At the bicycle manufacturer, the average cost per bicycle is $77.
To find the average cost per bicycle, we need to find the total cost of making all three bicycles and divide that by the number of bicycles.
The total cost is of the bicycles is given by -
$72 (cost of first bicycle) + $83 (cost of second bicycle) + $77 (cost of third bicycle) = $232
Now to find the average cost per bicycle, we will divide the total cost by the number of bicycles.
Hence, $232 ÷ 3 = $77
Therefore, the average cost per bicycle is $77.
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Mia borrowed $5000 from her grandparents to purchase her first car. Her grandparents charge her 1.75% simple Interest. How much interest will Mia pay her grandparents after 6 years
[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$5000\\ r=rate\to 1.75\%\to \frac{1.75}{100}\dotfill &0.0175\\ t=years\dotfill &6 \end{cases} \\\\\\ I = (5000)(0.0175)(6) \implies I = 525[/tex]
what is the standard for of y= 4/9x - 3
The Standard form of y= 4/9x - 3 is 4x - 9y = 27.
What is standard form of an equation?
The general form of a linear equation, commonly referred to as the standard form, is written as Ax + By = C.
Given equation : y= 4/9x - 3
Taking LCM on both sides
we get, 9y = 4x - 27
Since the standard form of a linear equation is Ax + By = C.
So, we can write it as 4x - 9y = 27
where A= 4, B = -9 and C= 27.
Hence, the standard form of y= 4/9x - 3 is 4x - 9y = 27.
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"Graph the following lines on the sketchpad."
hi please explain how i graph this
The graph of equations y - 1 = - 3(x - 2) and y = - 3x + 7 is illustrated below with the attached image.
What is a graph?The set of ordered pairings (x, y) where f(x) = y makes up the graph of a function.
These pairs are Cartesian coordinates of points in two-dimensional space and so constitute a subset of this plane in the general case when f(x) are real values.
Given, An equation of a line y - 1 = - 3(x - 2) in point-slope form.
y - 1 = - 3x + 6.
y = - 3x + 7.
The next equation is 3y = x - 9.
y = (1/3)x - 3.
Now, The graph of these two equations can be sketched by assuming two or more arbitrary values of 'x' that correspond to different values of 'y'.
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a farmer owns three full sections, four half-sections, and two quarter-sections. how many acres is this?
The correct option is Option 1 - 3520.
A farmer owns 3520 acres in which three full sections, four half-sections, and two quarter-sections are there.
Three of a farmer's sections were full. Let's say a full section is 640, which is
=3 x 640,
= 1,920.
He had four half portions as well. Divide 640 by two to get 320 (640/2), which is
= 4 X 320
= 1,280.
He had three quarter portions as well. Divide 640 by 4 to create a quarter piece (640/4 = 160)
= 2 X 160
= 320.
Now we have to add all these,
Three full sections = 1920
Four half-sections = 1280
Two quarter-sections = 320
= 1,920 + 1,280 + 320
= 3,520.
Therefore the acres a farmer had is 3520.
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The following question may be like this:
A farmer owns three full sections, four half-sections, and two quarter-sections. How many acres is this?
3520324044404020what are the domain and range of F(x)= 2 1 (x+4) 2 −11?
rewrite x+1/6-y in the values of a,b, and c.
It's worth noting that this form is known as the standard form of a linear equation, where the variables x and y appear only in the first degree and the constant term is on the right side of the equation.
What is the Quadratic Equation?
A quadratic equation is a type of polynomial equation that has the general form of ax^2 + bx + c = 0, where x is the variable, a, b, and c are constants, and a is not equal to zero. The degree of the equation is two, hence the name "quadratic".
x+1/6-y can be rewritten in terms of a,b, and c by using the following equation:
ax + by + c = 0
To get x+1/6-y in the values of a,b, and c we can rewrite the equation as follow:
a = 1, b = -1, c = -1/6
So, x+1/6-y can be written as:
1x - 1y - 1/6 = 0
or
ax + by + c = 0 where a=1, b=-1 and c=-1/6
It's worth noting that this form is known as the standard form of a linear equation, where the variables x and y appear only in the first degree and the constant term is on the right side of the equation.
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What is the slope of the line that passes through the points (1,6) and (1, 31)? Write
your answer in simplest form.
A line passing between the points (1, 6) and (1, 31) has an undefined slope.
What is the slope?
The slope of a line is a measure of its steepness. Mathematically, the slope is calculated as "rise over run" (change in y divided by change in x).
The slope of a line can be found using the formula:
m = (y2 - y1) / (x2 - x1)
where m is the slope of the line, (x1, y1) and (x2, y2) are two points on the line.
In this case, we have (x1, y1) = (1, 6) and (x2, y2) = (1, 31). Plugging these values into the formula:
m = (31 - 6) / (1 - 1)
Hence, the denominator is zero, the slope is undefined. This means that the line is a vertical line and has no slope.
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Quadrilateral ABCD has coordinates
A(0,2) B(3,4) C(4.2) D(3,0)
Determine the coordinates of the vertices of A’B’C’D’ after a translation along vector
< 2, -3 >
The coordinates of the vertices of quadrilateral A’B’C’D’ after a translation along vector <2, -3> is: A. A' (-2, 5), B' (1, 7), C' (2, 5), D' (1, 3).
What is a translation?In Mathematics, the translation of a geometric figure to the left simply means subtracting a digit from the value on the x-coordinate of the pre-image or function.
Note: We would move in the opposite direction of the given vector <2, -3>.
By applying a translation to the pre-image of quadrilateral ABCD vertically up by 3 units and horizontally left by 2 unit, the coordinates of the image of triangle A'B'C' include the following:
(x, y) → (x - 2, y + 3)
Coordinate A = (0, 2) → Coordinate A' (0 - 2, 2 + 3) = (-2, 5)
Coordinate B = (3, 4) → Coordinate B' = (3 - 2, 4 + 3) = (1, 7)
Coordinate C = (4, 2) → Coordinate C' = (4 - 2, 2 + 3) = (2, 5)
Coordinate D = (3, 0) → Coordinate D' = (3 - 2, 0 + 3) = (1, 3)
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asap. which is 1/3 + 1/4
Find the measures of the numbered angles.
Answer: ∠1= 53°
∠3, ∠6, ∠7 are all 127°
∠4,∠5,∠8 are all 53°
Step-by-step explanation: 127° and ∠1 are supplementary angles meaning they add up to 180° You subtract 127° from 180° to get 53°.
∠3 and 127°are vertical which makes them equal and both 127°.
∠4 is vertical to ∠1 which makes them equal and both 53°.
∠5 is corresponding to ∠1 so they are equal and both 53°.
∠6 is corresponding to 127° so they are equal and both 127°.
∠7 is vertical to ∠6 so they are equal and both 127°.
∠8 is vertical to ∠5 so they are equal and both 53°.
which of the following describes the domain of the piecewise function
Answer:
(c) (-∞, -2) ∪ (-2, 1) ∪ (1, ∞)
Step-by-step explanation:
You want the domain of the given piecewise-defined function.
x < 2For x < 2, the function is ...
[tex]g(x)=\dfrac{x^2+2x}{x^2+x-2}-\dfrac{x(x+2)}{(x-1)(x+2)}=\dfrac{x}{x-1}\quad x\ne\{-2,1\}[/tex]
Both of these exclusions are in the region x < 2, so both must be excluded from the domain.
x ≥ 2The log function is defined for all values x > -2, so there are no exclusions in this region.
The domain is (-∞, -2) ∪ (-2, 1) ∪ (1, ∞).
Two boxes need to be wrapped in paper (with no overlap). Both boxes are in the shape of right rectangular prisms.
Box A measures 1.2 feet high, 0.8 feet long, and 1 foot wide. Box B measures 1.6 feet high, 0.5 feet long and 0.8 feet wide.
The wrapping paper costs $6.79 per 80 square feet.
What is the cost of wrapping both boxes?
Enter your answer in the box.
The cost of wrapping both boxes is $0.92.
What is prism?In three-dimensional space, a prism is a polyhedron where two ends are similar.
Given:
Two boxes need to be wrapped in paper (with no overlap).
Both boxes are in the shape of right rectangular prisms.
Box A measures 1.2 feet high, 0.8 feet long, and 1 foot wide.
The surface area of the rectangular prism A,
= 2(1.2 × 0.8 + 1 × 0.8 + 1 × 1.2)
= 5.92 square feet.
Box B measures 1.6 feet high, 0.5 feet long and 0.8 feet wide.
The surface area of the rectangular prism A,
= 2(1.6 × 0.5 + 0.5 × 0.8 + 0.8 × 1.6)
= 4.96 square feet.
The wrapping paper costs $6.79 per 80 square feet.
That means,
unit rate = 6.79 / 80 = $0.08 per square feet.
The cost of wrapping both boxes,
= 5.92 x 0.08 + 4.96 x 0.08
= $0.92
Therefore, the cost is $0.92.
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Solve this system of equations by graphing. First graph the equations, and then type the solution.
3x-y=-6
y=x+4
The solution is (_,_)
By finding the intercept between the graphs of the equations, we can see that the solution is (-1, 3)
How to solve the system of equations?Here we have a system of linear equations:
3x - y = -6
y = x + 4
To solve the system of equations graphically, w ejust need to graph both equations on the same coordinate axis and find the point where the lines do intercept.
The graph of the system of equations can be seen on the image at the end.
There you can see that the lines intercept at the point (-1, 3), so that is the solution of the system of equations.
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A company sells confetti in boxes in the shape of a triangular pyramid. Each box contains
240 cubic centimeters of confetti. If the height of the box is 15 centimeters, which of the
following could be the dimensions of the base?
A. Base, 8 cm; height, 4 cm
B. Base, 4 cm; height, 4 cm
C. Base, 6 cm; height, 8 cm
D. Base, 12 cm; height, 8 cm
The dimensions of the base would be: base: 12 cm ; height : 8 cm
The correct answer is an option (D)
We know that the formula for the volume of a pyramid is:
V = 1/3 × B × h
where B is the base area of the pyramid
h is the height of the pyramid
The shape of the box is a triangular pyramid.
Each box contains 240 cubic centimeters of confetti.
this means, the volume of the box is V = 240 cubic centimeters
Using above formula of the volume of a pyramid,
V = 1/3 × B × h
here V = 240 cubic centimeters and h = 15 centimeters
240 = 1/3 × B × 15
240 = B × 5
B = 240/5
B = 48 square centimeters
The dimensions of the base must be such that the area of the base would be 48 square centimeters.
Here, a pyramid has triangular base.
Using the formula for the area of triangle,
B = 1/2 × base of triangle × height of triangle
48 = 1/2 × base of triangle × height of triangle
base of triangle × height of triangle = 96
for the dimensions Base, 12 cm; height, 8 cm
12 × 8 = 96
Thus, the dimension of the base: base of triangle = 12 cm and the height of triangle = 8 cm
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PLEASE HELP ASAP
The tide at an Eastern seaport is at its maximum at 3 a. M. High tide is 24 ft deep. Low tide occurs at 9 a. M. With a depth of 4 ft. The water depths can be modeled by a sinusoidal function. Allow x=0 to represent midnight
The water depths can be modeled by a sinusoidal function. So the value of period is 18 hours, amplitude is 14.5, maximum is 24, equation of the midline is 10, and minimum is -4.
The tide at an Eastern seaport is at its maximum at 3 a.m.
High tide is 24 ft deep.
Low tide occurs at 9 a.m. with a depth of 4 ft.
We have to determine the period.
Period = time between two consecutive high tides
Period = 2 × Time between high and low tide
Time between 3 a.m. and 9 a.m. is 6 hours.
Period = 2 × 6
Period = 18 hours
We have to determine the Amplitude.
Amplitude = (High - Low)/2
Amplitude = (24 - (-5))/2
Amplitude = (24 + 5)/2
Amplitude = 29/2
Amplitude = 14.5
We have to determine the Maximum.
The maximum tide is 24.
We have to determine the Equation of the midline.
Equation of the midline = (max + min)/2
Equation of the midline = {24 + (-4)}/2
Equation of the midline = (24 - 4)/2
Equation of the midline = 20/2
Equation of the midline = 10
We have to determine the minimum.
The minimum tide is -4.
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The complete question is:
The tide at an Eastern seaport is at its maximum at 3 a.m. High tide is 24 ft deep. Low tide occurs at 9 a.m. with a depth of 4 ft. The water depths can be modeled by a sinusoidal function. Allow x=0 to represent midnight
Find the following and make sure to show work for the midline and amplitude:
period=
Amplitude=
Maximum=
Equation of the midline:
minimum:
Savannah is tiling her kitchen floor. She bought 8 cases of tile for $208. She realizes she bought too much tile and returns 2 unopened cases to the store. What was her final cost for the tile?
The final cost for the tile was $208 − $52 = $156.
An example of an algebraic equation?An algebraic equation is a statement of the equality of two expressions and is calculated by applying the algebraic operations of addition, subtraction, multiplication, division, raising to a power, and extraction of a root to a set of variables. Examples include x3 + 1 and (y4x2 + 2xy - y)/(x - 1) = 12.Consider the equation 3x + 5 = 14, in which the terms 3x + 5 and 14 are separated by the word "equal."A mathematical statement that establishes the equality of two mathematical expressions is the definition of an equation in algebra.208/8 = x/2
8x = 416
x = 416/8
x = 52
The price for the two unopened cases was $52.
Thus, The final cost for the tile was $208 − $52 = $156.
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A mass is rotated from rest at a radius of 4.0 m from the center of rotation to an angular velocity of 0.80 rad/s in 1.5 s.
a) What is the angular acceleration, α?
b) What is the tangential acceleration, a, at r = 4.0 m?
c) What is the radial (centripetal) acceleration, atang, at r = 4.0 m?
a) Angular acceleration is 0.53 rad/s^2
b) Tangential acceleration is 2.56 m/s^2
c) Centripetal acceleration is 2.56 rad/s^2
What is the angular acceleration?We know that the angular acceleration can be obtained from the equations of circular motion. We know that we have the equation for the circular motion as;
α = ω2 - ω1/t
α = angular acceleration
ω2 = final angular velocity
ω1 = initial angular velocity
α = 0.8 - 0/1.5
= 0.53 rad/s^2
b) The tangential acceleration = v^2/r
But V = ωr
V = 0.8 * 4
V = 3.2 m/s
Then;
(3.2)^2/4
= 2.56 m/s^2
c) Centripetal acceleration = ω^2 r
= (0.8)^2 * 4
= 2.56 rad/s^2
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Please answer these questions.. step-by-step
Refer to the image attached.
24÷h=6
h = 1, 3, 6, 8
Which equation is not a linear function?
Answer: B) 2x²-3y=9
Step-by-step explanation:
This is not a linear function because the equation for a linear function is mx+b=y this means that x cannot have an exponent which in B it does.
An electric pole 15 m high is supported by a wire fixing its one end on the ground at some distance from the pole. If the wire joining the top of the pole is inclined to the ground at an angle of 60°, find the length of the wire.
Step-by-step explanation:
Givenlength of the pole : 15 m
angle inclined by the wire to the pole from ground :60 deg
let the length of wire : x
therefore
sin (angle) = opposite/hypothesis
sin 60 = 15/x
√3/2 = 15/x
x= 2*15/√3
x = 30/√3
x = 17.320
the length of the wire is :17 m.
Austin must choose a number between 61 and 107 that is a multiple 4, 5 , of and 10 . Write all the numbers that he could choose. If there is more than one number, separate them with commas.
helppppppppppp
The numbers that Austin could choose from are: 80, 100 which have 4, 5, and 10 as their multiples
How to find the numbers Austin must chooseThe numbers between 61 and 107 are:
62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106
we will observe that only 70, 80, 90 and 100 have 10 and 5 as their multiple, amongst which, only 80 and 100 have 4 as their multiple.
Therefore, Austin must choose only the two numbers 80 and 100 which have 4, 5, and 10 as their multiples.
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A small business invests $10,000 in equipment to produce
a new soft drink. Each bottle of the soft drink costs $0. 65 to
produce and is sold for $1. 20. How many bottles must be
sold before the business breaks even?
The total number of 18,181 bottles should be sold to break the business even based on the investment.
Firstly calculating the profit earned on each soft drink. Based on this, the formula for profit to be used is -
Profit = Selling price - cost price
Keep the values in formula
Profit = 1.20 - 0.65
Performing subtraction on Right Hand Side of the equation
Profit = $0.55
For the business to break even, the total profit earned by company must be equal to the investment. So, let the number of bottles required to break even the business be x.
0.55 × x = 10,000
Performing multiplication on Left Hand Side of the equation
0.55x = 10000
x = 10,000/0.55
Performing division on Right Hand Side of the equation
x = 18181.8
Rounding off = 18181.
Thus, 18,181 bottles need to be sold.
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Gabriella and Ian are both driving along the same highway in two different cars to a stadium in a distant city. At noon, Gabriella is 550 miles away from the stadium and Ian is 950 miles away from the stadium. Gabriella is driving along the highway at a speed of 25 miles per hour and Ian is driving at speed of 50 miles per hour. Let � G represent Gabriella's distance, in miles, away from the stadium � t hours after noon. Let � I represent Ian's distance, in miles, away from the stadium � t hours after noon. Graph each function and determine the number hours after noon, � , t, when Gabriella and Ian are the same distance from the stadium.
Answer: Gabriella's distance from the stadium is modeled by the function G(t) = 550 - 25t.
Ian's distance from the stadium is modeled by the function I(t) = 950 - 50t.
To find the number of hours after noon when Gabriella and Ian are the same distance from the stadium, we need to set the two equations equal to each other and solve for t:
G(t) = 550 - 25t = I(t) = 950 - 50t
Combining like terms we get:
25t = 400
t = 16
So, 16 hours after noon, Gabriella and Ian will be the same distance away from the stadium.
To graph the functions, we can substitute different values of t into the equations to find the corresponding values of G(t) and I(t). Then we can plot the points on a coordinate plane and connect them to form the graph of the two functions.
It is important to note that we are assuming that both Gabriella and Ian don't make any stops, so the speed is constant through the whole trip and no time is wasted.
Step-by-step explanation:
*PLEASE HELP SOON* Use the laws of exponents to simplify each expression. Drag the tiles to the boxes to form the correct pairs.
Answer:
First one is 3^16
Second one is 3^10
Third one is 3^2 * 8^2
Forth one is 3^2/8^2
fifth one is 3^8/3^2
Step-by-step explanation:
It rained 0. 5 inches on Tuesday and 0. 2 inches on Wednesday.
It was warmer on Thursday than it was on Friday.
The humidity was 15% for 3 days of the week.
The lowest temperature overnight was 68∘F.
Which quantity is a variable?
the temperature on Friday
the lowest overnight temperature
the amount of rain on Wednesday
the number of days with humidity of 15%the number of days with humidity of 15 percent
The quantity is a variable is the lowest overnight temperature
In math the term variable is defined as variable is an alphabet which is used to represent the unknown number and this one represents the value.
Here we have know that it rained 0. 5 inches on Tuesday and 0. 2 inches on Wednesday.
And the climate was warmer on Thursday than it was on Friday.
Where the humidity was 15% for 3 days of the week and thus the lowest temperature overnight was 68∘F.
Here we have identified that the temperature is continually falling and it will lead the lowest temperature overnight.
Then the correct option is (c).
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Brody was comparing the price of pineapple juice at two stores. The equation y=0.7x represents what Brody would pay in dollars and cents, y for x bottles of pineapple juice at store A. The table below represents what Brody would pay in dollars and cents, y, for x bottles of pineapple juice at store B.
At store B, they charge $0.09 more for pineapple juice than store A.
What is the equation of a line?The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.
Given that, Brody was comparing the price of pineapple juice at two stores.
Equation to represent the cost of pineapple juice at store A is
y=0.7x
Equation to represent the cost of pineapple juice at store B is
From the table, we have (9, 7.11) and (13, 10.27)
Now, slope m= (10.27-7.11)/(13-9)
= 3.16/4
= 0.79
Substitute m=0.79 and (x, y)=(9, 7.11) in y=mx+c, we get
7.11=0.79(9)+c
7.11=7.11+c
c=0
So, the equation is y=0.79x
Cost of 1 bottle juice at store A is $0.7 and Cost of 1 bottle juice at store B is $0.79
Difference in cost =0.79-0.7=$0.09
Therefore, at store B, they charge $0.09 more for pineapple juice than store A.
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2434base6 divided by 42 base 6
The answer for the given senary expressions is 35₆.
What are senary numbers?
A senary numeral system (also known as base-6, heximal, or seximal) has six as its base. It has been adopted independently by a small number of cultures. Like decimal, it is a semiprime, though it is unique as the product of the only two consecutive numbers that are both prime (2 and 3). As six is a superior highly composite number, many of the arguments made in favor of the duodecimal system also apply to senary.
Now,
To find 2434₆/42₆
2434\(_6\) to base 10
2 \(\times\) 6\(^3\) + 4 \(\times\) 6\(^2\) + 3 \(\times\) 6\(^1\) + 4 \(\times\) 6\(^0\)
2 \(\times\) 216 + 4 \(\times\) 36 + 3 \(\times\) 6 + 4 \(\times\) 1
432 + 144 + 18 + 4 = 598
And: 42\(_6\) to base 10
4 \(\times\) 6\(^1\) + 2 \(\times\) 6\(^0\)
4 \(\times\) 6 + 2 \(\times\) 1
24 + 2 = 26
Then divide 598 by 26
= 23
Then convert 23\(_{10}\) to base 6
i.e. 35₆
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PLEASE IM BEGGING YOU HELP ME
A company manufactures a special type of sensor, and packs them in boxes of 4 for shipment. Then a new design increases the weight of each sensor by 9 grams. The new package of 4 sensors weighs 76 grams how much did each sensor weigh originally?
Which equation best models the situation here?
4x + 9 = 76
4(x+9) = 76
4(9x) = 76
If the new design increases the weight of each sensor by 9 grams. The new package of 4 sensors weighs 76 grams , then the equation best models the situation here is (b) 4(x+9) = 76 .
the number of sensor in the boxes is = 4 ;
let the weight of each of sensors be = x ;
So , in new design the weight of each sensor is increased by 9 grams ,
the new weight of sensor becomes = x + 9 ;
the new weight of 4 sensors will be = 4(x + 9) ;
the total weight of new package is = 76 grams ;
So , the equation representing the situation is (b) 4(x+9) = 76 .
The given question is incomplete , the complete question is
A company manufactures a special type of sensor, and packs them in boxes of 4 for shipment. Then a new design increases the weight of each sensor by 9 grams. The new package of 4 sensors weighs 76 grams how much did each sensor weigh originally ?
Which equation best models the situation here ?
(a) 4x + 9 = 76
(b) 4(x+9) = 76
(c) 4(9x) = 76
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WILL GIVE BRAINLIEST AND 30 POINTS IF SOMEONE HELPS
urrrrrrrrrrrrrrrf mooookoommm