Therefore ,the the the work done in propelling a 10-ton satellite to a height of 200 miles above Earth is 1904.7619 million ton.
Analyze the equation.An expression is composed of a number, a variable, both, or neither, and specific operation symbols. An equation is made up of two expressions, which are separated by an equal sign.
Here,
Use F(x) = C/[tex]x^{2}[/tex]
Where c is a constant and x is the radius of the earth
F(x) is satellite weight
We have to find c.
thus,
=> 10 = c /[tex]4000^{2}[/tex]
=> c =160000000
Therefore,
=> F(x) = 160000000/ [tex]x^{2}[/tex]
Workdone ,
=> W = [tex]\int\limits^{4200}_{4000} {F(x)} \, dx[/tex]
=>W = [tex]\int\limits^{4200}_{4000} {160000000 /x^{2} } \, dx[/tex]
=>W =[tex]\left \{ {{4200} \atop {4000}} \right. \frac{-160000000 }{x}[/tex]
=> W =1904.7619 million ton
Therefore ,the the the work done in propelling a 10-ton satellite to a height of 200 miles above Earth is 1904.7619 million ton.
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Why did he write (x+4), even though the root
is at negative 4?
The reason behind this is that when the negative root goes from the RHS to LHS, its sign gets converted, and it appears like (x + 4).
What is the quadratic equation?A 2nd equation in x is known as a quadratic function. Ax2 + bx + c = 0 is the quadratic equations in standard form, wherein there a and b are the coefficient, x is the constant, and c is the constant.
The presence of a non-zero component in the coefficient of x2 (a ≠ 0) is the first prerequisite for an expression to be a quadratic equation.
As per the given information in the question,
The root obtained is -4 or,
We can also write this thing as,
x = -4
So, when -4 will come to the LHS the sign will be converted to positive, and then it can be written as (x + 4).
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2x - y = 20
2x + y = 48
Answer:
Below
Step-by-step explanation:
2x-y = 20
2x + y = 48 add the two equations to get
4x = 68
x = 17 <==== use this value in either equation to calculate y = 14
PLS HELP ASAP pic attached
The slope and y-intercept, or the points, should be used to graph the line. Slope: 3 y-intercept: (0, 1 )
How to find the Calculation?g ( x ) = − 3 x − 1
Create an equation using the function.
y = − 3 x − 1
Calculate the slope and y-intercept using the slope-intercept form.
Less steps by tapping...
In the slope-intercept form, y = m x + b denotes the slope and the y-intercept, respectively.
y = m x + b
With the use of the formula y = m x + b, determine the values of m and b.
m = − 3 b = − 1
m is the line's slope, and is the value of the y-intercept.
B. Slope: 3 Y-intercept: (0, 1 )
Two points are all that are required to graph any line. To determine the associated y values, enter two x values into the equation.
Less steps by tapping...
Assign the x and y values to a table.
x y
0 − 1
1 − 4
The slope and y-intercept, or the points, should be used to graph the line.
Slope: 3 y-intercept: (0, 1 )
x y
0 1
1 4.
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In 1950, a U.S. population
model
was y = 151. (1.013)^t-1950 million
people, where t is the year. What did
the model predict the U.S. population
would be in the year 2000?
In a case whereby In 1950, a U.S. population model was y = 151. (1.013)^t-1950 million people, where t is the year, the model predict the U.S. population would be 288 million in the year 2000.
What is population model ?Population models are mechanical theories that link alterations in population structure and density to responses at the individual level (life history features in eco-evolutionary theory or vital rates in demographic theory).
The model was given as y=151x(1.013)^t-1950
where the future time t = 2000
Then we can substitute the given year 2000 as the value of 't'
then we will have y=[151x(1.013)^(2000-1950)] = 288 million
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Mark car can travel 22 km per liter of gas gas cost 200 per liter how many kilometers can mark travel on 1000 worth of gas
Mark can travel a distance of 110 km on 1000 worth of gas.
Mathematical operations:The operations that we use in daily life are problems like adding, subtracting adding multiple times, and dividing things are called Mathematical operations.
The four basic mathematical operations are
1. Adding, 2. Subtracting, 3. Multiplication, and 4. Division.
Here in this problem, we use Multiplication and Division to solve the
Here we have
Mark car can travel 22 km per liter of gas costs 200 per liter
Here we need to find how many kilometers can mark travel on 1000 worth of gas
Given the cost of 1 liter of gas = 200 Rs
=> Amount gas that can be worth 1000 = 1000/200 = 5 liter
Given Mark can travel 22 km with 1 liter
The distance can be travel with 5 liters = 5 × 22 = 110 km
Therefore,
Mark can travel a distance of 110 km on 1000 worth of gas.
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Ida wants to know if males and females prefer different brands of ready-made chocolate-chip cookie dough. She bakes eight dozen cookies from dough made by each of four manufacturers which she labels brands A, B, C, and D. She then selects a simple random sample of 96 students, records their gender, gives them one cookie of each brand and asks which brand they like best. Here are her results:
9. The conditional distribution for preferred cookie brand among males (in percents) is given by which of the following?
A. A: 27%; B: 19%; C: 25%; D: 29%
B. A: 4%; B: 6%; C: 13%; D: 15%
C. A: 11%; B: 16%; C: 34%; D: 39%
D. A: 23%; B: 13%; C: 11%; D: 14%
E. A: 38%; B: 21%; C: 19%; D: 22%
They like best brand C) A: 11%; B: 16%; C: 34%; D: 39%.
What is probability ?
Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.
Have given ,
Ida made four brands A , B , C and D
Mostly students like A brand 11% , B brand 16% , C brand 34% and D brand 39%
So this is best brand like by students male and female
They like best brand C) A: 11%; B: 16%; C: 34%; D: 39%.
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A recipe requires 3 cups of flour to make 15 servings and 7 cups of flour to make 35 servings how many cups of flour are needed to make 20 servings?
Answer:
a = 8
b = 2
c = 48
Step-by-step explanation:
3 cups of flour is needed to make 24 servings.
3:24
Simplify. First, divide 3 from both sides of the ratio.
(3)/3 : (24)/3
1:8
Next, solve for b. You multiply 2 to 8 to get 16. Next, multiply 2 to 1
1 x 2 = b = 2
Finally, multiply 8 to 6 to get c.
8 x 6 = c = 48
~
HELP ASAP!!!
1. Give the equation of the least-squares regression line. Define any variables you use.
2. Use the model from part (a) to predict the area covered by detergent at 5.5 seconds.
3. Based on the residual plot, do you expect the prediction you made in part (b) to underestimate or
overestimate the area covered by detergent? Justify your answer.
4. Is the least-squares regression line an appropriate model for these data? Justify your answer.
Answer:
When you run a regression, calculating and plotting residuals help you understand and improve your regression model. In this post, we describe the fitted vs residuals plot, which allows us to detect several types of violations in the linear regression assumptions. You may also be interested in qq plots, scale location plots, or the residuals vs leverage plot.
Step-by-step explanation:
Solve for x using the quadratic formula: x² - 6x + 9 = 0
X=
-b± √b²-4ac
2a
Ox=6
Ox=3
Ox=1
Ox=0
Answer:
[tex] \huge{ \boxed{x = 3}}[/tex]
Step-by-step explanation:
[tex] {x}^{2} - 6x + 9 = 0[/tex]
Using the quadratic formula that's,
[tex] \bold{x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a}} \\ [/tex]
Comparing the equation to the general form of a quadratic equation ( ax² + bx + c), we have.
[tex]a = 1 \\ b = - 6 \\ c = 9[/tex]
Substituting the values into the formula we have.
[tex]x = \frac{- ( -6) \pm \sqrt{( - {6})^{2} - 4(1)(9) } }{2(1)} \\ x = \frac{6 \pm \sqrt{36 - 36} }{2} \\ x = \frac{ 6 \pm\sqrt{0} }{2} \\ x = \frac{6}{2} \: \: \: \: \: \\ \\ x = 3 \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]
We have the final answer as
x = 3
Sami asked 50 people which drinks they liked from tea, coffee and milk.
All 50 people like at least one of the drinks
19 people like all three drinks.
16 people like tea and coffee but do not like milk. 21 people like coffee and milk.
24 people like tea and milk.
40 people like coffee.
1 person likes only milk.
Sami selects at random one of the 50 people. Work out the probability that this person likes tea.
Answer:
30
Step-by-step explanation:
not sure might be wrong lol soz
QUESTION ISDOWN BELOW
The Answers to the Question are solved below.
What is Cube root?A number's cube root is the factor that we multiply three times to get that number.
The symbol for cube root is 3 cube root of, end cube root(∛) .
Given:
1. [tex]5^{-2[/tex]
Using Exponents
[tex]a^{-m[/tex] = 1 / [tex]a^m[/tex]
So, [tex]5^{-2[/tex] = 1/5² = 1/25.
2. z+ 5= 12
z= 12-5
z= 7
3. Pythagorean triplet: m²-1, 2m, m²+1
2m= 6
m=3
and, m²-1 = 9-1= 8
and, m²+1 = 9+1= 10
3. Cube root of 64 = ∛64= ∛(4 x 4 x 4)= 4
4. 4z+ 3= 6+ 2z
2z = 3
z= 3/2
5. a- b+ ab, b- c + bc, c- a +ac
Adding: (a- b+ ab) + (b- c + bc) + (c- a +ac)
= ab+ bc+ ac
6. -1 x -2/5
= 2/5
The Multiplicative inverse = -5/2
7. y+3 = 10
y=7
8. 10³= 10 x 10 x 10= 1000
9. [tex]3^{-2[/tex]
= 1/3²
= 1/9
10. Volume = Base Area x height
900 = 180 h
h= 900/180
h = 5
11. 16 as sum of 4 add number
= 1 + 3 + 5 + 7
12. 78 x 82
(80- 2)(80+ 2)
= 80² - 2²
= 6400 - 4
= 6396
13. 2/3 x 100
= 200/3 %
14. (ab- bc)+ (bc - ca) + (ca- ab)
= [tex](-4)^5[/tex] ÷ [tex](-4)^8[/tex]
= [tex](-4)^{5-8}[/tex]
= [tex](-4)^{-3[/tex]
15. 4p² - 9q²
= (2p)² - (3q)²
= (2p - 3q) (2p + 3q)
16. 2y-1 = 14- y
3y= 15
y= 5
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Expand the polynomial (x + y)7 and write the coefficients of the terms.
Answer:
7x+7y siuuuuuuuuuuuuuuuuu
125x ^ 3 - 27 = 0
Solve this by grouping
The solution to the equation 125x³ - 27 = 0 is (5x−3)(25x ^2 +15x+9)
What is an equation?An equation is a mathematical expression that contains an equals symbol. Equations often contain algebra. Algebra is used in mathematics when you do not know the exact number in a calculationsolving the equation 125x³ - 27 = 0 by grouping
Rewriting 125x^ 3 −27 as (5x) ^3 −3³
The difference of cubes can be factored using the rule:: a ^3 −b^ 3 =(a−b)(a^ 2 +ab+b^ 2 )
Polynomial 25x^ 2 +15x+9 is not factored since it does not have any rational roots.
Hence, (5x−3)(25x ^2 +15x+9)
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the following is a listing of the amount of sugar in six popular snacks found on a high school campus: 35g 35g 43g 49g 52g 53g what is the median?
The median is 43 g. By using median formula and by simple observation method we can find median of the given data.Hence median is 43 g.
What is median?The middle number ,by ordering all data points and picking out the one in the middle.Arrange the all values from lowest to highest.Then we can find easily.Median is also type of average which is used to find centre value.
What is the formula we use to find median?There are the following formula we use to find median.
Median= (n+1)th/2 terms (if n is odd)
Where n is the number of observations.
So,if n is even then we use
Median= (n/2)th terms
if number of term is even,then the median is the simple average of the middle two numbers.
So we can find median by two methods
median= n/2 -th term
median =6/2 -th term
median = 3-th term
Hence our third term is 43 g so our median will be 43 g.
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Suppose that the function h is defined, for all real numbers, as follows.
=hx +−12x24 ≠if x2
−2 =if x2
Find h−3, h2, and h4.
The function h is defined, for all real numbers h(-3) = -1/2 , h(2) = -2 and h(4) = -4.
What is a function ?
When it comes to arithmetic, a function is represented as a rule that produces a different result for each input x. Mathematicians refer to functions as mapping or transformations.
The given function,
h(x) = -1/2 x^2 + 4 if x≠ 2
-2 if x=2
So, h(-3) = -1/2 (-3)^2 + 4
= - 9/2 + 4
= -1/2
h(2) = -2 ( given )
h(4) = -1/2 (4)^2 + 4
= -8 + 4
= -4 .
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If tan x = 3/4 find sin x and cos x.
Step-by-step explanation:
tan(x) = sin(x)/cos(x) = 3/4
in the trigonometric triangle sin(x) and cos(x) are the legs, and the radius is the Hypotenuse, the baseline (opposite of the 90° angle).
so, we can use Pythagoras to find the radius.
c² = a² + b²
with c being the Hypotenuse, a and b being the legs.
let's stay integer.
if sin(x) is equivalent to 3, and cos(x) to 4, then what is the radius ?
3² + 4² = c²
9 + 16 = c²
25 = c²
c = radius = 5
so,
3 = sin(x) × 5
4 = cos(x) × 5
sin(x) = 3/5 = 0.6
cos(x) = 4/5 = 0.8
The value of sin x is 3/5 and the value of cos x is 4/5.
What are trigonometry ratios?
The trigonometric functions in mathematics are real functions that connect the right-angled triangle's angle to the ratios of its two side lengths. They are extensively employed in all fields of geometry-related study, including geodesy, solid mechanics, celestial mechanics, and many others.
Given that tan x = 3/4.
The tangent of an angle is the ratio of height to the base of the right triangle.
Here the height of the triangle is 3 and the base is 4.
According to the Pythagorean theorem, the square of the hypotenuse is equal to the sum of the square of the base and height.
Thus,
hypotenuse = √(3² + 4²)
hypotenuse = 5.
The sine of an angle is the ratio of height to the hypotenuse.
Sin x = Height/ hypotenuse
sin x = 3/5
The cosine of an angle is the ratio of the base to the hypotenuse.
cos x = base/ hypotenuse
cos x = 4/5
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PLEASE HELP!! I will mark Brainliest
The expression to the scenario it's represent is as follows:
The price of a USB memory stick selling at 21% discount off it marked price(m) → 0.21m
The price of Cd that sells for 21% more than the amount (m) needed to manufacture the CD → 1.21m.
The final value of painting after the initial value, m increases by 2 / 5 → 7 / 5 m.
The total number of markers Nancy have if she gives away 2 / 5 of her m markers to Amy → 3 / 5 m
What is expression?An algebraic expression is made up of variables and constants, along with algebraic operations like subtraction, addition, multiplication and division.
Therefore, let's match the algebraic expression with the scenario.
The price of a USB memory stick selling at 21% discount off it marked price(m).
Hence, the expression is 21% of m = 21 / 100 m = 0.21m
The price of Cd that sells for 21% more than the amount (m) needed to manufacture the CD.
Hence, the expression is 21%m + m = 0.21m + m = 1.21m.
The final value of painting after the initial value, m increases by 2 / 5.
Hence, the expression is 2 / 5 m + m = 7 / 5 m.
The total number of markers Nancy have if she gives away 2 / 5 of her m markers to Amy.
Hence, the expression is m - 2 / 5 m = 3 / 5 m.
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I need help asap i don’t get it
∠SWV is congruent to ∠TWU because vertically opposite angle.
Define congruent.If one of the geometric figures can be superimposed on the other so that their entire surface coincides, then the two are said to be congruent, or to be in the relation of congruence. Two triangles are said to be congruent if their two sides and their included angle are the same in both of them. Congruence appears to be based on the concept of a "rigid body," which may be transported from one location to another without affecting the internal relationships between its components.
Given
∠SWV ≅ ∠TWU
Vertically opposite angle
∠SWV is congruent to ∠TWU because vertically opposite angle.
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on Monday Therease went to the doctor and got an antibiotic for strep throat. The doctor told her take a dose of 4.8 ml every 12 hours for 7 days. If Thereas took her first dose at 9:00 AM on Monday, what day and time should she take her 7th dose?
Theresa should take her 7th dose at 9:00 AM on Friday.
What are arithmetic operations?
Arithmetic operations is a branch of mathematics that studies numbers and the operations on numbers that are useful in all other branches of mathematics. It consists primarily of operations like addition, subtraction, multiplication, and division.
we have,
The doctor told her to take a dose of 4.8 ml every 12 hours for 7 days.
If Theresa took her first dose at 9:00 AM on Monday,
Simply add 12 hours every time up to the 7th dose,
First dose ----> 9:00 AM on Monday,
Second dose ----> 9:00 PM on Monday,
Third dose ----> 9:00 AM on Tuesday,
Fourth dose ----> 9:00 PM on Tuesday,
Fifth dose ----> 9:00 AM on Thursday,
Sixth dose ----> 9:00 PM on Thursday,
Seventh dose ----> 9:00 AM on Friday,
Hence, Theresa should take her 7th dose at 9:00 AM on Friday.
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Three students that share a townhouse find that their electric bill for October is $2.23 less than the September bill. The
total of both bills is $292.43, and each bill is split evenly among the roommates. How much did each owe in September?
Answer:
$47.48
Step-by-step explanation:
Let x = the amount owed Sept.
x + x - 2.23 = 292.43 Combine like terms
2x -2.23 = 292.43 Add 2.23 to both sides
2x - 2.23 + 2.23 = 292.43 + 2.23
2x = 294.66 Divide both sides by 2
[tex]\frac{2x}{2}[/tex] = [tex]\frac{294.66}{2}[/tex]
x = 147.33 this is the bill for September
Oct. 147.33 -2.23 = 145.10 This is the Bill for Oct.
Total:
147.33 + 145.10 = 292.43
292.43 ÷ 3 = 97.48 This is what each will owe rounded to the nearest penny.
the surface area of a sphere is 320 square centimeters what is the radius of the square
The radius of the sphere of surface area 320 cm² is 5.04 cm.
What is a radius?A radius is defined as half of a diameter. The unit of radius is meter.
To calculate the radius of the sphere, we use the formula below.
Formula:
r = √(A/4π)....................... Equation 1Where:
r = Radius of the sphereA = Surface area of the sphereπ = PieFrom the question,
Given:
A = 320 cm²π = 3.14Substitute these values into equation 1
r = √[320/(3.14×4)]r = √(25.48)r = 5.04 cmHence, the radius of the sphere is 5.04 cm.
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Digits a, b, and c can be chosen to make the following
multiplication work. What is the 3-digit number abc.
a b c
� 2 4
1 c b a 2
Answer:
1
Step-by-step explanation:
Match each step on the left with the procedure at that step on the right.
Step 1 a. calculate p-value
Step 2 b. write claim symbolically
Step 3 c. compare p-value to alpha
Step 4 d. reject or fail to reject null
Step 5 e. write null and alternative hypotheses
Step 6 f. write conclusion
Step 7 g. calculate test statistic
Step 8 h. identify test type and relevant statistic
the test type and relevant statistic, which will depend on the data and the hypothesis being tested.
Step 1 - g. calculate test statistic
Step 2 - b. write claim symbolically
Step 3 - c. compare p-value to alpha
Step 4 - d. reject or fail to reject null
Step 5 - e. write null and alternative hypotheses
Step 6 - f. write conclusion
Step 7 - a. calculate p-value
Step 8 - h. identify test type and relevant statistic
Step 1: Calculate the test statistic, which is a numerical measure of how likely the data is under the null hypothesis.
Step 2: Write the claim symbolically, which is a statement of what you are attempting to prove.
Step 3: Compare the p-value to the alpha level, which is the significance level of the test.
Step 4: Reject or fail to reject the null hypothesis, depending on whether or not the p-value is less than the alpha level.
Step 5: Write the null and alternative hypotheses, which are statements that describe the data and are used to test a hypothesis.
Step 6: Write a conclusion, which is a statement about the data based on the results of the test.
Step 7: Calculate the p-value, which is the probability of obtaining a result as extreme or more extreme than what was observed in the data, given that the null hypothesis is true.
Step 8: Identify the test type and relevant statistic, which will depend on the data and the hypothesis being tested.
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Given a number n, for each integer i in the range from 1 to n inclusive, print one value per line as follows: if i is a multiple of both 3 and 4, print FizzBuzz. If i is a multiple of 3 (but not 5), print Fizz. If i is a multiple of 5 (but not 3), print Buzz. If i is not a multiple of 3 or 5, print the value of i.
To begin, let’s create a for loop to account for the first line of the question. We know that the value of i is always either equal to or less than n, so let’s write that in.
Taking two count variables, say count3 and count5, to store the count of numbers divisible by 3 and 5 respectively.
Iterate over the range [1, N] using a variable, say i, and perform the following steps:
If the value of count3 and count5, print “FizzBuzz”.
If the value of count3 is equal to 3, print “Fizz”.
If the value of count5 is equal to 5, print “Buzz”.
If none of the above conditions match, then print i.
What is FizzBuzz?In a typical coding challenge during an interview, candidates are asked to create a solution that prints integers from 1 to N, designating any integers that are divisible by 3 as "Fizz," any integers that are divisible by 5 as "Buzz," and any integers that are both divisible by 3 and 5 as "FizzBuzz." Good coding practises can be reinforced by knowing how to solve it.
// C++ program for the above approach
#include <bits/stdc++.h>
using namespace std;
// Function to generate FizzBuzz sequence
void fizzBuzz(int N)
{
// Stores count of multiples
// of 3 and 5 respectively
int count3 = 0;
int count5 = 0;
// Iterate from 1 to N
for (int i = 1; i <= N; i++) {
// Increment count3 by 1
count3++;
// Increment count5 by 1
count5++;
// Initialize a boolean variable
// to check if none of the
// condition matches
bool flag = false;
// Check if the value of count3
// is equal to 3
if (count3 == 3) {
cout << "Fizz";
// Reset count3 to 0, and
// set flag as True
count3 = 0;
flag = true;
}
// Check if the value of count5
// is equal to 5
if (count5 == 5) {
cout << "Buzz";
// Reset count5 to 0, and
// set flag as True
count5 = 0;
flag = true;
}
// If none of the condition matches
if (!flag) {
cout << i;
}
cout << " ";
}
}
// Driver Code
int main()
{
int N = 15;
fizzBuzz(N);
return 0;
}
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NO LINKS!!
A cup of water at an initial temperature of 81°C is placed in a room at a constant temperature of 24°C. The temperature of the water is measured every 5 minutes during a half-hour period. The results are recorded as ordered pairs of the form (t, T), where t is the time (in minutes ) and T is the temperature (in degrees Celsius).
t T
0 81
5 69
10 60.5
15 54.2
20 49.3
25 45.4
30 42.6
a. Subtract the room temp. from each of the temp. in the ordered pairs. Use a graphing utility to plot the data points (t, T) and (t, T-24). An exponential model for the data (t, T-24) is T-24 = 54.4(0.964)^t. Solve for T.
T=
Graph the model. Compare the result with the plot of the original data.
b. Use a graphing utility to plot the points (t, ln(T-24)) and observe that the points appear to be linear. Use the regression feature of the graphing utility to fit a line to these data. This resulting line has the form ln(T-24) = at + b, which is equivalent to e^(ln(T-24)) = e^(at+b). Solve for T, and verify that the result is equivalent to the model in part (b). Round all numerical values to 3 decimal places).
T=
c. Fit a rational model to the data. Take the reciprocals of the y-coordinates of the revised data points to generate the points. (t, 1/(T-24))
Use a graphing utility to graph these points and observe that they appear to be linear. Use the regression feature of a graphing utility to fit a line to these data. The resulting line has the form 1/(T - 24) = at + b.
Solve for T. (Round all numerical values to 4 decimal places). Use a graphing utility the rational function and the original data points.
T=
Part (a)
Given data table.
[tex]\begin{array}{|c|c|} \cline{1-2}t & T\\\cline{1-2}0 & 81\\\cline{1-2}5 & 69\\\cline{1-2}10 & 60.5\\\cline{1-2}15 & 54.2\\\cline{1-2}20 & 49.3\\\cline{1-2}25 & 45.4\\\cline{1-2}30 & 42.6\\\cline{1-2}\end{array}[/tex]
where,
t = time in minutesT = temperature in CelsiusIt's unfortunate that T is used twice for these variables. It might cause some confusion.
This is what happens when we subtract 24 from each temperature.
[tex]\begin{array}{|c|c|} \cline{1-2}t & T-24\\\cline{1-2}0 & 57\\\cline{1-2}5 & 45\\\cline{1-2}10 & 36.5\\\cline{1-2}15 & 30.2\\\cline{1-2}20 & 25.3\\\cline{1-2}25 & 21.4\\\cline{1-2}30 & 18.6\\\cline{1-2}\end{array}[/tex]
The graph of each set of points is shown in figure A. I used GeoGebra to make the graph.
The first set of data points are in red. The second set in blue. Notice the set of blue points is the result of shifting the red points 24 units down.
The green exponential model is also shown as the curve through the set of red points.
The green regression exponential model doesn't go through each point perfectly. Rather it tries to get as close as possible.
To go from
T-24 = 54.4(0.964)^t
to
T = 54.4(0.964)^t + 24
we simply add 24 to both sides. This means there isn't much to show in terms of steps when solving for T.
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Part (b)
Use spreadsheet technology or something like GeoGebra to generate this data table.
[tex]\begin{array}{|c|c|} \cline{1-2}t & ln(T-24)\\\cline{1-2}0 & 4.043051\\\cline{1-2}5 & 3.806662\\\cline{1-2}10 & 3.597312\\\cline{1-2}15 & 3.407842\\\cline{1-2}20 & 3.230804\\\cline{1-2}25 & 3.063391\\\cline{1-2}30 & 2.923162\\\cline{1-2}\end{array}[/tex]
The values in the 2nd column are approximate.
Then plot each of those points on the same xy grid. Use technology of your choice to determine the regression line is roughly
y = -0.03723x + 3.99739
So we can say
ln(T-24) = -0.03723t + 3.99739
the right hand side fits the format at + b where
a = -0.03723b = 3.99739both of which are approximate.
Then,
e^(ln(T-24)) = e^(at+b)
T-24 = e^(at+b)
T-24 = e^(-0.03723t + 3.99739)
T-24 = e^(-0.03723t)*e^(3.99739)
T-24 = e^(-0.03723t)*54.45583
T-24 = 54.45583*e^(-0.03723t)
T = 54.45583*e^(-0.03723t) + 24
T = 54.456*e^(-0.037t) + 24
Let's verify that this is equivalent to the model found in part (a).
T = 54.456*e^(-0.037t) + 24
T = 54.456*(e^(-0.037))^t + 24
T = 54.456*(0.963676)^t + 24
T = 54.5*(0.964)^t + 24
which is very close to the model mentioned in part (a). There's some slight rounding error. That's to be expected in problems like this.
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Answer: T = 54.456*e^(-0.037t) + 24
See figure B for the graph. Like with the other regression curve, this straight line doesn't go through all of the points. It tries to get as close as possible.
=======================================================
Part (c)
Refer to the 2nd table mentioned in part (a).
We'll apply the reciprocal to each item in the column labeled T-24.
For instance, the item 57 becomes 1/57 = 0.017544 approximately.
This is what the data table looks like:
[tex]\begin{array}{|c|c|} \cline{1-2}t & 1/(T-24)\\\cline{1-2}0 & 0.017544\\\cline{1-2}5 & 0.022222\\\cline{1-2}10 & 0.027397\\\cline{1-2}15 & 0.033113\\\cline{1-2}20 & 0.039526\\\cline{1-2}25 & 0.046729\\\cline{1-2}30 & 0.053763\\\cline{1-2}\end{array}[/tex]
The values in the 2nd column are approximate.
The set of points and regression line are shown in figure C1. This line does not go through all of the points. Like with the others, it tries to get as close as possible to each point.
Use technology to determine the equation of the regression line is approximately:
y = 0.00121x + 0.01613
Which tells us that
1/(T-24) = 0.00121t + 0.01613
Let's solve for uppercase T.
1/(T-24) = 0.00121t + 0.01613
T-24 = 1/(0.00121t + 0.01613)
T = 1/(0.00121t + 0.01613) + 24
T = 1/(0.0012t + 0.0161) + 24
which is the approximate final answer.
Figure C2 shown below represents the original data points (t, T) in red. The blue curve is y = 1/(0.0012x+0.0161)+24, which is the rational regression curve we just found. This curve tries its best to get as close as possible to each red point.
Compare the regression curves of figure A and figure C2. We have a very close tie in terms of which curve does a better job of fitting the original data.
A recent survey found that about 73.2% of all gasoline purchases at a certain service station chain are paid with a credit or debit card. If 250 gasoline purchases completed at this chain are randomly selected, find the probability that at most 195 of those purchases are paid with a credit or debit card. • Use Excel to find the probability, rounding your answer to four decimal places.
The probability that at most 195 of those purchases are paid with a credit or debit card i.e P(X ≤ 195 ) is 0.9625..
We have given that,
Sample size , n=250
Sample proportion, p= 73.2% = 0.732
np = 183
n(1-p) = 67
both np & n(1-p) values are greater than 5, So normal approximation is applicable
mean, µ = np = 183
std. dev, σ = √np(1-p) =√250×0.732 ×(1-0.732) =7.0031
we have to calculate probability that at most 195 of those purchases are paid with a credit or debit card i.e P(X ≤ 195 )
= P( X < 195.5 )
= P((x - µ) / σ < (195.5 -183)/ 7.0031)
= P( Z < 1.78 )
= 0.9625
Required probability using Excel function ,
Excel command: =NORM.S.DIST(z,1)
= Norm.S.DIST(1.78,1)
= 0.9625
Hence, required probability is 0.9625..
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How do I solve this?
Answer:
Area = 5π/2 in^2
Perimeter = 3π + 2 in
Step-by-step explanation:
A=area of a circle. P=Perimeter of a circle
F=Area of first semi-circle
T=Area of Figure
Solve for Area:
A=πr^2
F=A/2
A=π(2)^2 ==> solve for A
A=4π
F=(4π)/2
F=2π ==> this is for the first semi-circle
S=Area of second semi-circle
S=(πr^2)/2
S=(π(2/2)^2)/2 ==> the radius is half the diameter, and the diameter is 2 in
S=(π(1)^2)/2
S=π/2
T=F+S ==> The total area is the area of both semi-circles
T=2π + π/2 ==> plugin 2π for F and π/2 for S
T = 4π/2 + π/2 ==> common denominators
T = 5π/2 in^2
Now solve for perimeter
P = 2πr.
q = perimeter of first semi-circle
q = P/2
q = 2πr/2
q = 2π(2)/2 ==> plugin 2 for r
q = 2π
R = Perimeter of second semi-circle
R = 2π(1)/2 ==> we calculated that the radius of the semi-circle is half of the
radius of the first semi-circle
R = 2π/2 ==> simplify
R = π
Also, add in side length DC into the perimeter as it is part of the perimeter.
E = Entire perimeter of figure
E = q + R + DC
E = 2π + π + 2
E = 3π + 2 in
DUE SOON! PLEASE SHOW HOW YOU KNOW! THIS IS A SSA SITUATION BUT NOT SURE HOW TO FIND OUT HOW MANY TRIANGLES ARE POSSIBLE!
This is a SAS situation, only one triangle is possible. Then the correct option is C.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180 °.
In triangle ΔABC, the angle ∠A is 22°. And the measure of the side BC is 18.9 cm and the measure of the side AC is 15.1 cm.
To fix a triangle, the known dimensions of the triangle should be three which one must be a side.
This is a SAS circumstance, just a single triangle is conceivable. Then the right choice is C.
More about the triangle link is given below.
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A real estate agent would like to develop a model for predicting sale price of homes in a suburban area. One variable that can be useful for predicting home value is home interior size, which is measured in square feet. Using 13 homes sold recently in the area, the real estate agent uses software to find a least-square line to summarize the relationship. The resulting equation is sale price hat = 0.152 (size) minus 32.84. A graph titled home price versus home size (square feet) has home size (Square feet) on the x-axis, and home price (thousands of dollars) on the y-axis. Points increase in a line with positive slope. A graph titled residuals versus home size (square feet) has home size (square feet) on the x-axis, and residual on the y-axis. Points are scattered throughout the graph. Based on the scatterplot and residual plot shown, is a linear model appropriate for summarizing the relationship? A linear model is appropriate because the residual plot shows no pattern. A linear model is appropriate because the mean of the residuals appears close to zero. A linear model is not appropriate because there are potential outliers in the residual plot. A linear model is not appropriate because of the random scatter of points in the residual plot.
Based on the information provided, a linear model is not appropriate for summarizing the relationship between home size and sale price because of the random scatter of points in the residual plot. In a linear model, the residuals should be randomly distributed around a mean of zero, without any discernible pattern. However, the residual plot shown in the question indicates that the residuals are randomly scattered throughout the graph, which suggests that a linear model may not be the best way to summarize the relationship between the variables. Therefore, a linear model is not appropriate for this data.
Answer:
Not Appropriate
Step-by-step explanation:
Based on the information provided in the problem, it appears that a linear model is not appropriate for summarizing the relationship between home size and sale price. This is because the residual plot shows a random scatter of points, which suggests that there is not a strong linear relationship between these variables. Furthermore, the scatterplot of home price versus home size shows a line with a positive slope, which indicates that there is some relationship between these variables, but it is not necessarily a linear relationship. In this situation, it would be more appropriate to use a non-linear model to summarize the relationship between home size and sale price.
Solve Please and Thank U
The solution to the systems are (1, 1), (-3, -1), (1, -2), (2, -1), (7, -1) and (-2, 2)
How to determine the solution to the system?System 1
In this case, the system of equations is given as
y = -3x + 4
y = 3x - 2
Next, we plot the graph of the system of equations
In this case, the point of intersection of the equations represent the solution to the system
From the graph, the lines intersect at (1, 1)
So, the solution is (1, 1)
System 2
In this case, the system of equations is given as
y = x + 2
x = -3
Next, we plot the graph of the system of equations
In this case, the point of intersection of the equations represent the solution to the system
From the graph, the lines intersect at (-3, -1)
So, the solution is (-3, -1)
System 3
In this case, the system of equations is given as
4x + y = 2
x - y = 3
Next, we plot the graph of the system of equations
In this case, the point of intersection of the equations represent the solution to the system
From the graph, the lines intersect at (1, -2)
So, the solution is (1, -2)
System 4
We have
y = 4x - 9
y = x - 3
Substitute y = 4x - 9 in y = x - 3
4x - 9 = x - 3
Evaluate the like terms
3x = 6
So, we have
x = 2
Recall that:
y = x - 3
So, we have
y = 2 - 3
y = -1
So, the solution is (2, -1)
System 5
We have
x + 7y = 0
2x - 8y = 22
Make x the subject in x + 7y = 0
x = -7y
Substitute x = -7y in 2x - 8y = 22
-14y - 8y = 22
Evaluate the like terms
-22y = 22
So, we have
y = -1
Recall that:
x = -7y
So, we have
x = -7(-1)
x = 7
So, the solution is (7, -1)
System 6
We have
-7x + 2y = 18
6x + 6y = 0
Make x the subject in 6x + 6y = 0
x = -y
Substitute x = -y in -7x + 2y = 18
7y + 2y = 18
Evaluate the like terms
9y = 18
So, we have
y = 2
Recall that:
x = -y
So, we have
x = -2
So, the solution is (-2, 2)
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