The parameters of the exponential function in this problem are given as follows:
c = 1.1.a = 0.56.R = -56%.What is an exponential function?The standard format of an exponential function is given as follows:
y = c(1 - a)^t.
This is the case for a decaying exponential function, and the meaning of each parameter is given as follows:
c is the initial value, value assumed by y when t = 0.a is the decay rate.In this problem, the function is given as follows:
f(x) = 1.1(0.44)^x.
Hence the values for the parameters are given as follows:
c = 1.1, which is the initial value.a = 0.56, as 1 - a = 0.44 -> a = 0.56.Then the percent of change is of -56%, as it is a decaying exponential function with a = 0.56.
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Select all the expressions that are equivalent to 2(x+3).
(Select all that apply.)
(x+3) . 2
2 . x+3
2x+5
2x+6
2x+3 . 2
Answer:
The correct answers are (x+3) . 2 and 2x+6.
In the first expression, (x+3) . 2, the parentheses indicate that x+3 should be treated as a single term and multiplied by 2. This is equivalent to 2(x+3).
In the second expression, 2x+6, the 2 is multiplied by x and the 3 from x+3, giving 2x+6, which is also equivalent to 2(x+3).
The other expressions are not equivalent because they do not properly distribute the multiplication. For example, in 2 . x+3, the 2 is only being multiplied by x, not x+3, and in 2x+5, the 2 is only being multiplied by x and not 3.
What is the correlation coefficient between the following variables?
Correlation Coefficient between the given variables is 0.0023
What is Correlation Coefficient?A statistical concept known as the correlation coefficient aids in establishing a relationship between expected and actual values gained through statistical experimentation. The estimated correlation coefficient's value explains how well the expected and actual values match.
Correlation Value of the coefficient is always between -1 and +1. If the correlation coefficient value is positive, the two variables have a similar and same relationship. Otherwise, it shows how the two variables are different.
The Pearson correlation coefficient is the result of dividing the covariance of two variables by the sum of their standard deviations. It is typically displayed as ρ(rho).
The correlation coefficient can be determined using the formula if the two variables being discussed are x and y.
Formula for Correlation Coefficient:
r×{[n∑x∧2-(∑x)∧2][n∑y∧2-(∑y)∧2]}=n(∑xy)-∑x×∑y.
Calculation:From given data:
∑x=3.95+4.18+7.5+6.19+6.35+7.23+7.98+8.15=51.53
∑y=16.12+15.75+21.45+20.08+22.60+21.95+26.42+28.38=172.75
∑x²=[tex]3.95^{2}+4.18^{2}+7.5^{2}+6.19^{2}+6.35^{2}+7.23^{2}+7.98^{2}+8.15^{2}=350.3393[/tex]
∑y²=[tex]16.12^{2}+15.75^{2}+21.45^{2}+20.08^{2}+22.60^{2}+21.95^{2}+26.42^{2}+28.38^{2}=3867.2291[/tex]
∑xy=[tex]3.95\cdot16.12+4.18\cdot15.75+7.5\cdot21.45+6.19\cdot20.08+6.35\cdot22.6+7.23\cdot21.95+7.98\cdot26.42+8.15\cdot28.38=1159.0163[/tex]
By substituting in formula:
[tex]r=\frac{8*1159.0163-51.53*172.75}{(8*350.3393-51.53^2)(8*3867.2291-172.75^2)}=\frac{370.3229}{147.3735*1095.2703}[/tex]
r=0.00229=0.0023
Correlation Coefficient between the given variables is 0.0023
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The correlation coefficient between the following variables is 0.76.
What is correlation?A statistical measure called correlation shows how much two or more variables fluctuate in connection to one another. When two variables rise or decrease simultaneously, there is a positive correlation; when there is a negative correlation, one variable increases as the other falls.
We know the coefficient of correlation is [tex]r = \frac{\sum{XY}}{\sum{X^{2}Y^2}}[/tex].
Now, [tex]\sum{XY}[/tex] = (3.95)×(16.12) + (4.18)×(15.75) + (7.50)×(21.45) + (6.19)×(20.08)
+ (6.35)×(22.60) + (7.23)×(21.95) + (7.98)×(26.42) + (8.15)×(28.38).
[tex]\sum{XY} =[/tex] 1159.02.
[tex]\sum{X} =[/tex] 51.53.
[tex]\sum{X^2} =[/tex] 463.35.
[tex]\sum{Y} =[/tex] 172.75.
[tex]\sum{Y^2} =[/tex] 5047.015.
∴ [tex]r = \frac{\sum{XY}}{\sum{X^{2}Y^2}}[/tex].
= [tex]\frac{1159.02}{\sqrt{463.35\times 5057.015}}[/tex].
= 1159.02/1530.74.
= 0.76.
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How can you interpret statements that use function notation without a graph?
Function notation, such as f(x) = 3x + 5, can be interpreted by plugging in different values for x and evaluating the resulting expression.
For example, if we plug in 2 for x, we get f(2) = 3(2) + 5 = 11. This means that the value of the function at x = 2 is 11. By plugging in different values for x, we can evaluate the function at any point on its domain.
What is a function notation?A connection between two variables can be expressed using function notation. We are accustomed to writing straight-line equations in the form y = m x + c .
We can express this in function notation as f (x) = m x + c by substituting y with f (x).
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What is the slop in the equation
Suppose a mutual fund qualifies as having moderate risk if the standard deviation of its monthly rate of return is less than 3%. A mutual-fund rating agency randomly selects 27 months and determines the rate of return for a certain fund. The standard deviation of the rate of return is computed to be 2.55 %. Is there sufficient evidence to conclude that the fund has moderate risk at the a= 0.05 level of significance? A normal probability plot indicates that the monthly rates of return are normally distributed. What are the correct hypotheses for this test?
The correct hypotheses for this test are:
Null hypothesis (H0): The standard deviation of the mutual fund's monthly rate of return is greater than or equal to 3%.
Alternative hypothesis (H1): The standard deviation of the mutual fund's monthly rate of return is less than 3%.
To determine if there is sufficient evidence to reject the null hypothesis and conclude that the fund has moderate risk, you would need to perform a hypothesis test. In this case, since you have a sample of 27 monthly rates of return and the normal probability plot indicates that the data is normally distributed, you can use a z-test for the population standard deviation.
To perform the test, you would need to calculate the test statistic and the p-value. The test statistic is calculated as follows:
test statistic = (sample standard deviation - population standard deviation) / (standard error)
where the sample standard deviation is 2.55%, the population standard deviation is 3%, and the standard error is calculated as:
standard error = sample standard deviation / sqrt(sample size)
Plugging in the values, the test statistic is:
test statistic = (2.55 - 3) / (2.55 / sqrt(27)) = -0.44
The p-value is the probability of observing a test statistic at least as extreme as the one calculated, given that the null hypothesis is true. To calculate the p-value, you can use a z-table or a statistical software package.
If the p-value is less than the chosen level of significance (a=0.05 in this case), you can reject the null hypothesis and conclude that the fund has moderate risk. If the p-value is greater than the level of significance, you cannot reject the null hypothesis and cannot conclude that the fund has moderate risk.
In the coordinate plane, the point A(-4, 0) is translated to the point A'(0, -4). . Under the same translation, the points B(-8, 3) and C(-1, -3) are translated to B' and C', respectively. What are the coordinates of B And C'?
Part 1) The rule of the translation is (x,y) ------> (x+4,y+5) ,Part 2) B'(4,8) Part 3) C'(3,3)
What are the coordinates of B And C'?Part 1)Find out the rule of the translation
we know that
The transformation of the point A to A' is equal to
A(-4,1) ------> A'(0,6)
so
The rule of the translation is equal to
(x,y) ------> (x + a ,y + b)
(-4,1) ------> (-4 + a, 1 + b)
Find the value of a
-4 + a = 0 -----> a = 4
Find the value of b
1 + b = 6 -----> b = 5
substitute the values of a and b
(x,y) ------> (x+4,y+5)
That means -----> The translation is 4 units at right and 5 units up
Part 2)Find out the coordinates of B'
Applying the rule of the translation
(x,y) ------> (x+4,y+5)
so
B(0,3) ------> B'(0+4,3+5)
B(0,3) ------> B'(4,8)
Part 3)Find out the coordinates of C'
Applying the rule of the translation
(x,y) ------> (x+4,y+5)
so
C(-1,-2) ------> C'(-1+4,-2+5)
C(-1,-2) ------> C'(3,3)
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Solve The Problem
There are 54 children at a park. They want to make teams with 7
children on each team. Three of the children go home. How many
complete teams can they make? Explain
Answer:
7
Step-by-step explanation:
54 - 3 = 51
51 divided by 7 is 7 with 2 left over
Hello may I please get some help with this question
Find k so that the line through (4, -3) and (k.1) is
a. parallel to 3x + 5y = 10,
b. perpendicular to 4x - 3y = - 1
a. k=
Answer:
a. k = -8/3 = -2 2/3
b. k = 32/5 = 6.4
Step-by-step explanation:
You want to find the values of k that place the point (k, 1) on the line through the point (4, -3) when that line is (a) parallel to 3x +5y = 10, and (b) perpendicular to 3x +5y = 10.
a. ParallelThe equation of the parallel line will have the same x- and y-coefficients, but will have a constant that make the equation true at the point (4, -3).
3x +5y = 3(4) +5(-3) = 12 -15 = -3
The equation of the parallel line is
3x +5y = -3
When y=1, the value of k is ...
3k +5(1) = -3
3k = -8
k = -8/3 = -2 2/3 . . . . . . on line parallel to 3x+5y=10
b. Perpendicular
The equation of the perpendicular line will have swapped x- and y-coefficients, with one of them negated. The constant will be chosen to make the equation true at the point (4, -3).
5x -3y = 5(4) -3(-3) = 20 +9 = 29
The equation of the perpendicular line is
5x -3y = 29
When y=1, the value of k is ...
5k -3(1) = 29
5k = 32
k = 32/5 = 6.4 . . . . . . on th eline perpendicular to 3x+5y=10
To indirectly measure the distance across a river, Sebastian stands on one side of the river and uses sight-lines to a landmark on the opposite bank. Sebastian draws the diagram below to show the lengths and angles that he measured. Find PRPR, the distance across the river. Round your answer to the nearest foot.
Sebastian uses the method of similar triangles to find the distance across the river, and the distance across the river is 372 foot.
What is a Triangle?A triangle is a polygon with three sides and three vertices.
The triangle's total number of angles comes to 180°.
The distances between the formed the sight-lines are;
RB = 210 feet
OC = 275 feet
The distance between the point close to the river and the next point further from the river = 115 feet
In triangles ΔPRB and ΔPOC,
we have;
∠PRE = ∠POC = 90°
Given;
∠PER ≅ ∠PCO
By corresponding angle formed between two parallel lines and a common transversal.
Using angle-angle similarity theorem;
∴ ΔPRE is similar to ΔPOC Which gives;
PR / PO = RE / OC
Let x represent the distance across the river,
we have;
PR = x
PO = 115 + x
Which gives;
x / (115+x) = 210 / 275
275x = 210 × (115 + x)
275x = 24150 + 210x
275x - 210x = 24150
65x = 24150
x = 371. 54
Therefore, the distance across the river is 372 foot.
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I rent a gym for $150 for 30 students. Another time I rent the gym for $350 for 70 students. What is my rate per student?
The rate per student for the gym is given as $5.
What are arithmetic operations?The arithmetic operations are the fundamentals of all mathematical operations. The example of these operators are addition, subtraction, multiplication and division.
The rent of gym for 30 students is $150.
And, for 70 students it is $350.
The rate of rent in both the cases can be found by taking the ratio as follows,
The unit cost in the first case = Total rent ÷ Number of students
= 150 ÷ 30 = $5
And, the unit cost in the second case = 350 ÷ 70 = $5
Hence, the required rate is obtained as $5 per student for both the cases.
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Suppose the COMBINED area is known to be 0.10416, assume there is equal area on each side. Determine the corresponding Z-scores.
A) z=±1.62 B) z=±1.58 C) z=±1.72 D) z=±1.66 E) z=±1.69 F) z=±1.49 G) None of These
The solution is once more 1.28 since a combined area of 0.10416 to the right implies that it must also have an area of 0.90 to the left.
Since each normally distributed random variable has a slightly different distribution shape, standardizing the variable to give it a mean of 0 and a standard deviation of 1 is the only method to determine regions using a table. How do we go about doing that? Employ the z-score!
Z = ( x - μ)/σ
If a mean and standard deviation are present for the random variable X,
Then a random variable with a mean of 0 and a standard deviation of 1 is produced by converting X using the z-score!
With that in mind, all that remains is to understand how to find areas under the standard normal curve, which can then be applied to any random variable with a normal distribution.
Since an area of 0.10416 to the right means that it must have an area of 0.90 to the left, the answer is once again 1.28.
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Task: Gym Membership
Instructions
Function c is defined by the equation c(n) = 50 + 4n. It gives the monthly cost, in dollars, of visiting a gym as a function of the number of visits, n.
Complete each of the 2 activities for this Task.
Activity 1 of 2
Find the value of c(7).
Activity 2 of 2
Explain what the value of c(7) you found means in this situation.
The value of c(7) = 78 and 78 represents the monthly cost of visiting the gym 7 times.
Finding p(a) from p(x)
To find p(a) for a given polynomial p(x) we need to substitute x = a in the given polynomial i.e in place of x.
Here we have
Function c is defined by the equation c(n) = 50 + 4n.
It gives the monthly cost, in dollars, of visiting a gym as a function of the number of visits n.
Activity 1 of 2
Find the value of c(7).
=> c(7) = 50 + 4(7)
=> c(7) = 50 + 28
=> c(7) = 78
Activity 2 of 2
Explain what the value of c(7) you found means in this situation.
In c(n) = 50 + 4n, n represents the number of visits in a month and 50+4n will represent the monthly cost in dollars
If we apply the above statement to c(7) = 78
then 7 represents the number of visits and 78 represents the monthly cost of visiting the gym 7 times
Therefore,
The value of c(7) = 78 and 78 represents the monthly cost of visiting the gym 7 times.
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There are only 2.1 x 108 metric tonnes of usable fossil fuels existing on Earth.
Assuming an estimated rate of fossil fuel use of 1 x 105 metric tonnes per year, calculate an order of magnitude estimation of the time left before the fossil fuel reserves run out.
Give your answer to one significant figure.\
The answer is 2000 but I cannot figure out how they got it.
The time that is left before the fossil fuel reserves run out would be= 2000 years.
What is a fossil fuel?A fossil fuel is defined as the type of fuel that is gotten from dead and decayed organic matter that has been buried for years underneath the earth surface.
The quantity of usable fossil fuel existing on earth = 2.1 x 10⁸metric tonnes.
The rate of fossil fuel used per year = 1 x 10⁵
Mathematically,
If 1 year = 1 x 10⁵
X years = 2.1 x 108
make X years the subject of formula;
X years = 2.1× 10⁸/1× 10⁵
X years = 2.1 × 10³ or 2100
X year = 2000( to one significant figure)
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Solve for x: −7 < x − 1 < 8
6 < x < 9
−6 > x > 9
6 > x > −9
−6 < x < 9
The solution for the given inequality is -6 < x < 9.
What is linear equality?
In mathematics a linear inequality is an inequality that involves a linear function. A linear inequality contains one of the symbols of inequality. It shows the data which is not equal in graph form.
The given inequality is:
-7 < x - 1 < 8
−7 + 1 < x − 1 + 1 < 8 + 1 -------- (Add 1 to all parts)
-6 < x < 9
Hence, the solution for the given inequality is -6 < x < 9.
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One student surveys the number of pens which are sold in two stationary shops.The pens of both shops are sold in a week.In the first shop 60 pens are sold in the first day and 6 pens are sold more in everyday as comparison of previous day.Similarly in the second shop 5 pens are sold in the first day and the double number of pens are sold in everyday as comparison of previous day.Now in which shop how manv nens are sold more? Find it.Ans: 89 more in second shop
Answer: 224 pens more sold in 2nd shop
Step-by-step explanation:
Given,
1st shop, 6 pens are sold more than previous day,
1st day : 60
2nd day : 60+6 =66
3rd day : 66+6 =72
4th day : 72+6 =78
5th day : 78+6 =84
6th day : 84+6 =90
7th day : 90+6 =96
Then,
2nd shop, each day doubles the previous sold,
1st day: 5
2nd day:5*2 =10
3rd day:10*2 =20
4th day:20*2 =40
5th day:40*2 =80
6th day:80*2 =160
7th day:160*2 =320
Therefore, second shop sells more in a week which is calculated by 320-96=224 more sold than the 1st shop.
Order the ratios from least to greatest.
5:8 11:16 18:32
The least to greatest of the ratio is 18 : 32, 5 : 8, and 11 : 16
Arrange from least to greatestLeast to greatest arrangement can also be referred to as ascending order. Ascending order is the order such that each element is greater than or equal to the previous element.
5 : 8
= 5/8
= 0.625
11 : 16
= 11/16
= 0.6875
18 : 32
= 18/32
= 0.5625
Therefore, the ratio can be arranged as 18 : 32, 5 : 8, and 11 : 16 in ascending order.
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find the equation of the tangent to the circle 4x²+4y²=25 what are parallel to the line 3x+5y+7=0
Answer:
Step-by-step explanation:
To find the equation of the tangent to the circle 4x^2 + 4y^2 = 25 that is parallel to the line 3x + 5y + 7 = 0, we can use the following steps:
Rewrite the equation of the circle in standard form: (x - a)^2 + (y - b)^2 = r^2, where (a, b) is the center of the circle and r is the radius.
In this case, the equation of the circle is already in standard form, so we can skip this step.
Find the slope of the line 3x + 5y + 7 = 0. The slope is -3/5.
Find the slope of the tangent to the circle. The slope of the tangent will be equal to the slope of the line, which is -3/5.
Substitute the slope of the tangent and the coordinates of a point on the circle into the point-slope form of the equation of a line: y - y1 = m(x - x1), where (x1, y1) is a point on the circle and m is the slope.
In this case, we can substitute the coordinates of the center of the circle (which is (0, 0)) and the slope of the tangent (-3/5) into the point-slope form to get:
y - 0 = (-3/5)(x - 0)
Simplify to get the equation of the tangent: y = -3/5x.
Therefore, the equation of the tangent to the circle 4x^2 + 4y^2 = 25 that is parallel to the line 3x + 5y + 7 = 0 is y = -3/5x.
The table below gives values of a function g at selected values of x. x 0 1 3 7 g(x) 24 35 42 68
Which of the following statements, if true, would be sufficient to conclude that there exists a number c in the interval [0,7] such that g (c) = 50 ? I. g is defined for all in the interval (0,7). II. g is increasing for all in the interval (0,7]. III. g is continuous for all o in the interval 0,7). (A) II only (B) Ill only (C) I and Ill only (D) I, ll and III
g is continuous for all x in the interval [0,7] is correct statement that would be sufficient to conclude that there exists a number c in the interval [0,7] such that g (c) = 50.
Here the given function g(x) gives values for selected values of x.
Now we are to find a condition which will conclude that there exist a number 'c' in the interval [0,7] such that g(c)=50
If a function f : a, b [tex]\rightarrow[/tex] R be continuous on R with [tex]$\mathrm{f}(\mathrm{a}) \neq \mathrm{f}(\mathrm{b})$[/tex] then the function f(x) attains every value between f(a) and f(b) at least once in the interval [a, b]
I. The option is false.
Because if the function is defined in the interval [0,7] then it is not necessary that there exist a point in this interval, where the function will attain the value 50.
II. The given option is false.
Because if the function is increasing in the interval [0,7] then it is not necessary that there exist a point in this interval, where the function will attain the value 50.
III. This option is correct.
Since g(0) = 24 and g(7) = 68 and 'g' is continuous on the interval [0,7] , so the function g(x) attains every value between 24 and 68 at least once in the interval [0,7].
That is there must be a point 'c' in the interval [0,7] such that g(c)=50.
Therefore option (B) is correct.
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he equations of two lines are given. determine whether the lines are parallel, perpendicular, or neither. y
By definition, perpendicular strains are strains intersecting at a proper attitude. The letters T and L are examples of perpendicular strains. By definition, parallel strains are strains at the equal aircraft that in no way intersect.
The letters N and Z include pairs of parallel linetwo non-vertical strains which are withinside the equal aircraft has the equal slope, then they may be stated to be parallel. Two parallel strains might not ever intersect. If non-vertical strains withinside the equal aircraft intersect at a proper attitude then they may be stated to be perpendicular.
We can decide from their equations whether or not strains are parallel with the aid of using evaluating their slopes. If the slopes are the equal and the y-intercepts are different, the strains are parallel. If the slopes are different, the strains aren't parallel. Unlike parallel strains, perpendicular strains do intersect.
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Perform the following mathematical operation, and report the answer to the appropriate number of significant figures.
1204.2 + 4.72613 = [?]
The value of 1204.2 + 4.72613 is 1208.92613.
What is meaning of significant figures of a number?
Significant figures are the number of digits that add to the correctness of a value, frequently a measurement. The first non-zero digit is where we start counting significant figures. Determine how many significant digits there are given a range of numbers.
Given number is 1204.2 and 4.72613.
If add zeros after the last digit of the decimal number, then the number will remains same.
The rewrite form of 1204.2 is 1204.20000.
Before combining two decimal integers, make sure they both have the same number of digits after the decimal point. If they don't, move a number's right by a number of zeros until they do.
Then, place the decimal points vertically and write one number on top of the other. Bring the decimal point directly below the decimal point and add as you would with full numbers.
The sum of 1204.20000 and 4.72613
1204.20000
+4.72613
__________
1208.92613
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In the function y= 5x, what is the value of x?
08
O There is only one solution for x.
It can be any number.
OIt is unknown and can't be found.
Answer:
It can be any number.
Step-by-step explanation:
The x xalue is an independent variable, which means its value does not depend on that of another variable (y)
Evaluating Linear Piecewise Functions
Consider the function:
f(x) =
7/2+ 2x, x≤-1
-5+3x/2, -1
1/4x, x≥3
< -5_-4_-3_-2_-1_0_1_2_3_4_5 >
What are these values?
f(-3) =[-19/2]ᵒʳ[-5/2]ᵒʳ[-3/4]ᵒʳ[5/2]
f(-1) =[-13/2]ᵒʳ[-3/2]ᵒʳ[-1/4]ᵒʳ[-3/2]
f(3) =[-7/4]ᵒʳ[-1/2]ᵒʳ[3/4]ᵒʳ[19/2]
PLEASE HELP ME ON A SERIOUS TIME CRUNCH!!
Im a bit stuck can I get some help
The relationship's slope and common difference are both 70 and constant.
What is the slope of the line?The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.
here,
As the relationship given in the table is linear,
The slope of the relationship is given as,
M = (y₂ - y₁) / (x₂ - x₁)
Now, putting values from the table,
m = 140 - 70 / 2 - 1
m = 70 jumps per minute
Now,
The common difference between the consecutive minutes of jumping,
d = 140 - 70 = 210 - 140
d = 70 = 70
From the above evaluation, it can be said that the common difference and rate are constant.
Thus, the slope of the relationship and the common difference is 70, as well as constant.
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can u answerr for me pls
Part A:
The graph of the line intersects the x-axis at the point (4, 0).
Part B:
The point represents the distance of Shari from the home.
After 4 minutes, Shari rushed past her house.
What is a graph?A function graph is a visual representation of a relation. A function is actually equal to its graph in set theory and current mathematical foundations. For instance, when deciding whether or not a function is onto (surjective), a codomain should be taken into account. The graph of a function alone does not reveal the codomain. Although they relate to the same thing, the terms "function" and "graph of a function" communicate different perspectives on it, which is why they are commonly employed.
The line's x-intercept is 4 minutes.
The time Shari will arrive at her house is indicated by the 4 minutes.
Shari's distance from home on her run across town is represented by the line 6x - 3y = 24......... (1), where y stands for blocks, and x for minutes.
Therefore, when y = 0, we obtain 6x - 0 = 24, which equals x = 4, from equation (1) above.
As a result, 4 minutes is the x-intercept of the line (1).
It is stated that Shari will get at her house in 4 minutes, and there are no blocks between them.
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6r^2-8r =8
need helpp
Answer:
r = 2/ r = -2/3
Step-by-step explanation:
so you move the terms to the left side
6r^2 - 8r = 8
6r^2 -8r - 8 = 0
the common factor
6r^2 - 8r -8 = 0
2(3r^2 - 4r - 4) = 0
then you divideboth side by the same factor
2(3r^2 - 4r - 4) = 0
3r^2 - 4r - 4 = 0
use the quadratic formula
you would get 2.3
then you simplify
r = 4+8 over 6
seperate the equations
r = 4+8 over 6 change the plus into a minus
after that rearrange and issolate variable
r = 2
r = -2/3
therfore your answer is -2/3
a rectangle in the first and second quadrants of the coordinate plane has its base along the x-axis and two vertices on the parabola defined by y
The area of rectangle with has its vertices defined on parabola is 32 square units.
What is rectangle?An example of a quadrilateral with equal and parallel opposite sides is a rectangle. It is a polygon with four sides and four angles that are each 90 degrees. A rectangle is a shape with only two dimensions.
What are other terms to describe rectangle?Square, figure, oblong, parallelogram, plane a.re terms to describe rectangle
Equation of Parabola is y = 12 - x^2 is an even function.
Therefore, its rectangle form also is even at the origin.
We know area of rectangle = length × width
Here,
length = 2x, width = y
Area, A = 2x(12 - x2)
⇒ A = 24x - 2x^3
Take derivative of A with respect to x
⇒ A' = 24 - 6x^2
The area is largest when A' = 0
⇒ 24 - 6x^2 = 0
⇒ x^2 = 4
⇒ x = 2
Put the value of x in y = 12 - x^2
⇒ y = 12 - 4
⇒ y = 8
Area = 2(2)(8) = 32
Therefore, the largest area of a rectangle is 32 square units.
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The product of three consecutive integers n - 1, n, and n + 1 is 210. Write and solve an equation to find the numbers.
We can write an equation to represent the relationship between the three integers n - 1, n, and n + 1 by multiplying these three numbers together:
(n - 1) * n * (n + 1) = 210.We can then solve this equation to find the value of n.
To solve the equation, we can first factor the left-hand side to get (n - 1) * (n + 1) * n = 210. This expression can be further simplified to n^2 - 1 = 210. We can then solve this equation by adding 1 to both sides to get n^2 = 211, and then taking the square root of both sides to get n = sqrt(211).
The value of n must be an integer, so the only possible value for n is 14. This means that the three consecutive integers are 13, 14, and 15.
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The coordinates of the vertices of a rectangle are (4, −3), (2, 3), (11, 6), and (13, 0).
What is the perimeter of the rectangle? Round each step to the nearest tenth.
Enter your answer, as a decimal, in the box.
The perimeter of the rectangle is equal to 2(√90 + √40).
What is coordinate geometry?A coordinate plane is a 2D plane which is formed by the intersection of two perpendicular lines known as the x-axis and y-axis. A coordinate system in geometry is a method for determining the positions of the points by using one or more numbers or coordinates.
The perimeter is defined as the sum of all the sides of the rectangle.
Given coordinates of the rectangle are (4, −3), (2, 3), (11, 6), and (13, 0). The length and width of the rectangle are calculated by the distance formula.
D = √ [ ( y₂ - y₁ )² + ( x₂ - x₁ )² ]
Here, D is the distance, and the y₂ and y₁ are the coordinates.
L = √(13-4)² + 3² = √90
W = √ ( 4-2)² + (3 + 3)² = √40
The perimeter is,
P = 2(L + W)
Here, P is the perimeter and L is the length, and W is the width.
P = 2 (√90 +√ 40)
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We want to estimate the average coffee intake of Coursera students, measured in cups of coffee. A survey of 1,000 students yields an average of 0.55 cups per day, with a standard deviation of 1 cup per day. Which of the following is not necessarily true?
A. The sample distribution is right skewed.
B.0.55 is a point estimate for the population mean.
C. μ=0.55, Ï=1
D. x bar = 0.55, s=1
to estimate the average coffee intake of Coursera students, measured in cups of coffee. C) μ=0.55, σ=1 is not necessarily true.
Which of the given is not necessarily true?Given that survey is of 1000 students so n = 1000, average is 0.55 cups per day i.e. mean (x bar) = 0.55 and standard deviation is of 1 cup per day ,i.e. S.D (s) = 1 .
How to calculate standard deviation?First, determine the mean. Step 2: Calculate the square of each data point's variance from the mean. Add the values from Step 2 in Step 3. Divide by the total number of data points in step 4.
Just because the sample statistics are these values doesn't mean the population values will be exactly equal to them, therefore it's not necessarily true μ=0.55, σ=1 .
C) μ=0.55, σ=1 is not necessarily true.
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