Answer: We can use a system of equations to solve this problem. Let x be the number of oranges sold and y be the number of apples sold. Then we know that:
x + y = 15 (the total number of fruits sold)
1x + 2y = 25 (the total cost of the fruits sold)
We can use the first equation to solve for one variable in terms of the other.
For example, we can solve for x:
x = 15 - y
Now we can substitute this expression into the second equation:
1(15 - y) + 2y = 25
15 - y + 2y = 25
3y = 10
y = 10/3 = 3.333
We can round it to 3 apples sold
So we have 3 apples and 12 oranges sold.
This can be represented in a graph with a point (12,3)
Alternatively, we can solve for y:
y = 15 - x
Now we can substitute this expression into the second equation:
1x + 2(15 - x) = 25
1x + 30 - 2x = 25
-x = -5
x = 5
So we have 5 oranges and 10 apples sold.
This can be represented in a graph with a point (5,10)
Both solutions represent the same values, the number of oranges and apples sold, but represented in a different way.
Step-by-step explanation:
In addition, the balance of common stock at the beginning of the year was $550,000, and the balance of retained earnings was $46,000. During the year, the company issued additional shares of common stock for $32,000 and paid dividends of $24,000. Required: Prepare an income statement. Prepare a statement of stockholders’ equity.
Answer: Income Statement:
Revenue: _________
Expenses: _________
Net Income: _________
Statement of Stockholders' Equity:
Beginning Balance:
Common Stock: $550,000
Retained Earnings: $46,000
Total: $596,000
Additions:
Common Stock: $32,000
Total: $628,000
Deductions:
Dividends: $24,000
Total: $604,000
Ending Balance:
Common Stock: $550,000
Retained Earnings: $50,000
Total: $600,000
Note: I've left the Revenue, Expenses and Net Income section in the income statement blank as it is not provided in the question. It is also important to note that these are just examples and the numbers may not match with the actual financial statement.
Step-by-step explanation:
What is the value of x in this triangle?
[tex]\huge\underline{\red{A}\green{n}\blue{s}\purple{w}\pink{e}\orange{r} →}[/tex]
83°Step-by-step explanation:
As it is a triangle , so we know that sum of all angles of a triangle = 180°
therefore,=> 44 + 53 + x = 180
=> 97 + x = 180
=> x = 180 - 97
=> x = 83°
______________________________Hope it helps you ~Question 4Multiple Choice Worth 2 points)
(04.05 MC)
A chess player ran a simulation twice to estimate the proportion of wins to expect using a new game strategy. Each time, the simulation ran a trial of 1,000 games. The first
simulation returned 212 wins, and the second simulation returned 235 wins. Construct and interpret 95% confidence intervals for the outcomes of each simulation.
The confidence interval from the first simulation is (0.187, 0.237), and the confidence interval from the second simulation is (0.209, 0.261). For the first trial, we are
95% confident the true proportion of wins with the new game strategy is between 0.187 and 0.237. For the second trial, we are 95% confident the true proportion of
wins with the new game strategy is between 0.209 and 0.261.
The confidence interval from the first simulation is (0.187, 0.237), and the confidence interval from the second simulation is (0.209, 0.261). For the first trial, we are
90% confident the true proportion of wins with the new game strategy is between 0.187 and 0.237. For the second trial, we are 90% confident the true proportion of
wins with the new game strategy is between 0.209 and 0.261.
The confidence interval from the first simulation is (0.191, 0.233), and the confidence interval from the second simulation is (0.213, 0.257). For the first trial, we are
95% confident the true proportion of wins with the new game strategy is between 0.191 and 0.233. For the second trial, we are 95% confident the true proportion of
wins with the new game strategy is between 0.213 and 0.257.
The confidence interval from the first simulation is (0.191, 0.233), and the confidence interval from the second simulation is (0.213, 0.257). For the first trial, we are
90% confident the true proportion of wins with the new game strategy is between 0.191 and 0.233. For the second trial, we are 90% confident the true proportion of
wins with the new game strategy is between 0.213 and 0.257.
2
By constructing 95% confidence intervals for each simulation, we can be 95% confident that the true proportion of wins lies within the range of each interval.
What is Confidence Intervals?A confidence interval is a set of values that, given a specific level of certainty, are likely to include a population parameter like a mean or proportion.
The interval is derived using data drawn from a sample of the population and is frequently presented as a range of values with a 95% confidence level.
The probability that the range of values contains the genuine population parameter is quantified by the confidence level.
In the case of a 95% confidence interval, for instance, it means that 95% of the intervals would contain the real population parameter if we sampled the same population more than once and calculated a confidence interval each time.
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Car A is rated at 33 mi/gal (miles per gallon) for city driving and 28 mi/gal for highway driving. Car B is rated at 29 mi/gal city and 33 mi/gal highway. How many gallons of gas would each vehicle consume for the following amounts of driving? (a) 300 mi of city driving plus 100 mi of highway driving (b) 100 mi of city driving plus 300 mi of highway driving
The gallons consumed when car A travels 300 mi of city driving plus 100 mi of highway driving is 12.66 gallons
The gallons consumed when car B travels 300 mi of city driving plus 100 mi of highway driving is 13.37 gallons
The gallons consumed when car A travels 100 mi of city driving plus 300 mi of highway driving is 13.74 gallons
The gallons consumed when car B travels 100 mi of city driving plus 300 mi of highway driving is 12.54 gallons
How many gallons is consumed?Gallons consumed when car A travels 300 mi of city driving plus 100 mi of highway driving = (300 / 33) + (100 / 28)
= 9.09 + 3.57 = 12.66 gallons
Gallons consumed when car B travels 300 mi of city driving plus 100 mi of highway driving = (300 / 29) + (100 / 33)
= 10.34 + 3.03 = 13.37 gallons
Gallons consumed when car A travels 100 mi of city driving plus 300 mi of highway driving = (100 / 33) + (300 / 28)
= 3.03 + 10.71 =13.74 gallons
Gallons consumed when car B travels 100 mi of city driving plus 300 mi of highway driving = (100 / 29) + (300 /33)
= 3.45 + 9.09 = 12.54 gallons
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what is the angle (in degrees) north of east from the post office to the grocery store in centralburg? express your answer in degrees to two significant figures.
The angle θ measures 53.13⁰ with the east direction.
What is tangent of any angle?The tangent of an angle is a trigonometric function that is defined as the ratio of the side opposite the angle to the side adjacent to the angle in a right triangle. In other words, it is a measure of the steepness of a line that is tangent to a point on a function's graph and is represented by the symbol tan. It is one of the three main trigonometric functions, along with sine and cosine. The value of tangent is always positive in the first and fourth quadrants.
let the angle made be θ degree to the north of east from the post office to the grocery shop
so tan θ = p/b
where p is perpendicular , b is base of the triangle
so tan θ = 3/4
=> θ = 53.13 degree
so the angle θ measures 53.13⁰ with the east direction.
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Complete question :
what is the angle (in degrees) north of east from the post office to the grocery store in centralburg? express your answer in degrees to two significant figures.
When looking east, the angle is 53.[tex]13^{0}[/tex] degrees.
What does a tangent to any angle mean?
The ratio of a right triangle's side opposite to its side next to the angle is known as the tangent of an angle, which is a trigonometric function. It is a measurement of the steepness of a line that is tangent to a point on the graph of a function, and it is denoted by the symbol tan. One of the three primary trigonometric functions, together with sine and cosine, is it. In the first and fourth quadrants, tangent's value is always positive.
Let the angle formed between the post office and the grocery store be degrees to the north of east.
so tan θ = p/b
where p is perpendicular , b is base of the triangle
so tan θ = 3/4
=> θ = 53.13 degree
so the angle θ measures 53.13⁰ with the east direction.
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Complete question :
What is the angle (in degrees) north of east from the post office to the grocery store in centralburg? express your answer in degrees to two significant figures.
A commission of $300 was paid to a broker's agent for the sale of a bond. If the commission was 3/4% of the sales value of the bond, how much was the bond sold for?
Answer:
Look below
Step-by-step explanation:
Sale prince is $300
the commission is 3/4%
Commission amount is $2.25
Price + commission $302.25
Price - commission $297.95
I hope this gives you the answer you where looking for
is x-3y =15 and y = -3y + 4 perpindiculad paralleled or neither
The two lines are perpendicular because the product of their slopes is equal to 1
What is the slope-intercept form of a line?The slope-intercept form of a line is represented by y=mx+c where m=slope and c is the y-intercept of the line
Given here: The two lines x-3y =15 and y = -3y + 4
Rewriting the given expressions in slop-intercept form we get
y=x/3-5
y = -3y + 4
The respective slopes are given as 1/3 and -3
Thus the product of the two slopes is 1/3×-3=-1
Hence, The given lines are perpendicular.
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A rectangle has a length of 8.2cm and a height of 42mm. The area of the rectangle is mm2
Answer: To find the area of a rectangle, you can use the formula:
Area = Length x Height
In this case, the length is given in cm and the height is given in mm. Therefore, you need to convert the length to mm before you can calculate the area.
1cm = 10mm.
So, 8.2 cm = 8.2 x 10 = 82mm
Now you can find the area of the rectangle:
Area = Length x Height = 82mm x 42mm = 3,444 mm^2
So, the area of the rectangle is 3,444 mm^2
Step-by-step explanation:
Use the distributive property to write each expression as an equivalent
algebraic expression.
-2(x-4)
Answer:
the equivalent algebraic expression is -2x -8 after applying the distributive property.
Step-by-step explanation:
The distributive property states that for any real numbers a, b, and c, a(b+c) = ab + ac.
To apply the distributive property to the expression -2(x-4), we can distribute the -2 across the parenthesis, like this:
-2(x-4) = -2x + (-2)(-4)
Simplifying the last part of the expression:
-2(x-4) = -2x -8
So, the equivalent algebraic expression is -2x -8 after applying the distributive property.
find the 100th derivative of P(x)=(x^5+x+x^7)^10 (1+x^2)^11 (x^3+x^5+x^7)
The 100th derivative of P(x) = (x+x⁵+x⁷)¹⁰(1+x²)¹¹(x³+x⁵+x⁷) will be zero.
What is a polynomial?An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.
Given:
A polynomial,
P(x) = (x+x⁵+x⁷)¹⁰(1+x²)¹¹(x³+x⁵+x⁷).
To find the degree:
(x⁷)¹⁰(x²)¹¹(x⁷) = x⁹⁹.
The polynomial has a degree of 99.
If we think about it intuitively,
Therefore, if we were to multiply it all out,
the leading word would be x⁹⁹.
The term's first derivative is 99x⁹⁸,
followed by 99(98)x⁹⁷,
and 99(98)(97)x⁹⁶.
And finally,
the 99th derivative is 99×98×97×96×...4×3×3×2×1× (x⁰)
=99!
So, the 100th derivative will be zero.
Therefore, by the 100th derivative, all terms will cancel out.
100th derivative will be zero.
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Krystal drove at an average speed of 50 mi/h from her home in Houston to visit her sister in Philadelphia.
She stayed in Philadelphia 25 hours, and on the trip back averaged 60 mi/h. She returned home 46 hours
after leaving. How many miles is Houston from Philadelphia?
a) Write an equation using the information as it is given above that can be solved to answer this question.
Use t as your variable to represent the amount of time Krystal spent driving from Houston to Philadelphia.
Equation:
b) How many miles is Houston from Philadelphia?
Answer:
miles
Give your answer to the nearest mile
Answer: a. The equation using the information as it is given above that can be solved to answer this question is:
distance = speed x time
Let t be the amount of time Krystal spent driving from Houston to Philadelphia.
distance = 50t + 60(46 - 25 - t)
b. To find the distance between Houston and Philadelphia, we can substitute the known values into the equation and solve for t.
distance = 50t + 60(46 - 25 - t)
distance = 50t + 60(21) - 60t
distance = 50t + 1260 - 60t
distance = -10t + 1260
To find the total distance, we can set t = 25
distance = -10(25) + 1260
distance = -250 + 1260
distance = 1010
Therefore, Houston is 1010 miles from Philadelphia, to the nearest mile.
Step-by-step explanation:
Water leaks from a tank at the rate of r(t) gallons per hour. The rate decreased as time passed, and values of the rate at two-hour time intervals are shown in the table below. The total amount of water that leaked out is evaluated by a Riemann sum. Find the upper estimate (left end-points of each rectangle) for the total amount of water that leaked out by using five rectangles.
Give your answer with one decimal place
t(hr) r(t) (gal/hr)
0 10.7
2 8.6
4 6.6
6 5.2
8 5.0
10 4.5
The upper estimate (left end-points of each rectangle) for the total amount of water that leaked out by using five rectangles is 72.2 gallons.
R(t) gallons per hour of water leak from a tank. The values of the rate at two-hour intervals are shown in the table below. As time went on, the rate decreased. A Riemann sum is used to determine the overall volume of water that has leaked out.
An integral representation of the rate function would be the amount of water. Estimation with the Riemann sum and left endpoints:
F(x) ≅ ∑f(xi-1)Δx where Δx=10/5 = 2 for this case and i = 1 to 5
W = (10.7 + 8.6 + 6.6 + 5.2 + 5.0)2
= 36.1•2
= 72.2 gallons
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how do you solve -2x=8
Answer:
All you have to do is divide by -2 on both sides. You're trying to get x by itself, so divide by a number by cancels itself out. Don't forget the negative sign as well, or else you'll be left with -x instead of just x. A positive number divided by a negative number will become negative.
-2x=8
x=-4
HELP PLEASE 100 POINT WILL GIVE BRAINLIEST
Answer:
no clue sorry I was not able to help
An alloy is a mixture of metals. Suppose that a certain alloy is made by mixing 120 g of an alloy That contains 42% copper with 200 g of pure copper
The mixture is 78.25% copper for the given alloy.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
To solve the given situation, we utilize material balancing before and after mixing.
Let the total amount of material after mixing is 320.
Let x be the percent copper of the mixture and applying copper balance,
⇒ (0.42)(120 g) + (1)(200) = 320x
Solving the above equation, we get the value as
⇒ x = 0.7825
Thus, the mixture is 78.25% copper.
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Kayden and his children went into a grocery store where they sell apples for $ 0.75 each and mangos for $2 each. Kayden has $20 to spend and must buy a minimum of 16 apples and mangos altogether . Also, he must buy no less than 16 apples. If represents the number of apples purchased and y represents the number of mangos purchased, write and solve a system of inequalities graphically and determine one possible solution .
The system of inequalities is:
x + y ≥ 16
x*0.75 + y*2 ≤ 20
And its graph can be seen below, there we can see that one possible solution is (14, 2)
How to write and solve the system of inequalities?
Let's define the variables:
x = number of apples.
y = number of mangos.
Kayden needs to buy not less than 16 items, so the first inequality is:
x + y ≥ 16
And he can spend at most $20, then:
x*0.75 + y*2 ≤ 20
The system of inequalities is then:
x + y ≥ 16
x*0.75 + y*2 ≤ 20
To graph it just graph the two lines and shade the region correspondent, for the first inequality shade the region above the line, for the second one shade the region below the line.
You should get.
The solution set is the region where both shaded areas intercept. Then a possible solution is:
x = 14
y = 2
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(CO 2) You flip a coin 3 times. The sample space is \{HHH, HHT, HTH, THH, HTT, THT, TTH. TTT\}. Which of the following is a compound event? A. You get exactly 2 tails B. You get exactly 3 tails C. This is not an event D. You get exactly 3 heads
A compound event is a combination of multiple simple events that can occur simultaneously or independently. When talking about coin flipping, the sample space is the set of all possible outcomes of the experiment, which in this case is flipping a coin 3 times. In this case, the sample space is {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}.
Option A, You get exactly 2 tails, is a compound event because it consists of three simple events, THT, HTH, and TTH. These events can happen independently of one another and therefore, it is a compound event.
Option B, You get exactly 3 tails, is not a compound event because it only consists of one simple event, TTT. This event is not a combination of other simple events and is, therefore, not a compound event.
Option C, This is not an event, is not a valid option as it is not a possible outcome.
Option D, You get exactly 3 heads, is also a compound event because it consists of one simple event, HHH. This event can happen independently of other simple events and it is, therefore, a compound event.
Hence, options A and D are compound events as they are a combination of multiple simple events that can happen independently or simultaneously.
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Explain why these triangles are congruent by AAS (Angle-Angle-Side) and not ASA (Angle-Side-Angle).
The triangles are congruent by AAS (Angle-Angle-Side) and not by ASA (Angle-Side-Angle)
Properties of congruent triangles.When the corresponding length of sides or measure of the internal angles of two or more triangles are equal, then the triangles are said to be congruent. The congruency can be expressed in terms angles, sides, or the combination of sides and angles. An example is the SAA (Side-Angle-Angle) property which implies that a side that is not an included angle and other angles are congruent.
Considering triangles ABC and CDE, it can be seen that two angles are congruent and a side of both are congruent. Since the congruent side is not an included angle, then the congruent relations is AAS (Angle-Angle-Side).
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Help with all please
Answer:
A is ST, PR, and UV
B is rays SQ and QT
C is point Q
D is Points S, Q, and T
Read the following prompt and type your response in the space provided.
Create a real-life representation of the following multiplication problem. Explain what the result represents in the problem.
15 (2/5)=6
Answer: In a real-life representation of the multiplication problem "15 (2/5) = 6," we can imagine a bag of 15 items, each of which is 2/5 of a whole. To find out how many whole items are in the bag, we can multiply 15 (the number of items) by 2/5 (the fraction of each item that is a whole).
The result of 6 represents the number of whole items in the bag.
Step-by-step explanation:
A door frame that appears to be rectangular has a height of 213 cm, width of 92 cm, and one diagonal that measures 231 cm. Determine if the door frame is rectangular. Explain your thinking.
The door frame is not rectangular.
Is the door frame rectangular?If the door frame is rectangular, the sum of the square of the height and the width would be equal to the square of the diagonal.
Height² + width = diagonal²
213² + 92²
45,369 + 8,463 = 53,833
231² = 53,361
53,833 ≠ 53,361
The door frame is not rectangular because the sum of the height and the width is not equal to the diagonal.
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What is the answer for
15 + x = 28
Answer: x = 13
Step-by-step explanation:
First you have to move 15+ to the other side to 28.Then when 15+ moves to the other side it will be 15-. After that you subtract 28 with 15 that will make 13. So x is equal to 13.
By numbers:
15+x=28
x=28-15
x=13
find the volume v of the described solid s. the base of s is the triangular region with vertices (0, 0), (5, 0), and (0, 5). cross-sections perpendicular to the x-axis are squares.
Using the disk method, it can be concluded that the volume of the solid is 125π /3 cubic units.
Disk Method is a method used to determine the volume of a solid formed by revolving the region about the x-axis and the interval [a, b]. The volume of the solid is the integral of the area of the base times dx.
V = π ∫ Ax dx
From the question, we know that the base of the figure is a triangular region and the coordinates are (0,0), (5,0), and (0,5).
The square is perpendicular to the x-axis. Thus, we can find the side of the square, that is the straight line passing through (5,0) and (0,5) which meet the y = mx + b equation.
First, we determine the slope of the line (m).
m = (y₂ - y₁) / (x₂ - x₁)
= ( 5 - 0 ) / ( 0 - 5 )
= 5 / -5
= -1
To find b, we input the value of m into the equation for point (5,0):
y = mx + b
0 = -1*5 + b
0 = -5 + b
b = 5
So we got the side of the square:
y = mx + b
y = -x + 5
y = 5 - x
Thus the area of the square is:
A = side²
= (5 - x)²
= 25 + x² - 10x
The volume of the solid can be calculated as follows:
V = π ∫ Ax dx
= π ∫₀² (25 + x² - 10x) dx
= π (25x + 1/3x³ - 5x² |₀⁵)
= π (25*5 + 1/3*5³ - 5*5² - 0)
= π (125 + 125/3 - 125 - 0)
= 125π /3 cubic units
Thus, the volume of the solid is 125π /3 cubic units
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Find the range and standard deviation of the set of data.
11, 8, 5, 11, 25
The range is
(Simplify your answer.)
The Range and standard deviation of the set of data 11, 8, 5, 11, 25 is 20 and 7.68 respectively.
What is mean ?
Mean can be defined as the ratio sum of the observations and total number of observations.
Given
set of data,
11, 8, 5, 11, 25
we have to find the range and standard deviation,
We know that,
range = max - min
here max = 25
min = 5
range = 25-5
range = 20
Standard deviation ,
= √( ( Σx^2 - (Σx)^2 / n ) / (n-1) )
= √( ( Σ11^2+8^2+5^2+11^2+25^2 - (Σ60)^2 / 5 ) / (5-1) )
= √( ( 956 - (3600)^2 / 5 ) / (5-1) )
= √( ( 956 - 720) / 4 )
= √( 59 )
= 7.68
Hence, The Range and standard deviation of the set of data 11, 8, 5, 11, 25 is 20 and 7.68 respectively.
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A soda company would like to replace the label on a can of soda with a radius of 2 and three fourths cm. If the label touches end to end with no overlap, what is the length of the label? Use 22 over 7 for π.
121 over 7 cm
121 over 14 cm
121 over 28 cm
121 over 56 cm
The length of the perimeter will be 121/7 cm.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that a soda company would like to replace the label on a can of soda with a radius of 2 and three fourths cm. The label touches end to end with no overlap.
Perimeter of a circle is the length of the boundary of the circle. It is given by : P = 2πrThe length of the label will be its perimeter. We can write -
P = 2πr
P = 2 x 22/7 x 11/4
P = 2 x 22/7 x 11/4
P = 22/7 x 11/2
P = 11 x 11/7
P = 121/7
Therefore, the length of the perimeter will be 121/7 cm.
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? ÷ 2/5 = 4
Draw a diagram to represent the situation.
Given expression ?/(2/5)=4 where ?=x gives x=8/5.
what are expressions?
Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between. The mathematical operators can be of addition, subtraction, multiplication, or division. For example, x + y is an expression, where x and y are terms having an addition operator in between. In math, there are two types of expressions, numerical expressions - that contain only numbers; and algebraic expressions- that contain both numbers and variables.
e.g. A number is 6 more than half the other number, and the other number is x. This statement is written as x/2 + 6 in a mathematical expression. Mathematical expressions are used to solve complicated puzzles.
Now,
Given expression ? ÷ 2/5 = 4
let x=?
Therefore,
x=4*2/5
x=8/5
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The graph of (c•d)(x) is shown.
Plot a point at the ordered pair that represents (c•d)(4) on the graph of the combined function.
The ordered pair that represents (c•d)(4) on the graph of the combined function is (4, -12)
How to determine the graph of the ordered pair?From the question, we have the following parameters that can be used in our computation:
The graph
The function of the graph is a combined function (c . d)(x)
To calculate (c . d)(4), we trace the point x = 4 to the curve
So, we have
(c . d)(4) = -12
See attachment for the graph
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HELP ASAP (BRAINLIEST)
The table shows the relationship between the participants walking and running for the week's cross-country practices.
Walk (laps) 3 B 15
Run (laps) 5 10 D
Total (laps) A C 40
At this rate, how many laps will the participants walk if the total distance is 24 miles? How many miles will they run?
They will walk 7 laps and run 17 laps for a total of 24 miles.
They will walk 15 laps and run 9 laps for a total of 24 miles.
They will walk 9 laps and run 15 laps for a total of 24 miles.
They will walk 6 laps and run 18 laps for a total of 24 miles.
Option C. They will walk 9 laps and run 15 laps for a total of 24 miles.
How to calculate for the tableThe table is given as Walk (laps) 3 B 15
Run (laps) 5 10 D
Total (laps) A C 40
The total for walk and run is 3 + 5 = 8
Walk is 3
Run is 5
We are to find the laps of both categories with respect to the total distance of 24 miles
for walk = 3/8 * 24
= 9
For run we would have 5 / 8 * 24 = 15
Hence They will walk 9 laps and run 15 laps for a total of 24 miles.
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What is the intersection of y=2x-2 and y= -2x^2 +4x+ 3?
The intersection of equations y=2x-2 and y= -2x^2 +4x+ 3 is y = 3
How to determine the intersection of the linesThe general formula for the equation of a line is expressed as;
y = mx + c
Where the parameters are;
c is the intercept of the line on the y - axism is the slope of the linex is a point on the x-axisy is a point on the y -axisFrom the information given, we have the equation of the lines as;
y=2x-2 y= -2x^2 +5x+ 3Now, equate the lines, we have;
2x - 2 = -2x² + 5x + 3
collect the like terms
2x -5x + 2x² - 2 - 3 = 0
add the iike terms
2x² -3x - 5 = 0
Factorize the quadratic equation
2x² - 5x + 2x - 5 = 0
Group in pairs
(2x² - 5x) + (2x-5) = 0
x(2x -5) + 1(2x - 5) = 0
The intersection for when x = 5/2
y = 2x - 2
y = 2(5/2) - 2
y = 3
Hence, the value is 3
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What is the decimal expansion of the following fraction 1/3
The decimal expansion of the following fraction 1/3 would be; 0.33
What is a fraction?A fraction consisting of a quotient and remainder is a mixed fraction. we can convert the mixed fraction to improper fraction by first dividing the numerator by denominator and then taking the quotient as whole number and remainder as the numerator of proper fraction keeping the denominator same.
We need to find the expression of 1 divided by 3.
A negative divided by a negative is positive, then;
1/3 = 0.33
Therefore, The value of expression 1/3 would be; 0.33
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