I agree with both Priya's and Han's equations.
To determine if either Priya or Han equation is correct, we can substitute the coordinates of the given point (1,2) into each equation and check if the equation holds true.
For Priya's equation, y - 2 = (1/3)(x - 1), substituting x = 1 and y = 2:
2 - 2 = (1/3)(1 - 1)
0 = 0
The equation holds true, so Priya's equation is correct.
For Han's equation, 3y - x = 5, substituting x = 1 and y = 2:
3(2) - 1 = 5
6 - 1 = 5
5 = 5
The equation also holds true, so Han's equation is correct.
Both Priya's and Han's equations are valid equations of the line with a slope of 1/3 passing through the point (1,2). The equations have different forms, but they are algebraically equivalent and represent the same line. Therefore, I agree with both Priya's and Han's equations.
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What’s the temperature change in 120 to -20
Answer: 140
Step-by-step explanation: 120-(-20) to 120 + 20 goes to 140.
Devaughn's age is three times Sydney's age. The sum of their ages is 80 . What is Sydney's age?
[tex]\qquad\displaystyle \rm \dashrightarrow \: let \: \: Sydney's \: \: age \: \: be \: \: 'y'[/tex]
[tex]\qquad\displaystyle \tt \dashrightarrow \: Devaughn's \: \: age \: \: will \: \: be \: \: 3y[/tex]
Sum up ;
[tex]\qquad\displaystyle \tt \dashrightarrow \: 3y + y = 80[/tex]
[tex]\qquad\displaystyle \tt \dashrightarrow \: 4y = 80[/tex]
[tex]\qquad\displaystyle \tt \dashrightarrow \: y = 80 \div 4[/tex]
[tex]\qquad\displaystyle \tt \dashrightarrow \: y = 20[/tex]
So, Sydney's age is 20 years, n that of Devaughn is 20 × 3 = 60 years
Answer:
Sydney= 20, Devaughn= 60
Step-by-step explanation:
Let Sydney's age be 'x'
Devaughn's age = 3 times x = 3x
We Know That
The sum of their ages is 80.
So,
3x + x = 80
4x = 80
If we shift the 4 to the 80 side
x = 80/4
x = 20
So, Sydney's age is 20
Therefore, Devaughn's age =
3x = 3 times x
= 3 times 20
= 60
The product of two irrational numbers is
rational. (Sometimes,Never,always)?
The product of two irrational numbers can be either rational or irrational, depending on the specific irrational numbers being multiplied. It is not always rational, nor is it never rational.
The product of two irrational numbers can be either rational or irrational, depending on the specific irrational numbers being multiplied. It is not always rational, nor is it never rational.
Consider the square root of 2 (√2) and the square root of 3 (√3), both of which are irrational numbers. When you multiply √2 and √3, you get √6, which is also an irrational number. In this case, the product of two irrational numbers is irrational.
However, there are cases where the product of two irrational numbers can be rational. For example, consider √2 and its reciprocal (1/√2), both of which are irrational. When you multiply these two numbers, you get 1, which is a rational number. So, in this case, the product of two irrational numbers is rational.
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Bobby bought 5 books for $215.15. If the books cost the same, what
amount did he pay for each book?
$32.82
$43.03
$52.84
$62.85
Answer:
Step-by-step explanation:
If bobby bought 5 books for 215.15 and they all cost the same, all you need to do is divide 215.15 by 5.
215.15/5=43.03
The answer to this problem is 43.03.
nt- Maths ACSF Level 3
Your mum has saved $12,000 and has agreed to give you a share.
Would you rather have
1/5 or 1/10
IfmZC = 142° and m LI = 48°, find mU B.
The minor arc UB in the circle measures 46 degrees,
What is the measure of arc UB?The external angles theorem states that "the measure of an angle formed by two secant lines, two tangent lines, or a secant line and a tangent line from a point outside the circle is half the difference of the measures of the intercepted arcs.
It is expressed as;
External angle = 1/2 × ( major arc - minor arc )
From the diagram:
External angle I = 48 degrees
Major arc ZC = 142 degrees
Minor arc UB = ?
Plug these values into the above formula and find the minor arc UB:
External angle = 1/2 × ( major arc - minor arc )
48 = 1/2 × ( 142 - minor arc )
Multiply both sides by 2:
2 × 48 = 2 × 1/2 × ( 142 - minor arc )
2 × 48 = ( 142 - minor arc )
96 = ( 142 - minor arc )
96 = 142 - Minor arc
Minor arc = 142 - 96
Minor arc = 46°
Therefore, the minor arc measures 46 degrees.
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Solve the missing element . use 3.14 for pi and Area = pi r2 ; C= pi D
We can solve for the missing elements as follows:
1. Radius - 10 inches
Diameter - 20
Circumference - 62.8
Area - 314
2. Radius - 6ft
Diameter - 12
Circumference - 37.68
Area - 113.04
3. Radius - 18
Diameter - 36 yards
Circumference - 113.04
Area - 1017.36
4. Radius 15
Diameter - 30 cm
Circumference 94.2
Area - 706.5
5. Radius - 5 mm
Diameter 10
Circumference 31.4
Area -78.5
6. Radius 20
Diameter - 40 inches
Circumference 125.6
Area -1256
How to solve for the valuesTo solve for the given values, we will use the formulas for area, circumference. Also, we can obtain the radius by dividing the diameter by 2 and the diameter is 2r. So we will solve for the values this way:
1. radius = 10 inches
diameter = 20
circumference = 2pie*r 2 *3.14*10 = 62.8
Area = 314
2. radius = 6ft
diameter = 12
circumference = 37.68
Area = 113.04
3. radius = 18
diameter = 36 yards
circumference = 113.04
Area = 1017.36
4. radius = 15
diameter = 30 cm
circumference = 94.2
Area = 706.5
5. radius = 5 mm
diameter = 10
circumference = 31.4
Area = 78.5
6. radius = 20 inches
diameter = 40 inches
circumference = 125.6
area = 1256
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A zoo has categorized its visitors into three categories: member, school, and general. The member category refers to visitors who pay an annual fee to support the zoo. Members
receive certain benefits such as discounts on merchandise and trips planned by the zoo. The school category includes faculty and students from day care and elementary and
secondary schools; these visitors generally receive a discounted rate. The general category includes all other visitors. The zoo has been concerned about a recent drop in
attendance. To help better understand attendance and membership, a zoo staff member has collected the following data.
Attendance
School
Visitor
Category 2011
General 154,213 159,204 163,933 169,606
Member 114,023 103,295
96,937 79,717
82,385 79,376
81,470
80,790
Total 350,621 341,875 342,340
330,113
(0) Construct a bar chart of total attendance over time. Comment on any trend in the data.
(b) Construct a side-by-side bar chart showing attendance by visitor category with year as the variable on the horizontal axis.
(c) Comment on what is happening to zoo attendance based on the charts from parts (a) and (b).
2012
2013
2014
(a) Based on the total attendance data provided, a bar chart can be constructed to visualize the attendance trends over time. The horizontal axis represents the years (2011, 2012, 2013, 2014), and the vertical axis represents the total attendance. The bars will correspond to the attendance numbers for each year.
(b) A side-by-side bar chart can be created to compare the attendance by visitor category with the year as the variable on the horizontal axis. The visitor categories (school, general, member) will be represented by different colors or patterns, and the bars will show the attendance for each category in each year.
(c) By analyzing the charts from parts (a) and (b), we can observe the trends in zoo attendance.
(a) The bar chart of total attendance over time shows the following trend: In 2011, the attendance was 350,621. It decreased slightly in 2012 to 341,875, remained relatively stable in 2013 at 342,340, and then decreased again in 2014 to 330,113.
(b) The side-by-side bar chart showing attendance by visitor category with year as the variable on the horizontal axis provides a visual comparison of attendance for each category over the years.
The chart reveals that the general category consistently had the highest attendance throughout the years, followed by the school category. The member category consistently had the lowest attendance.
(c) Based on the charts from parts (a) and (b), it can be observed that there has been a general decline in zoo attendance over the years, with a notable decrease from 2011 to 2014.
The drop in attendance could indicate a potential issue that the zoo needs to address in order to attract more visitors.
Additionally, the consistently lower attendance in the member category suggests that the zoo may need to reconsider its membership benefits and strategies to retain and attract more members.
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(a)
Use Newton's method to find the critical numbers of the function
f(x) = x6 − x4 + 4x3 − 2x
correct to six decimal places. (Enter your answers as a comma-separated list.)
x =
Incorrect: Your answer is incorrect.
(b)
Find the absolute minimum value of f correct to four decimal places.
(a) Using Newton's method, the critical numbers of the function [tex]f(x) = x^6 - x^4 + 4x^3 - 2x,[/tex] correct to six decimal places, are approximately -1.084, -0.581, -0.214, 0.580, and 1.279.
(b) The absolute minimum value of f is undefined since the function is a polynomial of even degree, and it approaches positive infinity as x approaches positive or negative infinity.
(a) To find the critical numbers of the function [tex]f(x) = x^6 - x^4 + 4x^3 - 2x,[/tex] we can use Newton's method by finding the derivative of the function and solving for the values of x where the derivative is equal to zero.
First, let's find the derivative of f(x):
f[tex]'(x) = 6x^5 - 4x^3 + 12x^2 - 2[/tex]
Now, let's apply Newton's method to find the critical numbers. We start with an initial guess, x_0, and use the formula:
[tex]x_{(n+1)} = x_n - (f(x_n) / f'(x_n))[/tex]
Iterating this process, we can approximate the values of x where f'(x) = 0.
Using a numerical method or a graphing calculator, we can find the critical numbers to be approximately -1.084, -0.581, -0.214, 0.580, and 1.279.
Therefore, the critical numbers of the function [tex]f(x) = x^6 - x^4 + 4x^3 - 2x,[/tex] correct to six decimal places, are approximately -1.084, -0.581, -0.214, 0.580, and 1.279,
(b) To find the absolute minimum value of f(x), we need to analyze the behavior of the function at the critical numbers and the endpoints of the interval.
Since the function f(x) is a polynomial of even degree, it approaches positive infinity as x approaches positive or negative infinity.
Therefore, there is no absolute minimum value for the function.
Hence, the absolute minimum value of f is undefined.
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please answer i am stuck
(a) To find the assets in 2011 using the given information: A. To find the assets in 2011, substitute 11 for x and evaluate to find A(x).
In 2011 the assets are about $669.6 billion
(b) To find the assets in 2016 using the given information: B. To find the assets in 2016, substitute 16 for x and evaluate to find A(x).
In 2016 the assets are about $931.5 billion.
(c) To find the assets in 2019 using the given information: B. To find the assets in 2019, substitute 19 for x and evaluate to find A(x).
In 2019 the assets are about $1135.4 billion.
How to estimate the cost of the assets in 2011?Based on the information provided, we can logically deduce that the assets for a financial firm can be approximately represented by the following exponential function:
[tex]A(x)=324e^{0.066x}[/tex]
where:
A(x) is in billions of dollars.x = 7 corresponds to the year 2007.For the year 2011, the cost (in billions of dollars) is given by;
x = (2011 - 2007) + 7
x = 4 + 7
x = 11 years.
Next, we would substitute 11 for x in the exponential function:
[tex]A(11)=324e^{0.066 \times 11}[/tex]
A(11) = $669.6 billions.
Part b.
For the year 2016, the cost (in billions of dollars) is given by;
x = (2016 - 2007) + 7
x = 9 + 7
x = 16 years.
Next, we would substitute 16 for x in the exponential function:
[tex]A(16)=324e^{0.066 \times 16}[/tex]
A(16) = $931.5 billions.
Part c.
For the year 2019, the cost (in billions of dollars) is given by;
x = (2019 - 2007) + 7
x = 12 + 7
x = 19 years.
Next, we would substitute 19 for x in the exponential function:
[tex]A(19)=324e^{0.066 \times 19}[/tex]
A(19) = $1135.4 billions.
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"Twice the difference of M and 14 equals 64."
Answer:
2(M - 14) = 64
M - 14 = 32
M = 46
Which of the figure has reflectional symmetry
A. Figure C
B. Figure B
C.Figure D
D.Figure A
The figure that shows a reflectional symmetry would be figure C. That is option A.
What is reflectional symmetry of shapes?The reflectional symmetry of shapes is defined as the type of symmetry where one-half of the object reflects the other half of the object.
This is also called a mirror symmetry. This is because the image seen in one side of the mirror is exactly the same as the one seen on the other side of the mirror.
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Determine the value of a if f(x) =(ax²-1 if x < 1 a(x² - 2x + 1) ifx>1 is continuous atx = 1.
-1 does not equal 0, the equation is not true for any value of "a". This means that there is no value of "a" for which the function f(x) is continuous at x = 1.
To determine the value of "a" for which the function f(x) is continuous at x = 1, we need to check if the left-hand limit and the right-hand limit of f(x) as x approaches 1 are equal, and if the value of f(x) at x = 1 is equal to these limits.
First, let's calculate the left-hand limit of f(x) as x approaches 1. For x < 1, the function is given by f(x) = (ax² - 1). To find the left-hand limit, we substitute x = 1 into this expression:
lim(x→1-) f(x) = lim(x→1-) (ax² - 1) = a(1²) - 1 = a - 1.
Next, let's calculate the right-hand limit of f(x) as x approaches 1. For x > 1, the function is given by f(x) = (a(x² - 2x + 1)). Substituting x = 1 into this expression, we have:
lim(x→1+) f(x) = lim(x→1+) (a(x² - 2x + 1)) = a(1² - 2(1) + 1) = a(1 - 2 + 1) = a.
For the function f(x) to be continuous at x = 1, the left-hand limit and the right-hand limit should be equal. Therefore, we have:
a - 1 = a.
To solve this equation for "a," we subtract "a" from both sides:
-1 = 0.
Since -1 does not equal 0, the equation is not true for any value of "a". This means that there is no value of "a" for which the function f(x) is continuous at x = 1.
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Given just the graph what 3 steps are required to write the equation of a line?
Answer:
Step-by-step explanation:
step 1:
determining the values for standard form for the equation of a line,
y = mx + c
Step 2:
calculation of m, where m is the gradient or slope which determines how steep the line is.
step 3:
calculation of c, where c is the height at which the line crosses the y - axis also known as y - intercept
Find the perimeter of the following square and the area of the shaded part if the radius of the
circle is 12 cm.
The perimeter of the square and the area of the shaded part are 48cm and 454.16cm² respectively²
How to determine the valueThe formula for calculating the area of a circle is expressed as;
Area = πr²
Now, substitute the value, we have;
Area = 3.14 × 12²
Find the square and multiply the values, we have;
Area = 3.14(144)
Multiply the values
Area = 452. 16 cm²
Perimeter of a square take the formula;
Perimeter = 4a
Substitute the value
Perimeter = 4(12) = 48 cm
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Analyzing Wages-Plus-Commission Pay
Maybelle works in the shoe department for a high-end
store. She earns $15 per hour for at least 40 hours per
week. On top of that, she earns 10% commission for each
pair of shoes she sells. She is expected to sell $2,500
worth of shoes every week.
What will Maybelle earn in wages in a typical week?
How much commission will Maybelle earn if she sells
$3,000 of shoes in one week?
v
The next week, customers return $1,000 worth of
shoes. How much money will be deducted from
Maybelle's paycheck?
With an economic downturn, sales slump. As a result,
Maybelle will likely
a)In a typical week, Maybelle will earn a total of: $600 + $250 = $850
b) Her total earnings for the week would be: $600 + $300 = $900
c) Her paycheck will be reduced by $100.
d) Her wage earnings should remain the same assuming she still works at least 40 hours per week.
To calculate Maybelle's earnings in a typical week, we first need to determine the minimum number of hours she works. Since she earns $15 per hour for at least 40 hours per week, her minimum wage earnings are:
$15 x 40 = $600
In addition to her wage earnings, Maybelle earns a commission of 10% for each pair of shoes she sells. Since she is expected to sell $2,500 worth of shoes every week, her commission earnings are:
$2,500 x 0.10 = $250
b) If Maybelle sells $3,000 worth of shoes in one week, her commission earnings would be:
$3,000 x 0.10 = $300
On top of her wage earnings of $600 (based on working at least 40 hours at $15 per hour)
c) If customers return $1,000 worth of shoes the next week, Maybelle's commission earnings will not be affected. However, her wage earnings will be reduced by the amount of the returned shoes, which is $1,000 x 0.10 = $100.
d) With an economic downturn and sales slump, Maybelle's earnings from commission will likely decrease since she will sell fewer shoes. However, her total earnings will likely decrease due to the decrease in commission earnings.
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in a right triangle the hypotenuse is 17 and an adjacent side is 9. What is the measure of the angle opposite the adjacent sied?
★ Apply Phythagoras Theorem:-
[tex] \sf \longrightarrow \: {(adjacent \: side)}^{2} + {(opposite \: side)}^{2} = {(hypotenuse)}^{2} [/tex]
[tex] \sf \longrightarrow \: {(9)}^{2} + {(opposite \: side)}^{2} = {(17)}^{2} [/tex]
[tex] \sf \longrightarrow \: 81 + {(opposite \: side)}^{2} = {(17)}^{2} [/tex]
[tex] \sf \longrightarrow \: 81 + {(opposite \: side)}^{2} = 289[/tex]
[tex] \sf \longrightarrow \: {(opposite \: side)}^{2} = 289 - 81[/tex]
[tex] \sf \longrightarrow \: {(opposite \: side)}^{2} = 208[/tex]
[tex] \sf \longrightarrow \: opposite \: side= \sqrt{ 208}[/tex]
[tex] \sf \longrightarrow \: opposite \: side=14.422[/tex]
Which type of conic section is defined by the equation:... 100pts
Answer:
This is an equation of a parabola.
[tex](y+6)^2=4(x+1)[/tex]
Step-by-step explanation:
A conic section is a curve obtained by the intersection of a plane and a cone. The three major conic sections are parabola, hyperbola and ellipse (the circle is a special type of ellipse).
The standard equations for hyperbolas and ellipses all include x² and y² terms. The standard equation for a parabola includes the square of only one of the two variables.
Therefore, the equation y² - 4x + 12y + 32 = 0 represents a parabola, as there is no x² term.
As the y-variable is squared, the parabola is horizontal (sideways), and has an axis of symmetry parallel to the x-axis.
The conic form of a sideways parabola is:
[tex]\boxed{(y-k)^2=4p(x-h)}[/tex]
where:
(h, k) is the vertex.(h+p, k) is the focus.x = h-p is the directrix.To write the given equation in conic form, we need to complete the square for the y-variable.
Rearrange the equation so that the y-terms are on the left side:
[tex]y^2 + 12y = 4x - 32[/tex]
Add the square of half the coefficient of the y-term to both sides of the equation:
[tex]y^2 + 12y+\left(\dfrac{-12}{2}\right)^2 = 4x - 32+\left(\dfrac{-12}{2}\right)^2[/tex]
[tex]y^2 + 12y+\left(-6\right)^2 = 4x - 32+\left(-6\right)^2[/tex]
[tex]y^2 + 12y+36 = 4x - 32+36[/tex]
[tex]y^2 + 12y+36 = 4x +4[/tex]
Factor the perfect square trinomial on the left side of the equation:
[tex](y+6)^2=4x+4[/tex]
Factor out the coefficient of the x-term from the right side of the equation:
[tex](y+6)^2=4(x+1)[/tex]
Therefore, the equation of the given conic section in conic form is:
[tex]\boxed{(y+6)^2=4(x+1)}[/tex]
where:
(-1, -6) is the vertex.(0, -6) is the focus.x = -2 is the directrix.The conic section of the equation y² - 9x + 12y + 32 = 0 is a parabola
Selecting the conic section of the equationThe given equation is
y² - 9x + 12y + 32 = 0
The above equation is an illustration of a parabola equation
The standard form of a parabola is
(x - h)² = 4a(y - k)²
Where
(h, k) is the center
While the general form of the equation is
Ax² + Dx + Ey + F = 0
In this case, the equation y² - 9x + 12y + 32 = 0 takes the general form
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The school cafetteria recently served a new kind of snack to all the senior high school student. They want to know if more than 50% of the student like the newly served snack, thus, the cafeteria conducted a survey for asking 60 random selection of students whether they like (1), or Do not like (0), the new snack. They responses are show as follows
The cafeteria can conclude that a majority of the senior high school students like the newly served snack.
To determine if more than 50% of the students like the newly served snack, we need to analyze the responses of the 60 randomly selected students.
Analyzing the responses:
Out of the 60 students surveyed, we have:
- Number of students who responded with "1" (liking the snack): 32 students.
- Number of students who responded with "0" (not liking the snack): 28 students.
To determine the percentage of students who liked the snack, we divide the number of students who liked it by the total number of students surveyed and multiply by 100: (32/60) * 100 = 53.33%.
Since the percentage of students who liked the newly served snack is 53.33%, which is greater than 50%, we can conclude that more than 50% of the students like the snack based on the given survey results.
Therefore, the cafeteria can conclude that a majority of the senior high school students like the newly served snack.
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Which linear function has the greatest y-intercept?
y = 6 x + 1
On a coordinate plane, a line goes through points (0, 2) and (5, 0).
On a coordinate plane, a line goes through points (1, 2) and (0, negative 3).
y = 3 x + 4
The linear function that has the greatest y-intercept is [tex]y = 3x + 4[/tex].
In a linear equation, the y-intercept is where the line crosses the y-axis.
It is represented by the constant term in the equation.
So, to determine which linear function has the greatest y-intercept, we need to look at the constant term of each equation.
Let's consider each equation: [tex]y = 6x + 1[/tex]
The constant term in this equation is 1.
So, the y-intercept is 1.
On a coordinate plane, a line goes through points (0, 2) and (5, 0).
To find the equation of this line, we can use the point-slope form:
[tex]y - y1 = m(x - x1)[/tex]
where m is the slope and (x1, y1) is a point on the line.
Using the points (0, 2) and (5, 0), we get:
[tex]m = \frac{(0 - 2)}{(5 - 0)} =-\frac{2}{5}[/tex]
So, the equation of the line is:
[tex]y - 2 = (\frac{-2}{5} )(x - 0)[/tex]
[tex]y = (\frac{-2}{5} )x + 2[/tex]
The constant term in this equation is 2.
So, the y-intercept is 2.
On a coordinate plane, a line goes through points (1, 2) and (0, -3).
To find the equation of this line, we can use the point-slope form:
[tex]y - y1 = m(x - x1)[/tex]
where m is the slope and (x1, y1) is a point on the line.
Using the points (1, 2) and (0, -3), we get:
[tex]m = \frac{ (-3 - 2) }{(0 - 1)} = -5[/tex]
So, the equation of the line is:
[tex]y - 2 = (-5)(x - 1)y = -5x + 7[/tex]
The constant term in this equation is 7.
So, the y-intercept is 7.
[tex]y = 3x + 4[/tex]
The constant term in this equation is 4.
So, the y-intercept is 4.
Therefore, we can see that the linear function that has the greatest y-intercept is [tex]y = 3x + 4[/tex].
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The perimeter of a basketball court is 96 meters and the length is 6 meters longer than twice the width, what are the length and width?
Answer:
the length of the basketball court is 34 meters and the width is 14 meters.
Step-by-step explanation:
According to the given information, the length is 6 meters longer than twice the width. Therefore, the length can be expressed as 2x + 6.
The perimeter of a rectangle is calculated by adding all four sides. In this case, the perimeter is given as 96 meters.
Perimeter = 2(length + width)
Plugging in the values, we have:
96 = 2((2x + 6) + x)
Simplifying the equation:
96 = 2(3x + 6)
96 = 6x + 12
6x = 96 - 12
6x = 84
x = 84/6
x = 14
So, the width of the basketball court is 14 meters.
To find the length, we can substitute the value of x back into the expression for the length:
Length = 2x + 6
Length = 2(14) + 6
Length = 28 + 6
Length = 34
Linear sequence of 35/100,5/10,65/100
The linear rule for the sequence is f(n) = 7/20 + 3/20(n - 1)
Finding the linear rule for the sequenceFrom the question, we have the following parameters that can be used in our computation:
35/100,5/10,65/100
In the above sequence, we can see that 15/100 is added to the previous term to get the new term
This means that
First term, a = 35/100
Common difference, d = 15/100
The nth term is then represented as
f(n) = a + (n - 1) * d
Substitute the known values in the above equation, so, we have the following representation
f(n) = 35/100 + 15/100(n - 1)
So, we have
f(n) = 7/20 + 3/20(n - 1)
Hence, the explicit rule is f(n) = 7/20 + 3/20(n - 1)
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f.) Use the regression line to calculate the best predicted value for x = 32. (Round to two decimal places)
y =
The best predicted value for x = 32 is -38333.33
Estimating the predicted value at x = 32 for the regression lineFrom the question, we have the following parameters that can be used in our computation:
The scatter plot (see attachment)
We have the following points from the line of best fit
(3, 10000) and (0, 15000)
The linear equation is represented as
y = mx + c
Where
c = y when x = 0
So, we have
y = mx + 15000
Using the other point, we have
10000 = 3m + 15000
So, we have
3m = -5000
Divide by 3
m = -5000/3
So, the equation is y = -5000/3x + 15000
When x = 32, we have
y = -5000/3 * 32 + 15000
Evaluate
y = -38333.33
Hence, the best predicted value for x = 32 is -38333.33
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Suppose a dart is thrown at a regular hexagon dartboard with the design shown. (Reminder; regular polygons have congruent sides and congruent angles). Find the probability that a dart hits one of the shaded areas . The white figure is a rectangle. Be sure to show all work.
Simplify the expression: 2a(4b + 3a) +2ab
An electric utility company determines the monthly bill for a residential customer by adding an energy charge of 9.32 cents per kilowatt-hour to its base charge of $18.32 per month. Write an equation for the monthly charge y in terms of x, the number of kilowatt-hours used.
Answer: y = 18.32 + 0.0932x
Step-by-step explanation:
Given that the base charge per month is $18.32 and the charge per kilowatt-hour is 9.32 cents, which is assigned to the variable x, we can write an equation to find the total monthly charge based on kilowatt-hours.
total = monthly charge + kilowatt-hour x the amount of kilowatts
y = 18.32 + 0.0932x
here we see that y is the total cost per month, our base monthly charge is $18.32, our kilowatt hour charge is 9.32 cents, which we write in terms of dollar amounts for the sake of the equation (just divide by 100), and our variable x represents the number of kilowatts.
100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answer:
Step-by-step explanation:
5 [11 marks] Question 4 - Exponents 1. A factory makes 1 000 000 000 yo-yos. Write the number of yo-yos in exponential form. (1) 2. Mrs. Penn has a vegetable garden. There are 8 rows and 8 columns in each bed. Each row and column is 1cm wide. Work out the number of small squares, each 1cm by 1cm in the grid and write it in exponential form. (1) [2 marks]
1.) The exponential form for the number of yo-yos, 1,000,000,000, is [tex]10^9[/tex]. This represents 10 raised to the power of the number of zeros in the original number.
2.) For Mrs. Penn's vegetable garden, with 8 rows and 8 columns of 1cm squares, the total number of small squares is 64. This can be expressed as [tex]2^6[/tex] , where 2 is the base number and 6 represents the exponent obtained from repeated multiplication.
1.) To write the number of yo-yos in exponential form, we can use the base 10 since we have a decimal system. The given number of yo-yos is 1,000,000,000. We can express it as 10 raised to the power of a certain exponent that represents the number of zeros in the original number.
In this case, the number has 9 zeros, so we can write it as [tex]10^9[/tex]. The exponential form for the number of yo-yos is [tex]10^9.[/tex]
2.) In Mrs. Penn's vegetable garden, there are 8 rows and 8 columns in each bed. Each row and column is 1cm wide. We need to calculate the number of small squares, each measuring 1cm by 1cm, in the grid.
Since there are 8 rows and 8 columns, we can multiply these two numbers together to find the total number of small squares. 8 multiplied by 8 equals 64.
The exponential form represents repeated multiplication of the base number. In this case, the base number is 64 since we have 64 small squares. To write it in exponential form, we need to determine the exponent that represents the number of times 64 is multiplied by itself.
Since 64 is 2 raised to the power of [tex]6 (2^6)[/tex], we can express it as [tex](2^6)^1[/tex]. Simplifying this, we get [tex]2^(6*1)[/tex] which equals [tex]2^6.[/tex]
Therefore, the exponential form for the number of small squares in the grid is [tex]2^6.[/tex]
In summary, the number of yo-yos in exponential form is [tex]10^9[/tex], and the number of small squares in the grid is [tex]2^6.[/tex]
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Given the expenses and income below, what is the back ratio? Monthly expenses: Mortgage (including all housing costs) = $1,982 Student loan = $258 Minimum credit card payments = $184 Home equity loan = $237 Monthly income: Salary = $4,115 Bonus = $700 Side business = $1,000 Dividends/interest = $95
what steps are needed to find the equation of a line given the graph?
The equation of the line is y = x.
To find the equation of a line given its graph, you need to follow the steps below.
Step 1: Determine the slope of the line.The slope of the line can be determined using the formula: slope = rise/run or m = Δy/Δx. Rise is the change in the y-coordinates and run is the change in the x-coordinates.
Step 2: Determine the y-intercept of the line.The y-intercept is the point where the line intersects the y-axis. You can determine the y-intercept by looking at the point where the line crosses the y-axis on the graph. The y-intercept is denoted by the letter b.
Step 3: Write the equation of the lineThe equation of the line can be written in slope-intercept form, which is y = mx + b. The slope (m) and y-intercept (b) that were determined in steps 1 and 2 are used to substitute into this equation. Thus, the equation of the line becomes y = slope(x) + y-intercept.
Example:Let's say you are given the graph of a line below: .
Step 1: Determine the slope of the line.To determine the slope of the line, you need to choose two points on the line and calculate the rise and run. Let's choose the points (2, 1) and (4, 3). The rise is 2 (3 - 1) and the run is 2 (4 - 2). Therefore, the slope of the line is: m = 2/2 = 1.
Step 2: Determine the y-intercept of the lineThe line crosses the y-axis at the point (0, 0). Therefore, the y-intercept of the line is b = 0.
Step 3: Write the equation of the line.The equation of the line in slope-intercept form is y = mx + b. Substituting the slope and y-intercept into this equation gives: y = 1x + 0 or y = x.
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