1, 2), (-6, 2), (3,9), (5,3)} represents the relation which is a function.
Ultimately, the answer choice which represents a set of ordered pairs that represents a function is; {(1, 2), (-6, 2), (3,9), (5,3)}.
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Which is the same length as 65 km
Answer:
65000 metres
Step-by-step explanation:
65*1000=65000
(2a³) (3a4) simplify no negative exponents
6a7
Step-by-step explanation:
To simplify the expression (2a³) (3a4), you can use the laws of exponents. First, you can multiply the coefficients 2 and 3 to get 6. Then, you can add the exponents of 'a' which gives you a total of 3+4=7. Therefore, the simplified expression is 6a7. It does not have any negative exponents, and it represents the product of two expressions with the same base 'a' and coefficient multiplication.
Answer: 6a7
Step-by-step explanation: Got this right b4.
HURRY DUE TONIGHT
Danielle was completing her science project and mixed saline solutions A and B. Brand A was a six gallon 18% saline solution and she ended up with an 18 gallon 8% saline solution mixture. Find the percent of saline solution in brand B.
A. 21%
B. 3%
The percentage of saline solution in brand B is 3%.
Let x be Percentage of saline solution in brand B
We know that the overall volume of saline solution in the combination is 18% of 6 gallons plus x% of (18 - 6) gallons since Danielle blended brands A and B to make a total of 18 gallons of 8% saline solution.
Then the equation is given as,
0.18(6) + 0.01x(18 - 6) = 0.08(18)
Simplifying and solving for x, we get:
1.08 + 0.12x = 1.44
0.12x = 0.36
x = 3
Therefore, the percentage of saline solution in brand B is 3%.
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Direct Materials Purchases Budget Anticipated sales for Solid Grip Company were 66,000 passenger car tires and 20,000 truck tires. Rubber and steel belts are used in producing passenger car and truck tires as follows: Passenger Car Truck Rubber 33 lb. per unit 77 lb. per unit Steel belts 5 lb. per unit 13 lb. per unit The purchase prices of rubber and steel are $2.90 and $3.80 per pound, respectively. The desired ending inventories of rubber and steel belts are 62,000 and 13,000 pounds, respectively. The estimated beginning inventories for rubber and steel belts are 73,000 and 11,000 pounds, respectively. Prepare a direct materials purchases budget for Solid Grip Company for the year ended December 31, 20Y8. When required, enter unit prices to the nearest cent.
Direct Materials Purchases Budget is given by,
Rubber Steel
Expected production 3,718,000 lb. 590,000 lb.
Desired ending inventory 62,000 lb. 13,000 lb.
Total required 3,780,000 lb. 603,000 lb.
Less: Beginning inventory (73,000 lb.) (11,000 lb.)
Total to be purchased 3,707,000 lb. 592,000 lb.
Unit price $2.90/lb. $3.80/lb.
Total cost $10,749,300 $2,249,600
To prepare a direct materials purchases budget for Solid Grip Company,
The amount of rubber and steel belts needed for the production of 66,000 passenger car tires and 20,000 truck tires.
The desired ending inventories and estimated beginning inventories for each material.
First, let us calculate the amount of rubber and steel belts required for the production of passenger car and truck tires.
Passenger car tires,
Rubber,
66,000 tires x 33 lb. per unit = 2,178,000 lb.
Steel belts,
66,000 tires x 5 lb. per unit = 330,000 lb.
Truck tires,
Rubber,
20,000 tires x 77 lb. per unit = 1,540,000 lb.
Steel belts,
20,000 tires x 13 lb. per unit = 260,000 lb.
Next, let us calculate the total amount of rubber and steel belts needed for production.
Rubber,
2,178,000 lb. + 1,540,000 lb. = 3,718,000 lb.
Steel belts,
330,000 lb. + 260,000 lb. = 590,000 lb.
To calculate the total amount of rubber and steel belts required for purchase,
Add the desired ending inventories and subtract the estimated beginning inventories,
Rubber,
3,718,000 lb. + 62,000 lb. - 73,000 lb. = 3,707,000 lb.
Steel belts,
590,000 lb. + 13,000 lb. - 11,000 lb. = 592,000 lb.
Finally, calculate the total cost of rubber and steel belt purchases.
Rubber,
3,707,000 lb. x $2.90 per pound = $10,749,300
Steel belts,
592,000 lb. x $3.80 per pound = $2,249,600
Therefore, the direct materials purchases budget for Solid Grip Company for the year ended December 31, 20Y8 is as follows,
Direct Materials Purchases Budget
Rubber Steel
Expected production 3,718,000 lb. 590,000 lb.
Desired ending inventory 62,000 lb. 13,000 lb.
Total required 3,780,000 lb. 603,000 lb.
Less: Beginning inventory (73,000 lb.) (11,000 lb.)
Total to be purchased 3,707,000 lb. 592,000 lb.
Unit price $2.90/lb. $3.80/lb.
Total cost $10,749,300 $2,249,600
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Can someone help me put these in order please!
The order of steps of constructing an inscribed circle of a triangle:
Construct one of the angle bisectors of the triangle. Make sure that it intersects the side opposite of the angle.Construct another angle bisector of the triangle for a different angle. Make sure that it intersects the side opposite of the angle.Identify the point of intersection of the two angle bisectors. This is the incenter and is also the center of the inscribed circle.Construct a circle that has a radius of the length from the incenter to one of the points where an angle bisector intersects a side of the triangle.How to construct the circle ?Commence the process by sketching a line that cuts one angle of the triangle in two and intersects the opposing side at some point. Through this action, a pair of miniature triangles with congruent figures materialize.
Subsequently, draft an additional bisector for another angle of the triangle. The second dividing line needs to meet the side opposite to the situated angle at a specific location.
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The current mean weekly wage in a certain industry is 2,117. if the mean weekly wage increases by 4.75% what is the new mean average
The new mean annual wage is; $ 43,149.82.
Given that the initial mean weekly wage is $ 2.117.
The growth rate is 4.75%.
We need to find a new annual wage.
Consider the equation, A be the new annual wage.
Here R is the growth rate and P is the initial mean weekly wage and T is the number of weeks in a year.
The number of weeks in a year = 52 weeks.
Substitute P= 2,117, R =4.75% = 0.0475and T =52 in the equation.
A = 2.117 x 52(1 + 0.0475)
A = 43,149.82
The new mean annual wage is; $ 43,149.82.
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what radian measure is equivalent to 300
The equivalent radian to 300 degree is 5π/3.
The given angle measures 300 degree.
We know that, formula used to convert degrees is Radians = Degrees × π / 180
Here, Radians = 300×π/180
= 30 ×π/18
= 10π/6
= 5π/3
Therefore, the equivalent radian to 300 degree is 5π/3.
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Convert 7oz to ____ L.
what is the relationship between the area of a rectangle and a parallelogram
Answer: The relationship between the area of rectangle and area of parallelogram is that they both are equal in area.
Step-by-step explanation:
parallelogram is formed when two parallel lines intersects other two parallel lines and rectangle is a type of parallelogram in which the intersecting lines intersects at right angle.
rectangle and parallelogram shares the same property and If we consider same base and same parallel lines then the area of parallelograms formed is always equal and as I mentioned above rectangle is also a parallelogram.
hence area of rectangle is equal to the area of parallelogram in same base and same parallel lines.
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what base could be written in the blank to make the exponential function model 15% decay ? y= (____) ^t\12 what answer would I put in the blank?
The exponential function model is y = (0.85[tex])^{t/12[/tex].
We know, The form of the function should be
y= a bˣ
Where, A should be the initial amount and b decrease rate.
Now, y = [tex]b^{t/12}[/tex]
So, the value of base be
= (100 - 15) / 100
= 0.85
Then, the function should be y = (0.85[tex])^{t/12[/tex]
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Evaluate the following expression:
\left( \frac{16}{9} \right)^{2/3} \cdot \left( \frac{4}{3} \right)^{4/3} \cdot \left( \frac{9}{16} \right)^{2/3} \cdot \left( \frac{3}{4} \right)^{4/3}
We raise the fraction to the power of 4/3.
To evaluate the expression:
\left( \frac{16}{9} \right)^{2/3} \cdot \left( \frac{4}{3} \right)^{4/3} \cdot \left( \frac{9}{16} \right)^{2/3} \cdot \left( \frac{3}{4} \right)^{4/3},
we can simplify each term within the parentheses before multiplying them together.
Let's simplify each term step by step:
\left( \frac{16}{9} \right)^{2/3}:
To simplify this term, we raise the fraction to the power of 2/3.
\left( \frac{16}{9} \right)^{2/3} = \left( \left( \frac{2^4}{3^2} \right)^{1/3} \right)^2 = \left( \frac{2^{4 \cdot 1}}{3^{2 \cdot 1}} \right)^2 = \left( \frac{2^4}{3^2} \right)^2 = \left( \frac{16}{9} \right)^2 = \frac{16^2}{9^2} = \frac{256}{81}
\left( \frac{4}{3} \right)^{4/3}:
Similarly, we raise the fraction to the power of 4/3.
\left( \frac{4}{3} \right)^{4/3} = \left( \left( \frac{2^2}{3^1} \right)^{1/3} \right)^4 = \left( \frac{2^{2 \cdot 1}}{3^{1 \cdot 1}} \right)^4 = \left( \frac{2^2}{3^1} \right)^4 = \left( \frac{4}{3} \right)^4 = \frac{4^4}{3^4} = \frac{256}{81}
\left( \frac{9}{16} \right)^{2/3}:
We raise the fraction to the power of 2/3.
\left( \frac{9}{16} \right)^{2/3} = \left( \left( \frac{3^2}{2^4} \right)^{1/3} \right)^2 = \left( \frac{3^{2 \cdot 1}}{2^{4 \cdot 1}} \right)^2 = \left( \frac{3^2}{2^4} \right)^2 = \left( \frac{9}{16} \right)^2 = \frac{9^2}{16^2} = \frac{81}{256}
\left( \frac{3}{4} \right)^{4/3}:
We raise the fraction to the power of 4/3.
\left( \frac{3}{4} \right)^{4/3} = \left( \left( \frac{3^1}{2^2} \right)^{1/3} \right)^4 = \left( \frac{3^{1 \cdot 1}}{2^{2 \cdot 1}} \right)^4 = \left( \frac{3^1}{2^2} \right)^4 = \left( \frac{3}{4} \right)^4 = \frac{3^4}{4^4} = \frac{81}{256
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What is the area of this figure?
Answer:
142ft^2
Step-by-step explanation:
I hope this picture helps, but if you have any questions about the steps let me know
Please help
A line with a slope of 1/5 passes through the point (-4,-3). What is its equation in point slope form?
A line that includes the point (1,3) has a slope of nine. What is its equation in point slope form?
A line with a slope of -10 passes through the point (-4,-1) what is this equation in point slope form?
There is a line that includes the point (9,3) and has a slope of -1/6 what is its equation in point slope form?
A line passes through the points (1,2) and (2,10). What is its equation in point slope form?
When answering all these questions, you specific points in the equation
31. There are two gears that are connected to each other. One gear has 20 teeth and the other gear has 10 teeth. If the bigger gear turns around 5 times, how many times will the smaller gear turn?
10 times will the smaller gear turn.
What is the ratio?
The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.
Since the smaller gear has 10 teeth and the bigger gear 20, the smaller gear will turn twice for every rotation of the larger gear (20/10=2).
Therefore, if the larger gear rotates five times, the smaller gear will rotate two times five times, or ten times. The smaller gear will thus rotate 10 times.
So, if the bigger gear turns around 5 times, the smaller gear will turn around 5 x 2 = 10 times.
Therefore, the smaller gear will turn 10 times.
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PLS HELP ASAP!!!!!!!!!
Answer: 4m^5-3m^2+2m+21
Step-by-step explanation: you just have to put the exponents int he right order which we always put the highest first so you put 4m^5-3m^2+2m+21 which is the answer
What is the value of y in the formula shown when x = 4/5?
y = 4/x
+ √x + 0.2 - 5x
y =
(please look at photo)
Answer:
y = 2
Step-by-step explanation:
substitute x = [tex]\frac{4}{5}[/tex] ( = 0.8) into the formula
y = [tex]\frac{4}{0.8}[/tex] + [tex]\sqrt{0.8+0.2}[/tex] - 5(0.8)
= 5 + [tex]\sqrt{1}[/tex] - 4
= 5 + 1 - 4
= 6 - 4
= 2
A.solves routine and non-routine problems involving perceentage using appropriate strategies and tools.M5NS-IIIIb-40
Observe the solution to the given problem below.
christmas season is coming and ana is so excited to do her shopping in her list is a pair of shoes that she will wear for their christmas party.what made her more excited was when she saw that her dream pair of shoes is on sale.
from P 4 295, it is now sold with 20%
The sale price of the shoe is given as follows:
P3,436.
How to obtain the sale price of the shoe?The sale price of the shoe is obtained applying the proportions in the context of the problem.
The initial price is of:
P 4,295.
The shoe is sold at a discount of 20%, meaning that the sale price is 80% of the initial price, and the value is given as follows:
0.8 x 4295 = P3,436.
Missing InformationThe problem asks for the selling price of the shoe.
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finding the inverse of [tex]-(1/2)-log_{3}\sqrt{9-x}[/tex]
The inverse function of the function f(x) is [tex]g(y) = 9 - 3^-^(^y^ + ^1^/^2^)[/tex]
To find the inverse of the given function f(x) = -(1/2) - log₃√(9-x)
we need to solve for x in terms of y, where y = f(x).
Replace f(x) with y
Function y = -(1/2) - log₃√(9-x)
Solve for x
First, isolate the logarithmic term on one side of the equation.
y + (1/2) = -log₃√(9-x)
[tex]3^-^(^y^ +^ 1^/^2^) = 9-x[/tex]
[tex]x = 9 - 3^-^(^y^ + ^1^/^2^)[/tex]
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1.2 grams is how many grains
What are the polar coordinates of the point A shown below?
A point plotted on a polar coordinate plane.
Select the correct answer below:
(−2,3π4)
(1,−π4)
(1,−7π4)
(2,−π4)
(−2,π4)
(1,3π4)
Answer:(1,−7π/4)
Step-by-step explanation:
Note that the point is on the circle whose radius is labeled 1, so r=1 or −1. Of the choices available, only an angle of −7π4, drawn from the positive x axis plots at the point A. So θ=−7π4, and r must be positive, as the angle is measured from the positive x axis. Thus, the polar coordinates are (1,−7π4).
Type the correct answer in the box. Round off your answer to the nearest integer.
Two planes, A and B, start from the same place and move in different directions, making an angle of 50° between them. The speed of plane A is
200 miles per hour, and the speed of plane B is 300 miles per hour.
The two planes are
miles apart after one hour.
HELP PPPSKSKFJSJSJSJSJSHDHDDH
Answer:D
Step-by-step explanation:
got it right
Anyone else have this question figured out
The equation of line is,
⇒ y = 1/2x + 2
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
Two points on the line are (- 4, 0) and (0, 2).
Now,
Since, The equation of line passes through the points (- 4, 0) and (0, 2).
So, We need to find the slope of the line.
Hence, Slope of the line is,
m = (y₂ - y₁) / (x₂ - x₁)
m = (2 - 0) / (0 + 4)
m = 2 / 4
m = 1/2
Thus, The equation of line with slope 1/2 is,
⇒ y - 0 = 1/2 (x + 4)
⇒ y = 1/2x + 2
Therefore, The equation of line is,
⇒ y = 1/2x + 2
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Gordon runs for 28 minutes on Monday and 43 minutes on Wednesday. Write and solve an equation to find how many more minutes Gordon ran on Wednesday
Compared to Monday, Gordon ran for an additional 15 minutes on Wednesday.
Let x be the number of additional minutes Gordon ran on Wednesday compared to Monday. Then, we can write an equation based on the given information:
43 minutes (Wednesday) = 28 minutes (Monday) + x minutes (additional time on Wednesday)
To solve for x, we can isolate it on one side of the equation:
43 minutes - 28 minutes = x minutes
15 minutes = x
Therefore, Gordon ran 15 more minutes on Wednesday compared to Monday.
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Solve 19 × 6 using distributive law.
The solution to the given expression by using distributive law is 114
What is distributive law?The distributive property posits that an expression that is provided in the form of A (B + C) can be further expressed as A × (B + C) = AB + AC. This distributive law is also useful for subtraction and is expressed as, A (B - C) = AB - AC. This implies that operand A is distributed between the other two operands.
From the given information, we are to expand 19 × 6 using the distributive law. The first step would be to expand 19 into two integers.
Let the two integers be 10 and 9.
So, we can have can express this by using the addition distributive law: A(B+ C)
Mathematically, we have:
= 6(10 + 9)
= 6(19)
= 114
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Robert had 2 2/5 cups of chocolate syrup left in his freezer he used 1/4 cup of Chocolate syrup when he makes a milkshake what is the maximum number of milkshakes that Robert can make with the chocolate syrup
Robert can make a maximum of 8 milkshakes with the remaining chocolate syrup.
How to find the maximum number of milkshakes that Robert can make with the chocolate syrupConverting the mixed number 2 2/5 to an improper fraction: 2 2/5 = 12/5
Subtracting the amount of chocolate syrup used per milkshake from the total amount of chocolate syrup:
12/5 - 1/4 = (48 - 5) / 20 = 43/20
Therefore, Robert has 43/20 cups of chocolate syrup left, which is the maximum amount he can use to make milkshakes.
For maximum number of milkshakes:
(43/20) / (1/4) = (43/20) x (4/1) = 172/20 = 8.6
Since Robert cannot make a fraction of a milkshake, he can make a maximum of 8 milkshakes with the remaining chocolate syrup.
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