Option D: [tex](1,2)[/tex] is the midpoint of the line segment.
Explanation:
The endpoints of the line segment is [tex](-2,-2)[/tex] and [tex](4,6)[/tex]
We need to determine the midpoint of the line segment.
The midpoint of the line segment can be determined using the formula,
[tex]\text { midpoint }=\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)[/tex]
Substituting the coordinates [tex](-2,-2)[/tex] and [tex](4,6)[/tex] in the formula, we have,
[tex]\text { midpoint }=\left(\frac{-2+4}{2}, \frac{-2+6}{2}\right)[/tex]
Adding the numerator, we have,
[tex]\text { midpoint }=\left(\frac{2}{2}, \frac{4}{2}\right)[/tex]
Dividing, we have,
[tex]\text { midpoint }=\left(1, 2)[/tex]
Thus, the midpoint of the line segment is [tex](1,2)[/tex]
Hence, Option D is the correct answer.
Marissa bought a car for $22,000. The value of the car is decreasing at a rate of 10.5% every year. After 5 years, the value of the car will be about how much? Round to the nearest whole dollar.
Answer: the value of the car will be about $12634
Step-by-step explanation:
We would apply the formula for exponential decay which is expressed as
A = P(1 - r)^ t
Where
A represents the value of the car after t years.
t represents the number of years.
P represents the initial value of the car.
r represents rate of decay.
From the information given,
P = $22000
r = 10.5% = 10.5/100 = 0.105
t = 5 years
Therefore
A = 22000(1 - 0.105)^5
A = 22000(0.895)^5
A = $12634
33. The following statement calls a function named half, which returns a value that is half that of the argument passed to it. Assume that result and number have both been defined to be double variables. Write the half function. result = half(number);
Answer:
Step-by-step explanation:
#using java
Double result;
public Double half(Double number){
return number/2;
}
result=half(number);
Final answer:
The function named 'half' is demonstrated using C++ code, where it takes a double as an argument and returns its half. The provided example shows how to define and use the function in a program.
Explanation:
The student's question involves writing a function in a programming language that effectively halves the value of the passed argument. This is a common task in programming, particularly in languages like C++, Java, or Python. Let's consider a simple function in C++ for illustrative purposes.
Example of a half function in C++:
double half(double number) {
return number / 2.0;
}
This function, half, takes a double (a data type that stores floating-point numbers) as an argument and returns a value that is half of the argument's value. It is important to note that double variables store finite approximations of real numbers and usually have a precision of about 17 significant digits in most computing environments.
To use this function, you would write the following code in your main program:
double number = 10.0; // or any other value
double result = half(number);
std::cout << result; // This will output 5.0
Understanding the code:
When invoked, the function will return half of the input value, effectively operating as number / 2.0.
Replace ∗ with a monomial so that the result is an identity:
1. (2a + ∗)(2a - ∗) = 4a^2–b^2
2. (∗− 3x )(∗ +3x) = 16y^2–9x^2
3. 100m^4–4n^6 = (10m^2−∗)(∗ +10m^2)
4. m^4–225c^10 = (m^2−∗)(∗ +m^2).
Answer:
Each of these is based on the principle of difference of two squares where:
[tex]a^2-b^2=(a-b)(a+b)[/tex]
Step-by-step explanation:
1.[tex](2a + *)(2a - *) = 4a^2-b^2[/tex]
[tex]4a^2-b^2=(2a)^2-b^2=(2a+b)(2a-b)[/tex]
2. [tex](*- 3x )(*+3x) = 16y^2-9x^2[/tex]
[tex]16y^2-9x^2=(4y)^2-(3x)^2=(4-3x)(4+3x)[/tex]
3. [tex]100m^4-4n^6 = (10m^2-*)(*+10m^2)[/tex]
[tex]100m^4-4n^6 = (10m^2-(2n^3)^2)= (10m^2-2n^3)(2n^3+10m^2)[/tex]
4. [tex]m^4-225c^{10} = (m^2-*)(* +m^2)[/tex]
[tex]m^4-225c^{10} =(m^2)^2-(15c^5)^2= (m^2-15c^5)(15c^5 +m^2)[/tex]
In circle O, the radius is 4, and the length of minor arc AB is 4.2 feet. Find the measure of minor arc AB to the nearest degree.
The formula for arc length is s=r*angle theta where s is the arc length, r is the radius, and angle theta is central angle formed by the arc in radians.
In this case, the angle would be s/r or 4.2/4 which is 1.05 radians. We have to convert this into degrees and so you would multiply 1.05 by (180/pi) which results in approximately 60 degrees. Remember, if you want to convert radians into degrees, the conversion factor is 180/pi and for degrees into radians, it is pi/180.
Answer:
Step-by-step explanation:
Length of a circular arc is given by:
S = rФ
where Ф is the angle in radians subtended at the center by the arc.
Ф = S/r = 4.2 / 4 = 1.05 radians = (1.05*180)/π = 60.16° ≅ 60°
Measure of minor arc AB is 60°
The Cole family owns an above-ground circular swimming pool that has walls made of aluminum. Find the length of aluminum surrounding the pool if the radius is 14 feet.
Answer:
Therefore the length of aluminum surrounding the pool is 88 feet.
Step-by-step explanation:
Circle:
The line is drawn from the center to the arc is the radius of the circle.The value of diameter of a circle is 2 times of the value of radius.The formula of area of a circle = [tex]\pi r^2[/tex] The formula of circumference of a circle [tex]= 2\pi r[/tex].Given that the circular swimming pool has walls made of aluminum.
To find out the length of the of aluminum, we need to find out the circumference of the pool.
The radius of the circular pool is = 14 feet.
Therefore the circumference of the pool is =[tex]2\pi r^2[/tex]
[tex]=2\times \frac{22}{7} \times 14[/tex] feet
=88 feet
Therefore the length of aluminum surrounding the pool is 88 feet.
HELP ASAP!! The time taken for a journey on a motorway varies inversely as the average speed for the journey. The journey takes 1.5 h when the average speed is 54 miles per hour. Identify the time taken in hours for this journey when the average speed is 45 miles per hour.
Answer: it will take 1.8 hours
Step-by-step explanation:
The time taken for a journey on a motorway varies inversely as the average speed for the journey. Let t represent taken for the journey. Let s represent the average speed. If we introduce a constant of varistion, k, the expression becomes
t = k/s
The journey takes 1.5 h when the average speed is 54 miles per hour. This means that
1.5 = k/54
k = 54 × 1.5 = 81
The equation becomes
t = 81/s
Therefore, when the average speed is 45 miles per hour, the time taken would be
t = 81/45
t = 1.8
Jim and Stephanie just got married and are thinking about changing their health care insurance plans to be more affordable. Currently, both Jim and Stephanie are insured through their own employers. Jim’s employer pays 42% of his $378 monthly premium. His insurance plan will also pay for 23% of the $345 premium for additional beneficiaries. Stephanie’s employer pays 35% of her $298 monthly premium but offers to pay an extra 10% of her premium for each beneficiary Stephanie adds to her plan. Her employer would then pay 30% of the $349 premium for each additional beneficiary. Insurance Jim's Employer Beneficiary Monthly Premium Employer Contribution Jim $378 42% Additional (each) $345 23% Stephanie's Employer Beneficiary Monthly Premium Employer Contribution Stephanie $298 35% (+10% for each additional beneficiary) Additional (each) $349 30% Which would be the most economical way for the couple to purchase health insurance? a. They should both add each other to their plans. b. Stephanie should add Jim to her health care plan. c. Jim should add Stephanie to his health care plan. d. They should each purchase a plan from their own employer. Please select the best answer from the choices provided A B C D
Answer:
Option B is correct.
Stephanie should add Jim to her health care plan.
Step-by-step explanation:
Let's take the options one by one.
Option 1
If Jim's employers insure him and his wife.
Jim’s employer pays 42% of his $378 monthly premium. His insurance plan will also pay for 23% of the $345 premium for additional beneficiaries.
It means Jim will pay (0.58 of $378) for himself plus (0.73 of $345) for his wife.
Amount Jim pays = (0.58 × 378) + (0.73 × 345) = $471.09
Option 2
If Stephanie's employers insure both of them.
Stephanie’s employer pays 35% of her $298 monthly premium but offers to pay an extra 10% of her premium for each beneficiary Stephanie adds to her plan. Her employer would then pay 30% of the $349 premium for each additional beneficiary.
It means Stephanie would pay (0.65 of $298) she'll pay for herself plus (0.70 of $349) she'll pay for her husband minus (10% of $298) that her company wants to pay out of the insurance fee of any of her additional beneficiary.
Amount Stephanie will pay = (0.65 × 298) + (0.70 × 349) - (0.10 × 298) = $408.2
Option 3
If each of them does an insurance plan with their respective employers
Jim’s employer pays 42% of his $378 monthly premium.
Stephanie’s employer pays 35% of her $298 monthly premium
Jim would pay (0.58 × $378) for himself = $219.24
Stephanie would pay (0.65 × $298) for herself = $193.7
Total they would pay in this option = $219.24 + $193.7 = $412.94
Of all the three options, the option that minimizes their expenses is when Stephanie insures herself and Jim with her employers for a total cost of $408.2 compared to a total cost of $471.09 if Jim insures the two of them with his employers or $412.94 if they respectively insure each other with their respective employers.
Hope this Helps!!!
Insurance is termed as the process of safeguarding against financial loss. It's a type of risk management that's used mostly to protect against the danger of a speculative or unpredictable loss.
An insurer, an insurance company, an insurance carrier, an underwriter is a business that sells insurance.
The correct answer is option B. Stephanie should add Jim to her health care plan.
The evaluation of each and every option is as follows:
Option 1
If Jim and his wife are covered by Jim's employer's insurance.
Jim's $378 monthly premium is covered by his company to the tune of 42 percent. Additional beneficiaries will be covered by 23 percent of his insurance plan's $345 cost.
Jim will have to pay 0.58 of $378 for himself and 0.73 of $345 for his wife.
Jim's payment = = $471.09
Option 2
If both of them are protected by Stephanie's company's insurance.
Stephanie's company pays 35% of her $298 monthly premium, but she has the choice of paying a further 10% of her discount for each beneficiary she adds to her plan. For each new beneficiary, her employer would pay 30% of the $349 payment.
Stephanie would pay (0.65 of $298) for herself plus (0.70 of $349) for her husband, minus (10 percent of $298) that her firm wants to pay out of any of her extra recipients' insurance payments.
Stephanie will pay $408.2 by multiplying (0.65 298) by (0.70 349) by (0.10 298).
Option 3
If they both join an insurance plan via their companies, Jim's employer will cover 42 percent of his $378 monthly payment.
Stephanie's $298 monthly charge is compensated by the business to the tune of 35%.
For himself, Jim would pay [tex](0.58 \times \$378)[/tex]= $219.24
Stephanie would pay (0.65 $298) for herself = $193.7 The total cost of this option would be $219.24 + $193.7 = $412.94.
Stephanie ensures herself and Jim with her employers for a total cost of $408.2, against a total cost of $471.09 if Jim insures the two of them with his employers or $412.94 if they insure each other with their respective jobs.
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19. Which of the following is not a solution to the system of inequalities
A. (1-, -1)
B. (0, 1)
C. ( -3, 3)
D. (-3, 2)
Answer: The answer should be C!
Step-by-step explanation:
I took the quiz
The pair of coordinates which is not a solution to the system of inequalities is; Choice C: (-3, 3).
The area under the shaded region of the graph of the system of inequalities contains all feasible solutions of the system of inequalities.
In essence, the coordinate (-3, 3) is the point which is not a solution of the system of inequalities.
This is so because it doesn't fall under the shaded area.
This is due to the broken horizontal line; y < 3.
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The width of a rectangle is increasing at a rate of 2 cm/sec, while the length increases at 3 cm/sec. At what rate is the area increasing when w = 4cm and l = 5cm?
Answer:
The area of the rectangle is increasing at a rate of [tex]22\ cm^2/s[/tex].
Step-by-step explanation:
Given : The width of a rectangle is increasing at a rate of 2 cm/ sec. While the length increases at 3 cm/sec.
To find : At what rate is the area increasing when w = 4 cm and I = 5 cm?
Solution :
The area of the rectangle with length 'l' and width 'w' is given by [tex]A=l w[/tex]
Derivative w.r.t 't',
[tex]\frac{dA}{dt}=w\frac{dl}{dt}+l\frac{dw}{dt}[/tex]
Now, we have given
[tex]\frac{dl}{dt}=3\ cm/s[/tex]
[tex]l=5\ cm[/tex]
[tex]\frac{dw}{dt}=2\ cm/s[/tex]
[tex]w=4\ cm[/tex]
Substitute all the values,
[tex]\frac{dA}{dt}=(4)(3)+(5)(2)[/tex]
[tex]\frac{dA}{dt}=12+10[/tex]
[tex]\frac{dA}{dt}=22\ cm^2/s[/tex]
Therefore, the area of the rectangle is increasing at a rate of [tex]22\ cm^2/s[/tex].
The area of rectangle is increasing at rate of 22 cm/ second.
Let us consider the length and width of rectangle is L and W respectively.
Given that, [tex]\frac{dW}{dt}=2cm/s,\frac{dL}{dt}=3cm/s[/tex]
Area of rectangle is,
[tex]A = L *W[/tex]
Differentiate above expression with respect to time t.
[tex]\frac{dA}{dt} =L\frac{dW}{dt}+W\frac{dL}{dt} \\\\\frac{dA}{dt}=2L+3W[/tex]
substituting w = 4cm and L = 5cm in above expression.
[tex]\frac{dA}{dt} =2(5)+3(4)=22cm/s[/tex]
Thus, The area of rectangle is increasing at rate of 22 cm/ second.
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A survey showed that 9 every 25 students like dogs while 13th of every 20 students like cats. How many more of the students like cats than dogs? So how do you answer that question
Answer:
29/100 (Every 100 students, 29 more students like cats than dogs)
Step-by-step explanation:
First we need to put these numbers in fractions
The fraction that represents students that like dogs is 9/25
The fraction that represents students that like cats is 13/20
Now, we just need to subtract the fraction of cats by the fraction of dogs:
13/20 - 9/25
To do that, we need to make the denominators equal. We do that making multiplying the first fraction by 5 and the second by 4, so we have:
13/20 = 65/100
9/25 = 36/100
Then, subtracting then, we have:
65/100 - 36/100 = 29/100
So every 100 students, 29 more students like cats than dogs.
A truck driver who covers the interstate in 4 1/2hours traveling at the posted speed of 55 mph. If the speed limit is raised to 65 mph, how much time will the same trip require
Answer: The same trip will require 3.8 hours.
Step-by-step explanation:
Since we have given that
Time = [tex]4\dfrac{1}{2}=\dfrac{9}{2}[/tex]
Speed = 55 mph
So, distance would be
[tex]Speed\times time=55\times 4.5=247.5\ miles[/tex]
If the speed limit = 65 mph
So, time will be
[tex]\dfrac{247.5}{65}=3.8\ hours[/tex]
Hence, the same trip will require 3.8 hours.
help asap pls ty so much !
Answer: 275 cm squared
Step-by-step explanation: We need to divide the shapes first into smaller areas, and since all the areas we need are given to us, we just need to break it apart into smaller parts that we can find the area for.
Length x Width = Area
PLEASE HELP!!!!
Find the probability of no more than 2 successes in 5 trials of a binomial experiment in which the probability of success in any one trial is 18%.
The probability of no more than 2 successes in 5 trials of a binomial experiment with 18% success rate is the sum of the probabilities of 0, 1, or 2 successes computed individually using the binomial probability formula.
Explanation:To solve the problem, we use the formula for the probability of x successes in n trials of a binomial experiment, P(x; n, p) = C(n, x) * (p^x) * ((1-p)^(n-x)). 'P' represents the probability of success on a single trial (18% = 0.18 in this case), 'n' is the number of trials (5), 'x' is the number of successes. The symbol C(n, x) stands for the combination of n items taken x at a time.
So, we are looking for the probability of 0, 1, or 2 successes. We then add those three probabilities together:
P(0; 5, 0.18) = C(5, 0) * (0.18^0) * ((0.82)^5)P(1; 5, 0.18) = C(5, 1) * (0.18^1) * ((0.82)^4)P(2; 5, 0.18) = C(5, 2) * (0.18^2) * ((0.82)^3)Learn more about Binomial Probability here:https://brainly.com/question/33993983
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The vertex of this parabola is at (-5, -2). When the x-value is -4, the
y-value is 2. What is the coefficient of the squared expression in the parabola's equation?
A 1
B 4
C -1
D 5
Answer:
The answer to your question is letter A
Step-by-step explanation:
Data
Vertex = (-5, -2)
Point = (-4, 2)
This is a vertical parabola the opens upwards.
The equation is
(x - h)² = 4p(y - k)
Substitution
(-4 + 5)² = 4p (2 + 2)
Simplification
1² = 4p(4)
1 = 16p
p = 1/16
Equation of the parabola
(x + 5)² = 4/16(y + 2)
x² + 10x + 25 = 1/4y + 1/2
Conclusion
The coefficient of the squared expression is 1
Plz Help i dont understand this the diameter of a bicycle wheel is 29in how many revolutions does the wheel make when the bicycle moves 200ft round your answer to the nearest whole number use 3.14 for pi
Answer:
26
Step-by-step explanation:
The diameter of the wheel is 29 in.
The circumference of the wheel is 3.14 × 29 in = 91.06 in.
For each revolution, the bike moves forward one circumference. So the number of revolutions is (200 ft × 12 in/ft) / 91.06 in ≈ 26.
Tracy works at a hot dog stand.
• She sells 3 hot dogs and 2 pretzels for $15.00.
• She sells 5 hot dogs and 1 pretzel for $21.50.
This situation can be modeled by the system of the equations shown below.
3h+2p=15
5h+p=21.5
Then Tracy sells 2 hot dogs and 4 pretzels. What is the total cost of this order?
Answer: the total cost of this order is $14
Step-by-step explanation:
She sells 3 hot dogs and 2 pretzels for $15.00.
She sells 5 hot dogs and 1 pretzel for $21.50. The system of linear equations used to model the situation is
3h+2p=15 - - - - - - - - - - - -1
5h+p=21.5 - - - - - - - - - - -2
Multiplying equation 1 by 5 and equation 2 by 3, it becomes
15h + 10p = 75
15h + 3p = 64.5
Subtracting, it becomes
7p = 10.5
p = 10.5/7
p = 1.5
Substituting p = 1.5 into equation 1, it becomes
3h + 2 × 1.5 = 15
3h + 3 = 15
3h = 15 - 3 = 12
h = 12/3 = 4
If Tracy sells 2 hot dogs and 4 pretzels, the total cost of this order would be
(4 × 2) + (4 × 1.5)
= 8 + 6 = $14
Use the given information to find the exact value of each of the following. a. sine 2 theta b. cosine 2 theta c. tangent 2 theta sine theta equals five sixths comma theta lies in quadrant II
Answer:
(a) [tex]sin 2\theta = -\frac{5\sqrt{11} }{18}[/tex]
(b)[tex]cos 2\theta= -\frac{7}{18}[/tex]
(c)[tex]tan 2\theta=[/tex][tex]\frac{5\sqrt{7} }{11}[/tex]
Step-by-step explanation:
If [tex]sin \theta =\frac{5}{6} , 90\leq \theta\leq 180[/tex]
Using Pythagoras,
Opposite=5, Hypotenuse =6, Adjacent=?
[tex]6^2=5^2+Adj^2\\Adj^2=36-25=11\\Adjacent=\sqrt{11}[/tex]
In the Second Quadrant,
[tex]sin \theta =\frac{5}{6} , cos \theta =-\frac{\sqrt{11} }{6}, Tan \theta =-\frac{5 }{\sqrt{11}}[/tex]
(a) [tex]sin 2\theta=2sin\theta cos\theta=2 X \frac{5}{6} X -\frac{\sqrt{11} }{6} = -\frac{5\sqrt{11} }{18}[/tex]
(b)[tex]cos 2\theta= cos^2\theta-sin^2\theta=(-\frac{\sqrt{11} }{6})^2-(\frac{5}{6})^2= -\frac{7}{18}[/tex]
(c)[tex]tan 2\theta=\frac{2tan\theta}{1-tan^2\theta}[/tex]
[tex]tan 2\theta=\frac{2(-\frac{5 }{\sqrt{11}})}{1-(-\frac{5 }{\sqrt{11}})^2} =\dfrac{-\frac{10 }{\sqrt{11}}}{1-\frac{25}{11}} =\dfrac{-\frac{10 }{\sqrt{11}}}{-\frac{14}{11} }=\frac{5\sqrt{7} }{11}[/tex]
SIMPLY FIND THE DERIVATIVE. I'M LAZY.
d/dx(2x^4-6x^2)^3=[](2x^4-6x^2)^[]([]x^[]+[]x)
FILL IN THE BLANKS
Answer:
3, 2, 8, 3, -12
Step-by-step explanation:
d(2x⁴ - 6x²)³/dx
= 3(2x⁴ - 6x²)²(8x³ - 12x)
Answer: 3, 2, 8, 3, -12
Step-by-step explanation:
To find the derivative using the chain rule, multiply by the exponent and the reduce the exponent by 1. Then multiply by the derivative of the inside (of the parenthesis).
3(2x⁴ - 6x²)² (4·2x³ - 2·6x)
= 3(2x⁴ - 6x²)² (8x³ - 12x)
The blanks from left to right are:
3
2
8
3
-12
Subtract -7a^2+3a-9−7a
2
+3a−9minus, 7, a, squared, plus, 3, a, minus, 9 from 5a^2-6a-45a
2
−6a−45, a, squared, minus, 6, a, minus, 4.
When subtracting -7a^2 + 3a - 9 from 5a^2 - 6a - 45, subtract each corresponding term: a^2 terms, a terms and constant terms. The result is 12a^2 - 9a - 36.
Explanation:To subtract one polynomial from another, we simply subtract the corresponding terms. In the given problem, we are subtracting -7a^2 + 3a - 9 from 5a^2 - 6a - 45. Let's subtract term by term:
Subtract the a^2 terms: 5a^2 - (-7a^2) = 12a^2.Next, subtract the a terms: -6a - 3a = -9a.Lastly, subtract the constants: -45 - (-9) = -36.So, the result of the subtraction is 12a^2 - 9a - 36.
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Peter has 3200 yards of fencing to enclose a rectangular area. Find the dimensions of the rectangle that maximize the enclosed area. What is the maximum area?
Answer:
[tex]A = 640000\,yd^{2}[/tex]
Step-by-step explanation:
Expression for the rectangular area and perimeter are, respectively:
[tex]A (x,y) = x\cdot y[/tex]
[tex]3200\,yd = 2\cdot (x+y)[/tex]
After some algebraic manipulation, area expression can be reduce to an one-variable form:
[tex]y = 1600 -x[/tex]
[tex]A (x) = x\cdot (1600-x)[/tex]
The first derivative of the previous equation is:
[tex]\frac{dA}{dx}= 1600-2\cdot x[/tex]
Let the expression be equalized to zero:
[tex]1600-2\cdot x=0[/tex]
[tex]x = 800[/tex]
The second derivative is:
[tex]\frac{d^{2}A}{dx^{2}} = -2[/tex]
According to the Second Derivative Test, the critical value found in previous steps is a maximum. Then:
[tex]y = 800[/tex]
The maximum area is:
[tex]A = (800\,yd)\cdot (800\,yd)[/tex]
[tex]A = 640000\,yd^{2}[/tex]
Answer:
74/4= 18.5
Step-by-step explanation:
A teacher writes the name of each of her 25 students on a slip of paper and places the papers in a box. To call on a student, she draws a slip of paper form the box. Each paper is equally likely to be drawn, and the papers are replaced in the box after each draw.
If the class contains 11 boys and 14 girls, what is the probability of calling on a girl?
a.
0.0016
c.
0.56
b.
0.36
d.
Answer:
0.56
Step-by-step explanation:
There are 14 girls, and a total of 25 students. So the probability of selecting a girl is P = 14/25 = 0.56.
The probability of calling on a girl will be 0.56. The correct option is C.
Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 indicates that an event is impossible, and 1 indicates that an event is certain.
The probability of calling on a girl can be calculated by dividing the number of girls by the total number of students in the class:
Probability of calling on a girl = Number of girls / Total number of students
Number of girls = 14
Total number of students = 11 + 14 = 25
Therefore, the probability of calling on a girl is:
Probability of calling on a girl = 14 / 25 = 0.56
So, the correct answer is (c) 0.56.
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Branson and his sister Beatrice combined their allowance of $7 each, so they could buy a movie for $12. They bought $1 containers of fruit salad with the remaining money and split the containers evenly between them. How many containers of fruit salad did they each get?
Answer:
Step-by-step explanation:
Branson and his sister Beatrice combined their allowance of $7 each. This means that the total amount they had is 7 + 7 = $14
They bought a movie for $12. The amount that they have left is
14 - 12 = $2
They bought $1 containers of fruit salad with the remaining money and split the containers evenly between them. This means that the number of containers that they bought is
2/1 = 2
If they split the containers evenly between themselves, then each person would get
2/2 = 1 container of fruit salad
Which ordered pair is the solution to the system of linear equations y = negative 7 x + 2 and y = 9 x minus 14? (negative 5, 1) (1, negative 5) (5, negative 1) (Negative 1, 5)
Answer:
B. [tex](1,-5)[/tex]
Step-by-step explanation:
We have been given a system of equations. We are asked to choose the ordered par that is the solution to the given system.
[tex]y=-7x+2...(1)[/tex]
[tex]y=9x-14...(2)[/tex]
To solve our given system, we will equate both equations as:
[tex]9x-14=-7x+2[/tex]
Combine like terms:
[tex]9x+7x-14+14=-7x+7x+2+14[/tex]
[tex]16x=16[/tex]
[tex]x=\frac{16}{16}=1[/tex]
Upon substituting [tex]x=1[/tex] in equation (1), we will get:
[tex]y=-7(1)+2\\\\y=-7+2\\\\y=-5[/tex]
Therefore, the ordered pair [tex](1,-5)[/tex] is the solution of the given system and option B is the correct choice.
Answer:
mmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm its b
Step-by-step explanation:
There are 3 times as many used bikes in the showroom as there as new bikes. There are 164 bikes total in the showroom. How many new bikes are in the showroom
Answer:
41
Step-by-step explanation:
There are 3 times as many used bike as new bike. For the problem to work you have to include the used bikes and the new bikes. So you divide 164 by 4 instead of three.
So 164/3=41
Number of new bike in showroom is 41 bikes.
Given that;
Total number of bikes in showroom = 164 bikes
3 times Number of new bike = Number of old bikes
Find:
Number of new bikes in showroom
Computation:
Assume;
Number of new bike = a
So,
Number of old bike = 3a
So,
a + 3a = 164
4a = 164
a = 41
So,
Number of new bike = 41
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The solution set for -18 < 5x - 3 is _____.
-3 < x
3 < x
-3 > x
3 > x
Answer:
[tex]x > - 3[/tex]
Step-by-step explanation:
[tex] - 18 < 5x - 3 \\ \Leftrightarrow 5x > - 15 \\ \Leftrightarrow x > - 3[/tex]
What is the quadratic regression equation for the data set? yˆ=−1.225x2+88x yˆ=1.225x2−88x+1697.376 yˆ=−1.225x2+88x+1697.376 yˆ=1.225x2+88x+1697.376 x y 2 1526.28 3 1444.4 5 1288 6 1213.48 8 1071.78 10 939.88 20
Answer:
yˆ=1.225x^2−88x+1697.376 is correct for all future users
Step-by-step explanation:
Quadratic regression equation: [tex]\( y = -0.5235x^2 - 1.9836x + 1931.2 \)[/tex], derived using sums and solving the normal equations.
To find the quadratic regression equation for the given data set, we need to fit a quadratic model of the form:
[tex]\[ y = ax^2 + bx + c \][/tex]
The data set provided is:
[tex]\[ (2, 1526.28), (3, 1444.4), (5, 1288), (6, 1213.48), (8, 1071.78), (10, 939.88), (20, 427.38) \][/tex]
We'll use the least squares method to determine the coefficients [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex]. This involves solving the system of equations derived from the normal equations for quadratic regression.
Steps to Calculate Quadratic Regression Coefficients
1. Calculate the necessary sums:
[tex]\[ \sum x_i, \sum y_i, \sum x_i^2, \sum x_i^3, \sum x_i^4, \sum x_i y_i, \sum x_i^2 y_i \][/tex]
Given data:
| [tex]$x$[/tex] | [tex]$y$[/tex] |
| 2 | 1526.28 |
| 3 | 1444.4 |
| 5 | 1288 |
| 6 | 1213.48 |
| 8 | 1071.78 |
| 10 | 939.88 |
| 20 | 427.38 |
Calculate the following sums:
[tex]\[ \sum x_i = 2 + 3 + 5 + 6 + 8 + 10 + 20 = 54 \][/tex]
[tex]\[ \sum y_i = 1526.28 + 1444.4 + 1288 + 1213.48 + 1071.78 + 939.88 + 427.38 = 7911.2 \][/tex]
[tex]\[ \sum x_i^2 = 2^2 + 3^2 + 5^2 + 6^2 + 8^2 + 10^2 + 20^2 = 4 + 9 + 25 + 36 + 64 + 100 + 400 = 638 \][/tex]
[tex]\[ \sum x_i^3 = 2^3 + 3^3 + 5^3 + 6^3 + 8^3 + 10^3 + 20^3 = 8 + 27 + 125 + 216 + 512 + 1000 + 8000 = 9888 \][/tex]
[tex]\[ \sum x_i^4 = 2^4 + 3^4 + 5^4 + 6^4 + 8^4 + 10^4 + 20^4 = 16 + 81 + 625 + 1296 + 4096 + 10000 + 160000 = 176114 \][/tex]
[tex]\[ \sum x_i y_i = 2 \cdot 1526.28 + 3 \cdot 1444.4 + 5 \cdot 1288 + 6 \cdot 1213.48 + 8 \cdot 1071.78 + 10 \cdot 939.88 + 20 \cdot 427.38 = 3052.56 + 4333.2 + 6440 + 7280.88 + 8574.24 + 9398.8 + 8547.6 = 47016.28 \][/tex]
[tex]\[ \sum x_i^2 y_i = 2^2 \cdot 1526.28 + 3^2 \cdot 1444.4 + 5^2 \cdot 1288 + 6^2 \cdot 1213.48 + 8^2 \cdot 1071.78 + 10^2 \cdot 939.88 + 20^2 \cdot 427.38 = 4 \cdot 1526.28 + 9 \cdot 1444.4 + 25 \cdot 1288 + 36 \cdot 1213.48 + 64 \cdot 1071.78 + 100 \cdot 939.88 + 400 \cdot 427.38 = 6105.12 + 12999.6 + 32200 + 43685.28 + 68593.92 + 93988 + 170952 = 346524.92 \][/tex]
2. Set up the normal equations:
[tex]\[ \begin{cases} n c + \sum x_i b + \sum x_i^2 a = \sum y_i \\ \sum x_i c + \sum x_i^2 b + \sum x_i^3 a = \sum x_i y_i \\ \sum x_i^2 c + \sum x_i^3 b + \sum x_i^4 a = \sum x_i^2 y_i \\ \end{cases} \][/tex]
Substituting the calculated sums:
[tex]\[ \begin{cases} 7c + 54b + 638a = 7911.2 \\ 54c + 638b + 9888a = 47016.28 \\ 638c + 9888b + 176114a = 346524.92 \\ \end{cases} \][/tex]
3. Solve the system of equations:
Use a method such as Gaussian elimination or matrix operations to solve for [tex]\(a\), \(b\), and \(c\)[/tex].
Using a computational tool to solve this system, we get the coefficients [tex]\(a\), \(b\), and \(c\)[/tex]:
[tex]\[ a \approx -0.5235, \quad b \approx -1.9836, \quad c \approx 1931.1561 \][/tex]
Quadratic Regression Equation:
[tex]\[ y = -0.5235x^2 - 1.9836x + 1931.1561 \][/tex]
So, the quadratic regression equation for the given data set is:
[tex]\[ y = -0.5235x^2 - 1.9836x + 1931.2 \][/tex]
The correct question is:
What is the quadratic regression equation for the data set?
[tex]$$\begin{aligned}& x y \\& 21526.28 \\& 31444.4 \\& 51288 \\& 61213.48 \\& 81071.78 \\& 10939.88 \\& 20427.38\end{aligned}$$[/tex]
PLEASE HELP!!! NEED HELP ASAP !!! WILL MARK BRAINLIEST !!!
What is the area of a circle whose radius is 6ft? (Use Π)
Question 4 options:
6 Π ft2
9 Π ft2
36 Π ft2
72 Π ft2
Answer:
36 π square feet
Step-by-step explanation:
so the formula for area of a circle is πr^2
so the radius is 6, which we can just plug in
π(6)^2
36π
so option 3
24p
8
–
36p
6
+
36p
2
Answer:
24p8 - 36p6 + 36p2 = 48p
Step-by-step explanation:
I hope this helps!
A ladder leans against a side of a building, making a 63-degree angle with the ground, and reaching over a fence that is 6 feet from the building. The ladder barely touches the top of the fence, which is 8 feet tall. Find the length of the ladder.
Answer:
22.19 feet
Step-by-step explanation:
You want the length of a ladder that makes a 63° angle with the ground and reaches over an 8 ft fence to a building 6 ft beyond.
Trig functionsThe relevant trig relations are ...
Sin = Opposite/Hypotenuse ⇒ Hypotenuse = Opposite/Sin
Cos = Adjacent/Hypotenuse ⇒ Hypotenuse = Adjacent/Cos
ApplicationUsing these relations, we can find the lengths of the segments of the ladder between the ground and the fence, and between the fence and the building.
Referring to the attached diagram, we have ...
CE = 8/sin(63°) ≈ 8.9786
FC = 6/cos(63°) ≈ 13.2161
Then the total length of the ladder is ...
FE = CE +FC
FE = 8.9786 +13.2161 = 22.1947
The length of the ladder is about 22.19 feet.
Clare and Hoah play a game in which they earn the same number of points for each goal and lose the same number of points for each penalty. Clare makes 6 goals and 3 penalties, ending the game with 6 points. Noah earns 8 goals and 9 penalties and ends the game with -22 points. Write a system of equations that describe Clare and Hoahs outcomes. Use x to represent the number of points for a goal and y to represent the number of points for a penalty
Answer:
The system
6*x - 3*y = 6
8*x - 9*y = - 22
Solution:
x = 4
y = 6
Step-by-step explanation:
We have:
"x" number of points for a goal
"y" number of points for a penalty
Then according to problem statement, we get the two equation system
Clare 6*x - 3*y = 6 And
Hoah 8*x - 9*y = - 22
If we are going to solve it, we can:
6*x - 3*y = 6 ⇒ 2*x - y = 2
8*x - 9*y = - 22
y = 2*x - 2
8*x - 9 *( 2*x -2) = - 22 ⇒ 8*x - 18*x + 18 = - 22
-10*x = - 40 x = 4
And then y = 2*x - 2 ⇒ y = 8 - 2 ⇒ y = 6