Answer: we first need to apply the transformation to the x- and y-coordinates of the point individually
Step-by-step explanation:
To transform the coordinates of a point (x, y) using the transformation (x, y) ⟶ (–y, x), we first need to apply the transformation to the x- and y-coordinates of the point individually. This means that the x-coordinate becomes –y and the y-coordinate becomes x.
In the case of point B, the original coordinates are (2, 5), so the transformed coordinates are (–5, 2). This means that the x-coordinate becomes –5 and the y-coordinate becomes 2.
Next, we need to apply the translation that moves the point 1 unit right and 4 units up. To do this, we simply add 1 to the x-coordinate and add 4 to the y-coordinate. After this translation, the coordinates of B′ become (–4, 6). Therefore, the final coordinates of B′ are (–4, 6).
Use upper and lower sums to approximate the area of the region using the given number of subintervals (of equal width). (Round your answers to three decimal places.) y = square root 6x
To use upper and lower sums to approximate the area of the region under the curve y = √6x, we need to divide the interval of integration into a certain number of subintervals of equal width.
Let's say that we want to divide the interval [a, b] into n subintervals of equal width. We can then define the points x0, x1, ..., xn as follows:
x0 = a
x1 = a + (b - a)/n
x2 = a + 2(b - a)/n
...
xn = b
The width of each subinterval is (b - a)/n.
We can then use these points to define the upper sum and lower sum as follows:
Upper sum = ∑ (b - a)/n * max(f(x))
Lower sum = ∑ (b - a)/n * min(f(x))
where the sum is taken over all subintervals, and max(f(x)) and min(f(x)) represent the maximum and minimum values of the function f(x) on each subinterval, respectively.
To calculate the upper and lower sums, we need to evaluate the function f(x) at each of the points x0, x1, ..., xn. For example, if we want to calculate the upper sum using 4 subintervals, we would evaluate the function at the points x0, x1, x2, and x3, and then use these values to calculate the upper sum using the formula above.
Once we have calculated the upper and lower sums, we can use them to approximate the area of the region under the curve. The area of the region is approximately equal to the average of the upper and lower sums.
For example, if the upper sum is 1.5 and the lower sum is 0.5, then the area of the region is approximately (1.5 + 0.5)/2 = 1.
In general, as we increase the number of subintervals, the upper and lower sums will get closer and closer to the actual area of the region, and the approximation will become more accurate.
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Factor completely 5x(x+3) + 6 (x+3)
Answer:
(x + 3)(5x + 6)------------------------------
Given
Expression 5x(x+3) + 6 (x+3)To factor it completely, factor out the common factor x + 3:
5x(x+3) + 6 (x+3) = (x + 3)(5x + 6)would you expect the proportion of stay-at-home residents to be higher in virginia than in arkansas? support your conclusion with the results obtained in parts (b) and (c). from the results obtained in parts (b) and (c), we would expect the number of stay-at-home residents to be higher correct: your answer is correct. in arkansas than virginia. the sample results show that, rounded to two decimal places, the estimated percentage of arkansas residents who were born there is %. the sample results also show that, rounded to two decimal places, the estimated percentage of virginia residents who were born there is %.
As per the estimated percentage, the test statistic is 0.6167 or 61.67%
What is the percentage?
The term percentage is defined as the number or ratio that can be expressed as a fraction of 100.
Here we have given that in Arkansas than Virginia. the sample results show that rounded to two decimal places, the estimated percentage of Arkansas residents who were born there is %. the sample results also show that rounded to two decimal places, the estimated percentage of Virginia residents who were born there is %.
And we need to find the test statistics.
While we looking into the given situation we have identified the following values,
=> H0 : p = 0.577
=> Ha : p ≠ 0.577
Now, we have estimated the proportion of stay-at-home residents in Arkansas is calculated as,
Here the Proportion of stay-at-home residents in Arkansas is written as,
=> p = 74/120 = 0.6167
Therefore, the test statistic is 0.6167.
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The graph below shows the average cost of renting a studio apartment in one city in each of the years 2002 through 2006. By what percentage does the average price increase from 2002 to 2003? Obtain a second version of the graph by sliding a piece of paper over the bottom of the graph so that the bars start at 300. In this new graph, by what percentage does the price appear to increase from 2002 to 2003?
In the new graph, the price appears that is increase from 2002 to 2003 is 25% and 100%. Hence, option A is correct.
What is the Percentage?The Latin phrase "per centum," which means "by the hundred," is where the English word "percentage" comes from.
Percentage segments are those with a numerator of 100. In other words, it is a connection where the whole is always deemed to be valued 100.
As per the data mentioned in the question,
Average cost to rent studio in 2002 = 400 and,
Average cost to rent studio in 2003 = 500
Then percent increase from year 2002 to 2003 will be,
% increase = (500 - 400)/400 × 100
% increase = 25%
Then, % increase from 2002 to 2003 is 25%,
(200 - 100)/100 × 100 = 100%.
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Calculate the area, in square units, bounded by f(x) = 3x³ -3x²-x+8 and
g(x) = 2x³ - 10x² + 29x + 8 over the interval [1, 5].
Answer:
164
Step-by-step explanation:
Assuming that you are allowed to use graphing tools:
f(x) is below g(x) for interval [1,3]
g(x) is below f(x) for interval [3,5]
Rules of finding area between two graphs:
[tex]\int\limits^a_b {|upper - lower|} \, dx[/tex]
For interval [1,3]:
[tex]\int\limits^3_1 {g(x) - f(x)} \, dx[/tex]
[tex]\int\limits^3_1 {|(2x^{3} - 10x^{2} +29x+8)-(3x^{3}-3x^{2} -x+8) } \, dx[/tex]
[tex]\int\limits^3_1 {-x^{3} -7x^{2} +30x} \, dx[/tex]
[tex]= [-\frac{1}{4}x^{4} - \frac{7}{3}x^{3} + 15x^{2}]^3_1[/tex]
[tex]= [-\frac{1}{4}3^{4} - \frac{7}{3}3^{3} + 15*3^{2}] - [-\frac{1}{4}1^{4} - \frac{7}{3}1^{3} + 15*1^{2}][/tex]
[tex]= -\frac{81}{4} - \frac{189}{3} + 135+\frac{1}{4} + \frac{7}{3}- 15\\[/tex]
[tex]= \frac{118}{3}[/tex]
For interval [3,5]
[tex]\int\limits^5_3 {f(x)-g(x)} \, dx[/tex]
[tex]\int\limits^5_3 {|(3x^{3}-3x^{2} -x+8)-(2x^{3} - 10x^{2} +29x+8)|} \, dx[/tex]
[tex]\int\limits^5_3 {|x^{3}+7x^{2} -30x|} \, dx[/tex]
[tex]= [\frac{1}{4}x^{4} +\frac{7}{3}x^{3} - 15x^{2}]^5_3[/tex]
[tex]= [\frac{1}{4}5^{4} +\frac{7}{3}5^{3} - 15*5^{2}] -[\frac{1}{4}3^{4} +\frac{7}{3}3^{3} - 15*3^{2}][/tex]
[tex]= \frac{625}{4} +\frac{875}{3} - 375 -\frac{81}{4}} -\frac{189}{3} + 135[/tex]
[tex]=\frac{374}{3}[/tex]
Total area
[tex]= \frac{118}{3} + \frac{374}{3}\\[/tex]
[tex]= 164[/tex]
Suraj took a slice of pizza from the freezer and put it in the oven.
The pizza's temperature (in degrees Celsius) as a function of time (in minutes) is graphed.
What was the pizza's temperature after 2 minutes?
The temperature of the pizza that Suraj took from the freezer, after 2 minutes, given the graph, is 10 degrees Celsius.
How to find the temperature ?The temperature of the pizza that Suraj took from the freezer and put in the oven, is shown on the graph. To find the temperature of this pizza after 2 minutes, given the line in the graph, look at the point where the 2 minutes on the x - axis, intercepts with the line.
This point on the y - axis is 10 degrees Celsius.
This simply means that at 2 minutes, Suraj's pizza slice had a temperature of 10 degrees Celsius.
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I need help with this its hard.
Solve this question
Answer:
the degree is 6
Step-by-step explanation:
pls help due in 1 hour!!!!!!
Step-by-step explanation:
{(3, 7), (3, 6), (5, 4), (4, 7)} Is not a function
{(1, 5), (3, 5), (4, 6), (6, 4)} is a function
{(2, 3), (4, 2), (4, 6), (5, 8)} is not a function
{(0, 4), (3, 2), (4, 2), (6, 5)} is a function
a vertex of a rooted tree is called a leaf if it has no children. vertices that have children are called internal vertices. if d is a vertex in a tree, the with d as its root is the subgraph of the tree containing d and its descendants and all edges incident to these descendants.
The root of a tree is the vertex from which all other vertices can be reached by following edges. The root of a tree is the only vertex that does not have an incoming edge.
In a rooted tree, a vertex is called a leaf if it has no children (i.e., it does not have any edges going out from it). Internal vertices are those that have children and are connected by edges to other vertices in the tree. If a vertex d is the root of a tree, the subgraph with d as its root is defined as the set of vertices that can be reached from d by traversing its edges, as well as the edges connecting them. The root is the only vertex that does not have an incoming edge, and all other vertices can be reached from the root.
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Help please!! So confused, determine the perimeter of the right triangle shown. Round your final answer to the nearest whole number if necessary.
The perimeter of the right triangle is 26 units.
From the given graph, the measure of side AB= 8 units and the measure of side BC= 7 units.
What is the perimeter?The perimeter of a shape is defined as the total distance around the shape. It is the length of the outline or boundary of any two-dimensional geometric shape. The perimeter of different figures can be equal in measure depending upon the dimensions.
By Pythagoras theorem,
AC²=AB²+BC²
⇒ AC²=8²+7²
⇒ AC²=113
⇒ AC=10.63
≈ 11 units
Perimeter =AB+BC+AC
= 8+7+11
= 26 units
Therefore, the perimeter of the right triangle is 26 units.
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expert that helps you learn core concepts.
See Answer
One item on a questionnaire asks students how many times in a typical week they eat at a fast-food restaurant. The responses for a sample of n = 10 students are summarized in the frequency distribution. What is the mean for this sample?
X f
5 or more 2
4 3
3 2
2 1
1 1
0 1
M = 4
M = 3.5
M = 31/10 = 3.1
The mean cannot be determined for these data.
The arithmetic mean for this value is M=3.1.we can calculate this data from frequency distribution.
what is arithmetic mean?It is sum of collection of number divided by the count of numbers.Its value can be positive or negative both.The collection is often a set of results from an experiments and observational study.
what is the use of arithmetic mean?It is often used as a parameter in statistical distribution or as a result to summarize the observations of an experiment survey.It is simplest way to used to measure the average.Its also measure frequency distribution by considering all of the observations.
Now we are using formula for arithmetic mean
A.M= Sum of (fx)/sum of (f)
by putting values in this formula we have
A.M= 31/10
A.M= 3.1
Hence 3.1 is the arithmetic mean for given frequency data.
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7 the area of the rhombus
The area of a rhombus is --336[tex]in^{2}[/tex]
A rhombus is a type of parallelogram where all the sides are equal in length. opposite sides of a rhombus are parallel to each other and opposite angles are equal.
The diagonals of a rhombus bisect each other at the right angle.
side of a rhombus (x) is - 25inone diagonal of a rhombus(a) is - 14inlet, another diagonal of a rhombus is -b in
another diagonal of a rhombus, b = [tex]\sqrt{4x^{2} -a^{2} }[/tex]
= [tex]\sqrt{4*25^{2} - 14^{2} }[/tex]
=[tex]\sqrt{4*625 - 196}[/tex]
=[tex]\sqrt{2500 - 196}[/tex]
= [tex]\sqrt{2304}[/tex]
= 48 in
Area of the rhombus (A) = [tex]\frac{a * b }{2}[/tex]
= [tex]\frac{14 * 48 }{2}[/tex] [tex]in^{2}[/tex]
= 7 * 48 [tex]in^{2}[/tex]
= 336 [tex]in^{2}[/tex]
The area of a rhombus is --336[tex]in^{2}[/tex]
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Suppose that the weekly sales volume y (in thousands of units sold) depends on the price per unit (in dollars) of the product according to the following formula. y = 32(3p + 1)−2/5, p > 0
(a) What is the rate of change in sales volume when the price is $22? (Round your answer to three decimal places.) dy dp = -0.107 CORRECT ANSWER
(b) Interpret your answer to part (a). (Round your answer to the nearest whole number.) If the price increases $1, the sales volume will decrease by : ?
The rate of change in sales volume when the price is $22 is -0.107 and When the price increases $1, the sales volume will decrease by -48
The rate of change formula gives the relationship describing how one quantity changes in relation to the change in another quantity
According to the question,
y denotes the weekly sales volume and p denotes the price per unit
Equation is [tex]y = \frac{32}{3p + 1^{\frac{-2}{5}}}[/tex]
(a) We have to find the rate of change in sales volume when price is $22
Differentiating the equation w.r.t p,
[tex]\frac{dy}{dp} = \frac{-32(3)}{(3p + 1^\frac{-2}{5})^2}[/tex]
Putting value of p = 22
=> [tex]\frac{dy}{dp} = \frac{-32(3)}{(3(22) + 1^\frac{-2}{5})^2}[/tex]
=> -96 / (66 + 1 - 2(22)(1))²
=> -96 / 897
=> -0.107
(b) To find If the price increases $1, the sales volume will decrease by
Replacing p = 1
=> dy/dp = -96/2
=> -48
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Name: Sally Jonas, single, 1 exemption.
Pay Rate: $5.95 per hour
Hours Worked: M-8, T-7, W-8, T-9, F-8
Total Hours Worked :
Wage for Week :
FICA Tax (7.65 %) :
Federal Tax :
State Income Tax (at 3%) :
City Income Tax (1.5%) :
Total Tax :
Paycheck after Taxes :
The total hours worked is 40 hours, the total wage for the week is $238, the Total tax is 12.15%, and the paycheck after taxes is $209.44
What is tax?Taxes are compulsory payments made by a government organization, whether local, regional, or federal, to people or businesses.
Given:
Pay Rate: $5.95 per hour,
Hours Worked: M-8, T-7, W-8, T-9, F-8,
FICA Tax (7.65 %),
State Income Tax (at 3%),
City Income Tax (1.5%),
Calculate the total working hours as shown below,
Total working hours = 8 + 7 + 8 + 9 + 8 = 40 hours
Calculate the total tax,
Total tax = 7.65 + 3 + 1.5 = 12.15%
Calculate total wage,
Total wage = no of hours × 5.95
Total wage = 40 × 5.95 = $238
Paycheck after-tax deduction = Total wage - 12.15 % of $238
Paycheck after-tax deduction = 238 - 28.56
Paycheck after-tax deduction = $209.44
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10
8
f(x)=x-2x-6 6
4
10 -8 -6 -4
20
-2
6
-8
0 3
-10
24 6 8 10
Function h is two times the square
of the difference of x and 1.
Select the correct answer from each drop-down.
-2
-1
0
1
2
3
k(z) = ¹ k
89
f
h
The function that has the least minimum value is function
The function that has the greatest minimum value is function
G
76
11
-4
-5
-4
11
Bz - 4
The function that has the least minimum value is the following function.
Function k(x).
What are the minimum values of each function?From the graph given, looking at it's vertex, the minimum value of function f(x) is given as follows:
-7.
From the table given, the minimum value of function g(x) is given as follows:
-5, due to the symmetry from x = 0 to x = 2.
Function h(x) is defined as follows:
h(x) = 2(x - 1)².
Which has a minimum value of zero, as the y-coordinate of the vertex is not changed with the transformation.
Using a graphing calculator, as shown by the image at the end of the answer, the minimum value of function k(x) is given as follows:
-9.
Which is the least minimum value of all these functions.
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Malik has 28 red marbles and he has 35 blue marbles. Malik wants to divide the marbles into groups so each group has the same contents. How many groups can Malik make, so there would be the same contents (red and blue marbles) in each group? There should be no marbles left over.
Answer:
This is a math equation about GCD { GREATEST COMMON DIVISOR }
7 groups
Each group [ 4 red marbles / 5 blue marbles ]
Step-by-step explanation: { I will use the . as mutiply }
So first let's take a little of analysis
We take a as the groups that should be made, a ∈ N*
In the question, we can see: 28 can be divisible to a / 35 can be divisible to a
Because of that, we know that a is the smallest so a is: GCD ( 28, 30 )
Now, let's factorize numbers into prime factors:
28 = [tex]2^{2} . 7[/tex]
35 = 5.7
Choose common prime factors: 2,3,5,7
[ Because we are doing GCD, we will need to choose the common prime factors as index number the smallest. ]
GCD ( 28, 30 ) = 7
So a = 420 groups
The red marbles in each group: 28 ÷ 7 = 4 marbles
The blue marbles in each group: 35 ÷ 7 = 5 marbles
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making the assumption of no compounding interest, suppose you purchase a perpetuity bond from sense/net corporation for $3,000 with an annual coupon rate of 3% . specify all answers to the nearest dollar, and assume a discount rate equal to that of the current interest rate.
Therefore for computing the annual return we simply fund with coupon rate in percentage is 90 dollar
What is a percent simple definition?
A percentage is a portion of a whole expressed as a number between 0 and 100 rather than as a fraction. All of something is 100 percent, half of it is fifty percent, none of something is zero percent. To determine a percentage, you divide the portion of the whole by the whole itself and multiply by 100.
The additional sum of money over the principal sum of deposit or loan is called compound interest.
The yearly return on $ 3 ,000 investment will be $90.
This can be estimated as:
Investment = $3,000
Coupon rate in percentage = 3%
The computation of yearly return can be estimated as:
= $3,000 × 3%
= $90
Therefore for computing the annual return we simply fund with coupon rate in percentage.
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16. A department store marks up winter boots at $150. This represents a 50% markup on cost. What's the cost of the boots?
A. $300
B. $100
C. $150
D. $200
The cost of the boots is (b) $100
How to determine the cost of the boots?From the question, we have the following parameters that can be used in our computation:
Markup rate = 50%
Markup price of the boot = $150
The cost of the boots can be calculated using the following equation
Markup price of the boot = cost of the boots * (1 + Markup rate)
Substitute the known values in the above equation, so, we have the following representation
150 = cost of the boots * (1 + 50%)
This gives
150 = cost of the boots * (1.5)
Divide by 1.5
cost of the boots = $100
Hence, the cost of the boots is $100
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Two sides and an angle are given below. Determine whether the given information results in one triangle, two triangles, or no triangle at all. Solve any resulting triangle(s).b=5 c=6 B=20 degreesA) single triangle is produced, where C degrees=___. A degrees=___ a=____B) Two triangles are produced, where the triangle with the smaller angle C has C1= ___ A1=____ and a1=____ / Triangle with the larger angles has C2=___ A2=___ and a2=____C) No triangles are produced
Using the Law of Sines, we get an angle of 2.41 degrees and no triangles are produced.
Option (C) is the correct one.
Given, Two sides and an angle are given below.
we have to determine whether the given information results in one triangle, two triangles, or no triangle at all.
If b = 5, c = 6 and B = 20 degrees in the triangle.
On using the concept of Laws of Sines, we get
sinA/a = sinB/b = sinC/c
sin 20°/5 = sin C/6
0.34/5 = sin C/6
0.007 = sin C/6
sin C = 0.042
C = 2.41
So, the angle C be 2.41 degrees.
which implies that no triangle can be formed or produced with the given data of the triangle.
Hence, No triangles are produced.
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Calculate curl(F and then apply Stokes' Theorem to compute the flux of curI(F) through the surface in the figure using line integral. The surface is a wedge-shaped box (bottom included, top excluded) with an outward-pointing normal. Assume that parameter a = 2. F= (x+yz - 16,x√(y^2 + 1)
(Express numbers in exact form: Use symbolic notation and fractions where needed ) curI(F) = ______ flux of curl(F) = _____
the flux of curI(F) through the surface area in the figure as with integral:
flux of curl(F) = x^2 + 4yz(2) + 2∫x√(y^2 + 1) dy - 32z + 2y^2z
First, we calculate the curl of F: curI(F) = (2z, -2x, 2y).
Next, we apply Stokes' Theorem to calculate the flux of curI(F) through the surface in the figure. We start by computing the line integral of F around the boundary of the surface. This is given by:
flux of curl(F) = 2 ∫ (x + 2yz) dx + 2 ∫ (x√(y^2 + 1))dy - 2 ∫ (16 - 2yz)dz
We can now evaluate this line integral by splitting it into a sum of integrals:
flux of curl(F) = 2 ∫ (x + 2yz) dx + 2 ∫ (x√(y^2 + 1))dy - 2 ∫ (16 - 2yz)dz
= 2∫x dx + 4∫yz dx + 2∫x√(y^2 + 1) dy - 32∫dz + 4∫yz dz
= 2x^2/2 + 4∫yz dx + 2∫x√(y^2 + 1) dy - 32z + 4yz^2/2
= x^2 + 4yz∫dx + 2∫x√(y^2 + 1) dy - 32z + 2y^2z
Finally, we can evaluate the flux of curI(F) through the surface in the figure as:
flux of curl(F) = x^2 + 4yz(2) + 2∫x√(y^2 + 1) dy - 32z + 2y^2z
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Evaluate the expression and enter your answer.
2 • |6 + 2|
Answer:
16
Step-by-step explanation:
2 × | 6 + 2 |
= 2 × | 8 |
= 2 × 8
= 16
you are measuring a process, and you are given the following information: overall average: 131 population stdev: 5 sample size: 11 determine the upper control limit if your desired confidence interval is 99.73%. enter your answer to one decimal place. it's ok if you get a negative number; in that case, just enter the minus sign in front of it.
The upper control limit is 16.4 if our desired confidence interval is 99.73%.
Given 131 population
standard deviation = 5
sample size = 11.
mean = 131/11 = 11.9.
determine the upper control limit if desired
confidence interval is 99.73%
What is Confidence interval?
In statistics, a confidence interval describes the likelihood that a population parameter will fall between a set of values for a given percentage of the time.
Confidence interval = sample mean ± margin of error
Upper limit = sample mean + margin of error.
margin of error = z* * population of standard deviation/[tex]\sqrt{n}[/tex].
margin of error = 3.00 * 5/[tex]\sqrt{11}[/tex].
value of z* for 99.73% confidence interval is 3.00.
so margin of error = 4.5.
Upper limit = 11.9 + 4.5
Upper limit = 16.4
The upper control limit is 16.4 if our desired confidence interval is 99.73%.
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What is the population standard deviation?
{5,8,8,5}
Enter your answer as a decimal, rounded to the nearest tenth, like this: 4.2
The population standard deviation of {5, 8, 8, 5} is 3
The given population is
{5, 8, 8, 5}
The mean of the population = Sum of the terms / Number of Terms
Find the values and substitute the values in the equation
Sum of terms = 5 + 8 + 8 +5
= 26
Number of terms = 4
The mean of the population= 26 / 4
= 6.5
The variance of the population = (5 - 6.5)^2 + (8 - 6.5)^2 + (8 - 6.5)^2 + (5 - 6.5)^2
= (-1.5)^2 + (1.5)^2 + 1.5^2 + (-1.5)^2
= 2.25 + 2.25 + 2.25 + 2.25
= 9
The standard deviation of the population = [tex]\sqrt{9}[/tex]
= 3
Therefore, the standard deviation is 3
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A group of friends is playing a board game. As part of the game, each player is given the same number of cards. There are 6 players and 58 cards. How many cards will each player get if each player gets the same number of cards?
Answer:Each player would get 9 cards each with a reaminder of 4 cards left
Step-by-step explanation:6 times 9 is 54 + 4 is 58
Answer: 9
Step-by-step explanation:
To figure out the given problem below:
P = 6
C = 58
You have to divide the problem.
So [tex]58[/tex] ÷ [tex]6 = 9[/tex].
There are two traffic lights on a commuter's route to and from work. Let X1 be the number of lights at which the commuter must stop on his way to work, and X2 be the number of lights at which he must stop when returning from work. Suppose that these two variables are independent, each with the pmf given in the accompanying table (so X1, X2 is a random sample of size n = 2).
x1 0 1 2 µ = 1.2, s2 = 0.56
p(x1) 0.2 0.4 0.4
(a) Determine the pmf of To = X1 + X2. to 0 1 2 3 4 p(to)
(b) Calculate µTo. µTo = How does it relate to µ, the population mean? µTo = · µ
(c) Calculate sTo2. sTo2 How does it relate to s2, the population variance?
sTo2 = · s2
(d) Let X3 and X4 be the number of lights at which a stop is required when driving to and from work on a second day assumed independent of the first day. With To = the sum of all four Xi's, what now are the values of E(To) and V(To)?
E(To) =
V(To) =
(e) Referring back to (d), what are the values of
P(To = 8) and P(To = 7)
[Hint: Don't even think of listing all possible outcomes!] (Enter your answers to four decimal places.)
P(To = 8) =
P(To = 7) =
A commuter passes through two traffic lights on their way to and from work. Let X1 represent the number of lights the commuter must stop at while traveling to work, and X2 represent the number of lights he must stop at. stop when returning from work. It is connected to the population mean.
a) P(To=0) = 0.2*0.2 = 0.04
P(To=1) = 0.2*0.4 + 0.4*0.2 = 0.24
P(To=2) = 0.4*0.4 + 0.2*0.2 + 0.4*0.2 = 0.36
P(To=3) = 0.2*0.4 + 0.4*0.4 = 0.24
P(To=4) = 0.2*0.2 = 0.04
b) µTo = 0*0.04 + 1*0.24 + 2*0.36 + 3*0.24 + 4*0.04 = 2
It is equal to the population mean µ.
c) sTo2 = (0-2)2*0.04 + (1-2)2*0.24 + (2-2)2*0.36 + (3-2)2*0.24 + (4-2)2*0.04 = 0.56
It is equal to the population variance s2.
d) E(To) = 0*0.04 + 1*0.24 + 2*0.36 + 3*0.24 + 4*0.04 + 5*0 + 6*0 + 7*0 + 8*0 = 2
V(To) = (0-2)2*0.04 + (1-2)2*0.24 + (2-2)2*0.36 + (3-2)2*0.24 + (4-2)2*0.04 + (5-2)2*0 + (6-2)2*0 + (7-2)2*0 + (8-2)2*0 = 0.56
e) P(To = 8) = 0
P(To = 7) = 0.2*0.2*0.2*0.2 = 0.0016
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For what value of x is the equation 2(x + 1) - x = 10
Answer:
x=8
Step-by-step explanation:
Simplify 2(x+1)−x.
Simplify each term.2x+2−x=10
Subtract x from 2x.x+2=10
Move all terms not containing x to the right side of the equation.
Subtract 2
from both sides of the equation.x1−2
Subtract 2 from x = 10-2
subtract 2 from 10
hope that helps!
Answer: 8
Step-by-step explanation:
First, let's write out the equation:
2(x+1) - x = 10
So, we need to find the value of x.
Let's take an estimate of what x could be.
So, we know it has to be 5-10, because that is over when we add x to one, then multiply by 2.
So, numbers 5-7 couldn't be it, because the value of x is lower than 10. So, we have to guess if it's 8 or 9
Let's use both numbers to solve if it's correct:
2(8+1) - 8 =10
18 - 8 = 10
or
2(9+1) - 8 =10
20 - 8 = 12
So, we have 8 as our answer.
So, x = 8
whenever suzan sees a bag of marbles, she grabs a handful at random. she has seen a bag containing four red marbles, five green ones, three white ones, and two purple ones. she grabs eight of them. find the probability of the following event, expressing it as a fraction in lowest terms. she has at least one green one.
For this problem, it is best to consider E to be the case in which she has all of the green ones, and then apply the formula for calculating the probability of a complement.
. To determine the likelihood that she will receive all of the green ones, we must first determine two values: the total number of possible outcomes, n(S), and the total number of favorable outcomes for the given event. Because she selects 8 marbles from a total of 11, n(S) = C(11, 8) = 165. To get all the green ones, she must first select three red marbles from a set of three, and then select the remaining five marbles.
from the 8 non-red ones. There are (3,3)(8, 5) = 56 ways to do this. Thus,
() =56/165
. The probability of not occurring is then (′) = 1 −56/165=109/165
, so this is the probability that she does get all the green one.
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There are 8 ounces in a cup, 2 cups in a pint, 2 pints in a quart, and 4 quarts in a gallon.
1 L≈ 0.26 gallons
7 KL= cups
fit a multiple regression model to describe the relationship between weight and the predictors length and age. (use x1 for length and x2 for age. round your numerical values to two decimal places.)
The statement " only the estimate intercept is statistically significant at the 5% level is wrong" is wrong about the estimate.
What is multiple regression?
A probit model is a type of regression in statistics where the dependant variable can only take two values.
We have:
Regress smoker on cubic polynomials of age
If we use linear probability model.
Here the data are missing, but we can say about the estimate that:
Only the estimate intercept is statistically significant at the 5% level is wrong,
Thus, the statement " only the estimate intercept is statistically significant at the 5% level is wrong" is wrong about the estimate.
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