The width of the rectangular garden is 40feet. The equation that represents the garden's perimeter is 2(60 + w) = 200.
A rectangular garden has a length of 60 feet (ft)
a width of w ft
and a perimeter of 200 ft.
The formula of perimeter of a rectangle is 2(lenght + width)
The equation that represents the garden's perimeter is 2(60 + w) = 200
2(60 + w) = 200
120 + 2w = 200
2w = 200 - 120
2w = 80
w = 40
Therefore, width of the rectangular garden is 40feet. The equation that represents the garden's perimeter is 2(60 + w) = 200
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A bicycle company has designed and built a new model of sports bicycle. They have determined that the profit for the sale of the bicycles can be modeled by the function ��(��) =− 2�� , where x is the price of each bicycle. Which of the 2+ 920�� + 84, 000 following is a sale price for the bicycles that will allow the company to achieve a profit of $189,800?
A. $210
B. $230
C. $250
D. $270
A sale price for the bicycles that would allow this company to achieve a profit of $189,800 is: B. $230.
How to determine the sale price for the bicycles?In order to determine the sale price for the bicycles that would make it possible for this company to achieve a profit of $189,800, we would simply evaluate the profit function by substituting the value of the profit as follows:
P(x) = −2x² + 920x + 84,000
189,800 = −2x² + 920x + 84,000
Re-arranging the profit function by collecting like terms, we have:
2x² + 920x + 189,800 - 84, 000 = 0
2x² - 920x + 105,800 = 0
Dividing both sides by 2, we have:
x² - 460x + 52,900 = 0
Next, we would solve the quadratic equation by using factorization method:
x² - 230x -230x + 52,900 = 0
x(x - 230) + 230(x - 230) = 0
(x - 230)(x + 230) = 0
x = 230 or -230
Since the price cannot be negative, the required sale price for this company is equal to $230.
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Complete Question:
A bicycle company has designed and built a new model of sports bicycle. They have determined that the profit for the sale of the bicycles can be modeled by the function P(x) = −2x² + 920x + 84,000, where x is the price of each bicycle. Which of the following is a sale price for the bicycles that will allow the company to achieve a profit of $189,800?
A. $210
B. $230
C. $250
D. $270
What are the lengths of the major and minor axes of the ellipse?
(x−3)212+(y+4)224=1
Drag a value to the boxes to correctly complete the table.
The lengths of the major and minor axis of the ellipse, [tex] \displaystyle{ \frac{ {(x - 3)}^{2} }{12} +\frac{ {(y + 4)}^{2} }{24} = 1}[/tex] are;
Length of major axis; 4•√6Length of minor axis; 4•√3What is an ellipse in coordinate geometry?An ellipse describes the locus of a point on a curve, such that the sum of the distance from two focal points from the points on the curve is a constant.
The given given function of the ellipse can be presented as follows;
[tex] \displaystyle{ \frac{ {(x - 3)}^{2} }{12} +\frac{ {(y + 4)}^{2} }{24} = 1}[/tex]
The above equation can be compared to the standard equation of an ellipse as follows;
[tex] \displaystyle{ \frac{ {(x - h)}^{2} }{ {b}^{2} } +\frac{ {(y - k)}^{2} }{ {a}^{2} } = 1}[/tex]
Where;
(h, k) = The coordinates of the center of the ellipse
a = The length of the semi major axis
b = The length of the semi minor axis
By comparison, we have;
(h, k) = (3, -4)
a = √(24) = 2•√6
b = √(12) = 2•√3
The length of the major axis = 2•a
The length of the minor axis = 2•b
The length of the major axis is therefore;
2•a = 2 × 2•√6 = 4•√6
The length of the minor axis is therefore;
2•b = 2 × 2•√3 = 4•√3
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Which one of these expressions doesn’t have a value less than 1 please help thank you if u do
Option D which is [tex](3^{5} )^{2}/3^{4}[/tex] doesn’t have a value less than 1 .
What are exponential power?A number's exponent demonstrates how many times we are multiplying a given number by itself. 34, for instance, indicates that we are multiplying 3 by four. 3333 is its expanded form. The power of an integer is another term for an exponent. A whole number, fraction, negative number, or decimal are all acceptable. How frequently a number is multiplied by itself is indicated by its exponent. As 2 is multiplied by itself 4 times, 2222 might be expressed as 24, for instance. The "base" in this case is 2 and the "exponent" or "power" is 4. The general definition of xn is "x multiplied by itself n times."
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2 ÷ 125.1
Round the answer to 3 decimals
pls help!!
6cm, 5cm, 9cm
How do you find average speed from aHow do you find average speed from a distance time graph?\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ distance time graph?
An average speed can be calculated from a distance time graph through the division is change in distance and change in its corresponding time.
What is distance time graph?A distance time graph is a type of graph that show the distance covered by an object with respect to time.
When plotting a distance time graph, the distance is plotted in the y-axis while time is plotted of the X -axis and a suitable scale of used to fill in the observed figures.
Speed is the product of distance travelled by an object with respect to its time. Therefore, an average speed can be calculated through the division is change in distance and change in its corresponding time.
That is ; average speed= ∆speed/∆ time
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What is the area of the triangle?
If mDH =(11x + 7) degrees , mGF = (5x + 9) degrees , and mEF = (10x - 22) degrees, find mDH
For this problem we use the arcs and chords theorem we know that
[tex]\begin{gathered} \measuredangle H\text{EF=}\frac{1}{2}(mGF+mDH) \\ \text{Substituting }\measuredangle HEF=10x-22,\text{ mGF=5x+9 and mDH=11x+7 we get} \\ 10x-22=\frac{1}{2}(5x+9+11x+7) \end{gathered}[/tex]Solving for x we get:
[tex]\begin{gathered} 10x-22=\frac{1}{2}(16x+16)=8x+8 \\ 2x=30 \\ x=15 \end{gathered}[/tex]Finally, we substitute x for mDH=(11x+7) degrees=(11*15+7) degrees=172 degrees.
mDH=172 degrees.
what is the median of this data set?[13,13,13,15,15,16,16,17,17]
Given the following data set:
[13,13,13,15,15,16,16,17,17]
Let's determine the median.
Step 1: Arrange the data points from smallest to largest.
The set is already arranged in ascending order.
[13,13,13,15,15,16,16,17,17]
Step 2:
a.) If the number of data points is odd, the median is the middle data point in the list.
b.) If the number of data points is even, the median is the average of the two middle data points in the list.
There are 9 data in the set, it is odd. The middle data is the 5th data.
[13,13,13,15,15,16,16,17,17]
The 5th data is 15.
Therefore, the median of the given set of data is 15.
Mrs. brown is putting different colored sand into cups for 4 daughters to make sand art bottles . pink is 3/4 and purple is 1/2. each color is divided equally among the daughters how much more pink sand will be available than purple sand for each girl
Using mathematical operations, we can say that the extra pink sand avaliable to each girl is 1/16.
What are mathematical operations?A function in mathematics known as an operation is one that transforms zero or more input values into a clearly defined output value. The operation's complexity is determined by its operand count. The rules that specify the order in which we should perform several operations to solve an expression are known as the order of operations. Parentheses, Exponents, Multiplication, Division (from left to right), Addition, and Subtraction are in the following order: PEMDAS (from left to right).So, more pink sand is available to each girl:
Pink sand is 3/4 and purple sand is 1/2.Sand available to each girl:
Pink: 3/4 ÷ 4 ⇒ 3/4 × 1/4 ⇒ 3/16Purple: 1/2 ÷ 4 ⇒ 1/2 × 1/4 ⇒ 1/8Pink sand more to each girl:
3/16 - 1/83 - 2/161/16Therefore, using mathematical operations, we can say that the extra pink sand avaliable to each girl is 1/16.
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What is the absolute value of -6? Use the number line to help answer the question.
-6
07
6543210
st
4+
3+
2+
7777777
Answer:
your answer is in the screenshot
Step-by-step explanation:
Determine the relative frequency for the third class as a simplified fraction
GIVEN:
We are given a frequency distribution table showing different classes of hours of study and the frequency of each class of data.
Required;
To determine the relative frequency for the third class
Step-by-step solution;
For a relative frequyency, we need to find the number of times an event occurs and express it as a fraction of the total events that occured in the survey/experiment.
The events in this case are hours of study and the occurrence is the total frequency for all classes of hours of study.
The total frequency is;
[tex]3+10+6+15+6=40[/tex]The relative frequency for the third class therefore would be;
[tex]\begin{gathered} Relative\text{ }Frequency_3=\frac{6}{40} \\ \\ Relative\text{ }Frequency=\frac{3}{20} \end{gathered}[/tex]ANSWER:
The relative frequency of the third class therefore is
[tex]\frac{3}{20}[/tex]How many vertices does a triangle prima have?
A triangle prima has six vertices. A triangular prism has five faces, three rectangular and two triangular, nine vertices, and six edges.
What is triangle?A triangle is a three-edged polygon with three vertices. It is a fundamental shape in geometry. Triangle ABC denotes a triangle with vertices A, B, and C. In Euclidean geometry, any three non-collinear points determine a unique triangle and, by stretching, a unique aircraft. Triangles are three-sided polygons with three vertices. The angles of the triangle are formed by connecting the three sides end to end at a point. The sum of the triangle's three angles equals 180 degrees. You've seen that a triangle is a simple closed curve made up of three line segments. It is made up of three vertices, three sides, and three angles.To learn more about triangle, refer to:
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Graphs present information to the reader
True
False
Answer:True
Step-by-step explanation:Graphs show information about information about the topic you are reading\researching so true they show you a lot of info on the topic.
Answer:True
Step-by-step explanation:Graphs show information about information about the topic you are reading\researching so true they show you a lot of info on the topic.
B. Write S if the expression is a sum of two cubes, D if a difference of two cubes, and N if neither.
1. 27x⁶ + y³=
2. 81 - b¹⁵=
3. 64x³ - 9z⁹=
4. 36m¹² - n⁶
5. 1 - d¹²=
6. 729 - y²⁹=
7. 343 - y⁶=
8. 4x³ + 8 =
9. 144 -125y² =
10. 64j⁶- k⁹=
Answers:
SNNNDNDNND==========================================================
Explanation:
Question 1
27x^6 = (3x^2)^3 which is one cube and y^3 is another cube
Therefore 27x^6+y^3 is a sum of two cubes.
It might help to think of it like A^3+B^3 where in this case A = 3x^2 and B = y.
----------------------------------------
Question 2
81 isn't a perfect cube since 81^(1/3) = 4.3267 approximately, which isn't a whole number. We need 81^(1/3) to be a whole number if we wanted 81 to be a perfect cube.
We don't even need to check b^15 since 81 being a non-perfect cube means the entire expression cannot be a sum of two cubes, nor a difference of cubes.
----------------------------------------
Question 3
64x^3 = (4x)^3 is a perfect cube
but 9z^9 is not a perfect cube
We can see this if we computed 9^(1/3) and the result is a non-whole number.
The answer here is the same as the previous question.
----------------------------------------
Question 4
36^(1/3) is not a whole number, so 36 isn't a perfect cube. By extension 36m^12 isn't a perfect cube either. The answer is the same as questions 2 and 3.
----------------------------------------
Question 5
1 is a perfect cube since 1 = 1^3
d^12 is a perfect cube because d^12 = (d^4)^3
Therefore, we have a difference of two cubes.
----------------------------------------
Question 6
729^(1/3) = 9 which rearranges to 9^3 = 729, showing 729 is a perfect cube.
However y^29 is not a perfect cube since the exponent 29 is not a multiple of 3.
The overall expression is "neither".
----------------------------------------
Question 7
343^(1/3) = 7 rearranges to 7^3 = 343, showing 343 is a perfect cube
y^6 is a perfect cube since (y^2)^3, i.e. the exponent 6 is a multiple of 3.
We have a difference of cubes.
----------------------------------------
Question 8
4 isn't a perfect cube since 4^(1/3) results in some decimal value that isn't a whole number. The entire expression is neither a sum nor difference of cubes.
----------------------------------------
Question 9
144^(1/3) isn't a whole number, so we get a similar result to problem 8.
----------------------------------------
Question 10
64j^6 = (4j^3)^3 is one cube
k^9 = (k^3)^3 is another cube
We have a difference of cubes
Graph the line by plotting any two ordered pairs with integer value coordinates that satisfy the equation.- 6x + 9y = 0AnswerKeypadKeyboard ShortcutsPoints can be moved by dragging or using the arrow keys. Any lines or curves will be drawn once allrequired points are plotted and will update whenever a point is moved.
Explanation
Step 1
get the slope-intercep form_
we need to use the function to graph the line,so let's convert the given equation in the slope-intercept form,to do that, isolate y
so
[tex]\begin{gathered} -6x+9y=0 \\ \text{add 6x in both sides } \\ -6x+9y+6x=0+6x \\ 9y=6x \\ \text{divide both sides by }9 \\ \frac{9y}{9}=\frac{6x}{9} \\ y=\frac{2}{3}x \end{gathered}[/tex]
so, the equation of the line is
[tex]y=\frac{2}{3}x[/tex]Step 2
now, let's use the equation to find 2 coordiantes of the line
a) for x =0
[tex]\begin{gathered} y=\frac{2}{3}x \\ \text{replace} \\ y=\frac{3}{2}(0)=0 \\ \text{hence, } \\ \text{ Point 1 ( 0,0)} \end{gathered}[/tex]b) for x= 3
[tex]\begin{gathered} y=\frac{2}{3}x \\ \text{replace} \\ y=\frac{2}{3}(3)=2 \\ \text{hence, } \\ \text{ Point 1 ( 3,2)} \end{gathered}[/tex]Step 3
finally, draw a line that passes through the points (0,0) and (3,2)
I hope this helps you
lia has taken a mathematics exam, and she wants to calculate an 88% confidence interval to represent the exam scores within her group of friends. what are the z statistics that fall at each line marking the middle 88% of scores in the distribution?
In the given scenario, in order to calculate an 88% confidence interval, the z statistics that fall at each line marking the middle 88% of scores in the distribution would be +/- 1.555 (from the table).
In a case of seeking 88% confidence interval, the implication is that there is 12% chance that the interval does not contain the true value i.e., α=0.12 Assuming a two-sided test, it means that there should be 6% chance attributed to each tail of the z statistics (distribution). Thus, zα/2= z0.06.This z value at α/2=0.06 is the coordinate of the Z-curve that has 6% of the distribution's area to its right, and thus 94% of the area to its left. It is determined by z-value by reverse-lookup in a z-table. Find the closest value in the table to 0.9400 as possible, then see what its row and column is. From observation, it is seen that 0.9394 and 0.9406 are in the table with z -values of 1.55 and 1.56 respectively.We use liner interpolation to find the experimental z-score:Hence the z score = 1.5550
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2/3×4/5 by using fraction bar step bystep
Answer: 8/15
Step-by-step explanation:
2/3 x 4/5, multiply numerators and denominators
8/15 or 0.533
A box of cereal states that there are
78 calories in a
3
4
-cup serving. What is the unit rate for calories per cup? How many calories are there in
4 cups of the cereal?
The unit rate for the cereal is 104 calories per cup and there are 416 calories in 4 cups
How to determine the unit rate for the cereal?From the question, the given parameters are
Calories = 78 calories
Size of cups = 3/4-cup
The unit rate of the calories per cup is calculated as
Unit rate = Number of Calories/Size of cup
Substitute the known values in the above equation
So, we have the following equation
Unit rate = 78/(3/4)
Evaluate the quotient
So, we have the following equation
Unit rate = 104
So, the unit rate is 104 calories per cup
For four cups of cereal, we have
Calories = 104 x 4
Evaluate
Calories = 416
So, the number of calories is 416 calories
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2(x + 7) = 6x + 9 - 4x
EXPLANATION
Given the equation:
2(x+7) = 6x + 9 -4x
Applying distributive property:
2x + 14 = 6x + 9 -4x
Adding similar terms:
2x + 14 = 2x + 9
Subtracting -2x to both sides:
14 ≠ 9
--->The equation hasn't got solution.
HELP ME PLEASE I NEED HELP I DONT KNOW HOW TO DO THIS
Answer:
convert miles to kilometers by multiply by 1.61 covert kilometers to miles by devide by 0.62(if am not wrong)
which is an equation of the line through the origin and (-5,6)
The equation of a line through the origin and (-5,6) is y = -1.2x
How to determine the equationIt is important to note that the equation of a line is expressed as;
y = mx + c
Where;
y is the point on the y - axism is the slope of the linex is the point on the x - axisc is the intercept on the y axisFrom the information given, we have the points;
(0, 0) and ( -5, 6)
The formula for slope is given as;
slope, m = y₂ - y₁/ x₂ -x₁
slope, m = 6 - 0/ -5 - 0
slope, m = 6/ -5
slope, m = - 1. 2
To determine the intercept, we have;
6 = -1. 2(-5) + c
expand the bracket
c = 6 - 6
c = 0
The equation is given as;
y = -1.2x
Hence, the equation is y = -1.2x
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Which of the following is a disadvantage of using a check casher, compared to a bank?
Responses
You wait longer to get your money at a check casher than at a bank
You wait longer to get your money at a check casher than at a bank
You pay a higher fee to cash checks at a check casher than at a bank
You pay a higher fee to cash checks at a check casher than at a bank
You can only cash checks worth more than $500 at a check casher
You can only cash checks worth more than $500 at a check casher
You can cash fewer checks at a check casher than at a bank
The main disadvantage of using a check cashier is that, 'You pay a higher fee to cash checks at a check casher than at a bank'
Check casher;
A check casher is someone who works in the check-cashing industry, with the exception of someone who doesn't cash checks for others on any one day that total more than $1,000 in cash, money, or other assets.
Disadvantage of Check cashers;
Fees for cash checking services can be as low as $1 or as much as 2% of the check amount depending on where you are. These costs reduce one's capacity to make ends meet or have extra money available. Always be aware of the prices and fees before using a check cashing service.
That is,
The main disadvantage of using a check cashier is that, 'You pay a higher fee to cash checks at a check casher than at a bank'
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Please helppp as fast as possible 20 points ***
FIND THE DOMAIN & RANGE OF THE FUNCTION
g(x)=|x + 4|
Please helppp as fast as possible
Answer:
Domain: (−∞,∞),{x | x ∈ R}
Range: [0,∞),{y|y≥0}
Step-by-step explanation:
The coordinates of the vertices of a quadrilateral are P (5,2), S (5,-6), H(-6-1), and B (-6,4). The figure is rotated 360° counterclockwise with the origin as the center of rotation to create quadrilateral P'S'H'B'
What are the coordinates of the vertices of quadrilateral P’S’H’B’?
P’ =
S’ =
H’ =
B’ =
14. A can of vegetables has a paper label that covers the lateral surface are can, 4 in. 2.6 in. What is the lateral surface area of the can onded to the
We will have that the lateral area will be the following:
*First, we can see that if we were to cut a straight vertical line and unfold the label, we would get a rectangle, thus the surface area of the label will be given by:
[tex]S_A=h\cdot C[/tex]Here h is the height of the label and C is the circumference of the base, that is:
[tex]S_A=h\cdot2\pi r[/tex]Now, we determine the radius of the base, that is:
[tex]r=\frac{2.6}{2}\Rightarrow r=1.3[/tex]Now, we replace the values and solve for the surface area:
[tex]\Rightarrow S_A=(4)\cdot(2)\pi(1.3)\Rightarrow S_A\approx32.7[/tex]So, the surface area of the label on the can is approximately 32.7 squared inches.
one thousand two hundred and seventy deer are living on an island that is eight hundred and thirty square kilometers in size. what is the population density of the deer per square kilometer?
Help me please i need help with my math hw
Answer:
answer of 1st picture
second is not under standing much
Morgan can make 4 cupcakes with 1 cup of flour. How many cupcakes can she make with 18 cups of flour?
Answer: She can make 72 cupcakes.
Step-by-step explanation:
Solve for d.
4d - 5 = 11
Answer:
d = 4
Step-by-step explanation:
4d - 5 = 11
a) Subtract 5 from both sides.
-5 + 5 = 11 + 5
4d = 16
b) Divide both sides by 4.
4d/4 = 16/4
16/4 = 4
Therefore, you're answer will be 4.