Answer:
There are two possibilities:
[tex]x_{1} = 3.5[/tex] and [tex]y_{1} = 6.4[/tex]
[tex]x_{2} = 6.4[/tex] and [tex]y_{2} = 3.5[/tex]
Step-by-step explanation:
Mathematically speaking, the statement is equivalent to this 2-variable non-linear system:
[tex]x + y = 9.9[/tex]
[tex]x^{2} + y^{2} = 53.21[/tex]
First, [tex]x[/tex] is cleared in the first equation:
[tex]x = 9.9 - y[/tex]
Now, the variable is substituted in the second one:
[tex](9.9-y)^{2} + y^{2} = 53.21[/tex]
And some algebra is done in order to simplify the expression:
[tex]98.01-19.8\cdot y +2\cdot y^{2} = 53.21[/tex]
[tex]2\cdot y^{2} -19.8\cdot y +44.8 = 0[/tex]
Roots are found by means of the General Equation for Second-Order Polynomials:
[tex]y_{1} \approx \frac{32}{5}[/tex] and [tex]y_{2} \approx \frac{7}{2}[/tex]
There are two different values for [tex]x[/tex]:
[tex]y = y_{1}[/tex]
[tex]x_{1} = 9.9-6.4[/tex]
[tex]x_{1} = 3.5[/tex]
[tex]y = y_{2}[/tex]
[tex]x_{2} = 9.9 - 3.5[/tex]
[tex]x_{2} = 6.4[/tex]
There are two possibilities:
[tex]x_{1} = 3.5[/tex] and [tex]y_{1} = 6.4[/tex]
[tex]x_{2} = 6.4[/tex] and [tex]y_{2} = 3.5[/tex]
need asap to get the points plz
the problaty of getting Gray tile is 6 time
The speed of an object in space is shown in the graph.
What is the slope of the line?
(picture) please and thank you
Answer:
1 / 15
Step-by-step explanation:
The vertical change (rise) is 6 - 3, or just 3. The horizontal change (run) is 0.4 - 0.2, or 0.2. Thus the slope of this line is m = rise / run = 0.2 / 3 = 2 / 30 = 1 / 15
Xavier invests $100 each month for 6 months in an account that pays 6% APR compounded monthly. What is the future value of Xavier's account after 6 months?
Answer:
$607.57
Step-by-step explanation:
Which expressions are equivalent to StartFraction 1 Over 36 EndFraction? Check all that apply. 3 Superscript negative 6 6 Superscript negative 2 StartFraction 6 cubed Over 6 Superscript 5 EndFraction StartFraction 6 squared Over 6 Superscript negative 1 EndFraction 6 times 6 Superscript negative 2 6 Superscript negative 9 Baseline times 6 Superscript 7
Answer:
6^-2
6^3/6^5
6^-9 *6^ 7
Step-by-step explanation:
We want the fractions equal to 1/36
We know that a^-b = 1/a^b
We also know that a^b / a^c = a^(b-c)
We also know that a^b * a^c = a^(b+c)
3^ -6 = 1/3^6 = 1/729
6^-2 = 1/6^2 = 1/36
6^3/6^5 = 6^(3-5) = 6^-2 = 1/6^2 = 1/36
6^2 / 6^-1 = 6^(2- -1) = 6^3 = 216
6*6^-2 = 6^(1-2) = 6^-1 = 1/6
6^-9 *6^ 7 = 6^(-9+7) = 6^ -2 = 1/6^2 = 1/36
Answer:
B C and F
Step-by-step explanation:
Ana purchased a gallon of milk for $2.22, bagels for $2.97, and a box of
cereal for $2.42. How much money did Ana spend in all? Do not include s in
your answer.
Answer:
7.61
Step-by-step explanation:
Sum all of the values
2.22+2.97+2.42=7.61
Answer:
761
Step-by-step explanation:
The size of a slow-growing bacteria strain increases continuously over time. This equation describes the predicted size of the bacteria strain, in square millimeters, after t minutes: y = 112(1.58)t. According to the equation, what will the approximate size of the bacteria strain be after 5 minutes?
Answer:
1102.8 mm^2
Step-by-step explanation:
We presume your equation is intended to be ...
y = 112(1.58)^t
Since t is in minutes, fill in the given value and do the arithmetic:
y = 112(1.58)^5 = 112(9.84658) ≈ 1102.8
The approximate size of the bacteria strain will be 1102.8 mm^2 after 5 minutes.
Answer:
Explanation:
To find the size of bacteria in five minutes, substitute 5 for t in the equation and simplify:
y = 112(1.58)5
= 112 ∙ 9.85
= 1,103.2.
Round the answer to the closest integer to get 1,103.
Step-by-step explanation:
Write the given second order equation as its equivalent system of first order equations. u′′−5u′−4u=1.5sin(3t),u(1)=1,u′(1)=2.5 Use v to represent the "velocity function", i.e. v=u′(t). Use v and u for the two functions, rather than u(t) and v(t). (The latter confuses webwork. Functions like sin(t) are ok.)
Answer:
hi your question options is not available but attached to the answer is a complete question with the question options that you seek answer to
Answer: v = 5v + 4u + 1.5sin(3t),
0 1 4 5 0 1.5sin(3t) 1 2.5Step-by-step explanation:
u" - 5u' - 4u = 1.5sin(3t) where u'(1) = 2.5 u(1) = 1
v represents the "velocity function" i.e v = u'(t)
As v = u'(t)
u' = v
since u' = v
v' = u"
v' = 5u' + 4u + 1.5sin(3t) ( given that u" - 5u' - 4u = 1.5sin(3t) )
= 5v + 4u + 1.5sin(3t) ( noting that v = u' )
so v' = 5v + 4u + 1.5sin(3t)
d/dt [tex]\left[\begin{array}{ccc}u&\\v&\\\end{array}\right][/tex]= [tex]\left[\begin{array}{ccc}0&1&\\4&5&\\\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}u&\\v&\\\end{array}\right][/tex] + [tex]\left[\begin{array}{ccc}0&\\1.5sin(3t)&\\\end{array}\right][/tex]
Given that u(1) = 1 and u'(1) = 2.5
since v = u'
v(1) = 2.5
note: the initial value for the vector valued function is given as
[tex]\left[\begin{array}{ccc}u(1)&\\v(1)\\\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}1\\2.5\\\end{array}\right][/tex]
the cost is 284 the operating expenses are 43 the reduced price is 299 what is the operating loss
Answer:
28
Step-by-step explanation:
operating loss is loss when value of operating loss is more than gross profit.
In the given problem
cost: 284
price : 299
profit = 299 - 284 = 15
but given that there is operating expense as well.
operating expenses = 43
as expense is greater than profit there is loss which is called operating loss.
operating loss = operating expense - profit = 43 - 15 = 28
Thus, operating loss is 28.
Question: I had $5.00 My Mom gave me $10.00 while my Dad gave me $30.00. My Aunt and Uncle gave me 100.00. I had another $5.00 How much money did I really have?
Answer:
I had $10
I have $150
Step-by-step explanation:
This is a riddle and not a math question
So
I had $5I received $10+$30+$100= $140I had another $5The answer to the question how much I had is:
$5 + $5 = $10The answer to the question how much I have is:
$5+ $10 + $30 + $100 + $5 = $150Here we need to perform an addition of several numbers.
We will find that the total amount of money that you have is $150.
We know that:
You had $5.00
Your mom gave you $10.00
Your dad gave you $30.00
Your aunt and uncle gave you $100.00
You had another $5.00
Now you want to find how much money do you have, so you just need to add these numbers.
We can add it as:
$5 + $10 + $30 + $100 + $5
We can perform the addition in any order we want, for example:
($5 + $5) + $10 + $30 + $100
$10 + $10 + $30 + $100
($10 + $10) + $30 + $100
$20 + $30 + $100
($20 + $30) + $100
$50 + $100 = $150
You have $150.
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Deepak is a landscaper who charges $30 for each job he does plus an additional $15 for each hour he works. He only accepts jobs if he will earn at least $90 the job. He writes this inequality to determine x, the number of hours he must work during each job in order to accomplish this. 30 + 15 x greater-than-or-equal-to 90 Which best describes the restrictions on the jobs Deepak will accept? He only accepts jobs that last 4 or more hours. He only accepts jobs that last 5 or more hours. He only accepts jobs that last 8 or more hours. He only accepts jobs that last 9 or more hours.
Answer:
(A)He only accepts jobs that last 4 or more hours.
Step-by-step explanation:
Deepak charges $30 for each job plus an additional $15 for each hour he works.
Let the number of hours =x
Deepak's Total Income for x hours =30+15x
Since he only accepts jobs if he will earn at least $90 the job.
[tex]\text{Total Income}\geq 90[/tex]
[tex]30+15x\geq 90[/tex]
We then solve the inequality for x
[tex]30+15x\geq 90\\$Subtract 30 from both sides\\30-30+15x\geq 90-30\\15x\geq 60\\$Divide both sides by 15\\15x\div 15\geq 60 \div 15\\x\geq 4[/tex]
We therefore conclude that Deepak only accepts jobs that last 4 or more hours.
The correct option is A.
Answer:
A) He only accepts jobs that last 4 or more hours.
Step-by-step explanation:
Correct me if i'm wrong sorry if i am :)
ive been struggling with cones so pls halp me TwT i appreciate it a lot
lateral area
surface area
volume
Answer:
Volume = PI * radius^2 * height / 3
Volume = 4,712.39 cubic feet
Lateral Area = PI * radius * slant height
slant height^2 = 20^2 + 15^2
slant height ^2 = 625 slant height = 25
Lateral Area = PI * 15 * 25 = 1,178.1 square feet
Surface Area = PI * radius^2 = 706.86 square feet
Step-by-step explanation:
The shaded region below is called an annulus sector. Calculate the area (in square feet) of the shaded region if the inner circle has radius 7 ft and the outer circle has radius 14 ft. Round your answer to the nearest square foot.
Answer:
462 ft²
Step-by-step explanation:
The area of the annulus sector is given by the area of the outer circle (radius of 14 ft) minus the area of the inner circle (radius of 7 ft).
The area of a circle is:
[tex]A=\pi r^2[/tex]
Therefore, the area of the annulus sector is:
[tex]A_A=A_O-A_I\\A_A=\pi*14^2-(\pi*7^2)\\A_A=147\pi\\A_A= 462\ ft^2[/tex]
The area, rounded to the nearest square foot, is 462 ft².
Data on a sample of 100 customers of Alibaba, a direct marketing company, for the current year. The variables are defined as follows: Customer = a code for the customer Own Home = 1 if customer owns home, o if renting Close = 1 if lives close to stores (with similar merchandise), O if not Salary = annual household salary in $ Catalogs = number of catalogs this customer was sent this year Amount Spent = Amount spent total on purchases this year You are given the result of the multiple regression with dependent variable = Amount Spent. Use this output to answer the questions
(a) - (g) below the output. SUMMARY OUTPUT Regression Statistics Multiple R 0.8366 R Square 0.6999 Adjusted R Squ 0.6873 Standard Error 512.72 Observations 100 ANOVA df f ignificance F 55.39 0 .000 Regression Residual Total 4 95 99 SS 58241400.88 24974011.87 83215412.75 M S 14560350.22 262884.34 Intercept Own Home Close Salary Catalogs Coefficients Standard Error -91.67 185.917 -229.47 121.800 -604.90 114.229 0.02216 0.002 42.62 8.451 t Stat -0.493 -1.884 -5.295 9.836 5.043 P-value Lower 95% Upper 95% 0.623 -460.76 277.42 0.063 -471.27 12.34 0.000 -831.67 -378.12 0.000 0.02 0.03 0.000 25.84 59.40
(b) Using the regression model in (a), predict the mean amount spent by Amy, a customer who has the following characteristics: does not own a home, but lives close to stores that have similar merchandise, salary is $60,000 and is sent 12 catalogs this year. Give the value rounded to the nearest cent.
(c) Suppose Brenda has the same characteristics as Amy but does not live close to store with similar merchandise. How much would you expect Brenda to spend? Give the value rounded to the nearest cent.
Answer:
a. [tex]\hat{amount} \ \hat{ spent} = -91.67 - (229.47* ownhome)-(604.90 * close) +(0.02216 * salary) + (42.62 * catalogs)[/tex]
b. the expected amount spent by Amy is $1144.47
c. the expected amount that Brenda is going to spend is $1749.37
Step-by-step explanation:
(a)
From the regression output; the equation for the regression model can be written as:
[tex]\hat{amount} \ \hat{ spent} = -91.67 - (229.47* ownhome)-(604.90 * close) +(0.02216 * salary) + (42.62 * catalogs)[/tex]
From the information given in the question;
(b)
Amy does not own a home but rent; the variables given also stated that ;
Own Home = 1 if customer owns home, 0 if renting
So for Amy ; Own Home = 0 (since it is rented)
Close = Yes(1)
Salary = $60,000
Catalogs = 12
Therefore;
the mean amount spent by Amy is by using the regression model is ;
[tex]\hat{amount} \ \hat{ spent} = -91.67 - (229.47* 0)-(604.90 * 1) +(0.02216 * 60000) + (42.62 * 12)[/tex]
[tex]\hat{amount} \ \hat{ spent} = -91.67 -0-604.90 +1329.6 + 511.44[/tex]
[tex]\hat{amount} \ \hat{ spent} =1144.47[/tex]
Thus; the expected amount spent by Amy is $1144.47
(c)
If Brenda has the same characteristics as Amy but does not live close to store with similar merchandise.
Then the Close for Brenda will be = No (0)
Thus; the amount spent by Brenda will be:
[tex]\hat{amount} \ \hat{ spent} = -91.67 - (229.47* 0)-(604.90 * 0) +(0.02216 * 60000) + (42.62 * 12)[/tex]
[tex]\hat{amount} \ \hat{ spent} = -91.67 -0-0 +1329.6 + 511.44[/tex]
[tex]\hat{amount} \ \hat{ spent} = 1749.37[/tex]
Thus, the expected amount that Brenda is going to spend is $1749.37
Statistical Process Control (SPC) is often described as an applied side of the Binomial, Poisson, and Normal distributions. Many have said that an X-bar control chart is simply a Normal distribution turned on its side. Some argue that our statistics course shouldn't try to cover these applications because they represent an analytical skill rather thana statistical technique. Discuss, first whether or not you agree with the notion that SPC is an application of what we're learning in this class, and second, whether coverage of the topic is helpful in this class. How might your outcomes after this class be affected - positively or negatively - by whether or not we cover Chapter 16 in the text?
Answer: The answer is provided below
Step-by-step explanation:
Statistical Process Control (SPC) is described as the applied side of binomial, poisson, and the normal distributions. It has been often said that an X-bar control chart is a normal distribution that is turned on its side. Some people argue that statistics shouldn’t cover these applications because it represent an analytical skill rather than statistical technique. It's an application of what is learnt on statistics.
Statistical Process Control(SPC) is very useful in our lives. As a statistics student, one should be thorough with every mathematical concepts and its applications.
Can someone please help me :)
Answer:
90 degree
Step-by-step explanation:
Three points A, B, and C are added and shown in attached picture.
As the property of inscribed angle in circle:
angle BAC = (1/2) x 88 = 44 deg
As the property of complement angle:
angle ABC = 180 - 89 = 91 deg
As the property of sum of three angles in a triangle:
angle ACB + angle ABC + angle BAC = 180 deg
=> angle ACB = 180 - angle ABC - angle BAC = 180 - 44 - 91 = 45 deg
One more time, we use the property of inscribed angle in circle:
x = 2 x angle ACB = 2 x 45 = 90 deg
Hope this helps!
Does anyone know how to solve this?
What is the range of f(x) = (3/4)^x -4
{yly>-4}
{yly>3/4}
{yly<-4}
{vly<3/4}
Answer:
the range for this problem is the first one
The range of f(x) =(3/4)ˣ- 4 function is {yly>-4}, Option A is correct.
What is a function?A relation is a function if it has only One y-value for each x-value.
The function f(x) = (3/4)ˣ- 4 is an exponential function with a base of 3/4. The base is between 0 and 1, which means that the function is decreasing as x increases.
The function has a vertical asymptote at x = infinity, since the base is between 0 and 1, and the function approaches 0 as x approaches negative infinity.
As the exponential function (3/4)ˣ approaches 0 as x approaches infinity, we have:
lim((3/4)ˣ) = 0 as x -> infinity
So, the range of the given function is all real numbers greater than -4.
Hence, the range of function f(x) =(3/4)ˣ- 4 is {yly>-4}, Option A is correct.
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The function g(x) = x^3 has the point(-3, -27) on its graph. Determine g(3) without using substitution. What is the output based on the eve/odd nature of the function?
-27
27
not enough information
Answer:
27
Step-by-step explanation:
Any positive integer to 3rd power will have positive answer.
Odd functions with number next to x^3 that is positive are increasing from left to right and thay also have a rotational symmetry with respect to the origin.Whe you put this together it's clear that the answer is 27
How do I solve this?
Answer:
h(x-11)=-5
Step-by-step explanation:
just put the equetion from the top
h(x-11)=-5
Q1.
Diaries are sold in boxes of 12
Pencils are sold in boxes of 10
Rulers are sold in boxes of 6
A teacher wants to buy the same number of diaries, pencils and rulers.
Work out the smallest number of boxes of each item he could buy.
boxes of diaries
boxes of pencils
boxes of rulers
Tebal
Answer:
5 boxes of diaries
6 boxes of pencils
10 boxes of rulers
Step-by-step explanation:
In order to find the smallest number of units that would be possible to buy, find the least common multiple between the number of units in each box:
[tex]12\ \ 10\ \ 6\ |2\\6\ \ \ \ 5\ \ \ 3\ |2\\3\ \ \ \ 5\ \ \ 3\ |3\\1\ \ \ \ 5\ \ \ 1\ |5\\1\ \ \ \ 1\ \ \ 1\ | = 2*2*3*5=60[/tex]
The number of boxes required for each item to get 60 units is:
[tex]d=\frac{60}{12} = 5\ boxes \\p=\frac{60}{10} = 6\ boxes \\r=\frac{60}{6} = 10\ boxes[/tex]
the smallest number of boxes of each item he could buy is:
5 boxes of diaries
6 boxes of pencils
10 boxes of rulers
A company employs six women and eight men. The company randomly selects one employee to receive additional vacation time. Using the classical approach, what is the probability that the selected employee will be a woman
Answer: 6/14 or 3/7
Step-by-step explanation:
There are a total of 14 employees hired so it would like like this: 1/14 if you were to chose one of all 6 women and 8 men hired.
There are 6 women that may be chosen out of all 14 employees of which 8 are men, now what this would look like is : 6?14 or simplified, (3/7).
This means there is a 6/14 chance of choosing a woman instead of a man in these 14 hired employees. just because the question asks, "what is the chance of a woman getting chosen", of the other 5 women and 8 men hired, so the answer is 6/14 or 3/7 to chosen as a women instead of men in all the 14 employees that may/might be chosen. hope this helps love yawl!!
STAY SAFE !!! LOVE YOU !!! <3 <3 <3 <3
..... <3 <3 <3 <3 <3 <3 <3 .....
00:00
Use the Distributive Property to find the product of 6 x 3,584. Enter your answer in the box.
Answer:
21,504
Step-by-step explanation:
This is the usual method multiplication is done "by hand."
6 × 3584 = 6 × (3000 +500 +80 +4)
= 6×3000 +6×500 +6×80 +6×4
= 18000 +3000 +480 +24
= 21000 +504
= 21,504
_____
Many of us are taught in grade school to do the multiplication right to left:
= 6×4 +6×80 +6×500 +6×3000
... writing down the digit corresponding to the place value of the product, and "carrying" any more significant digits to add to the next product.
Here, that looks like 6×4 = 24, write down 4, carry 2. 6×8 = 48, add 2 to get 50, write down 0, carry 5. 6×5 = 30, add 5 to get 35, write down 5, carry 3. 6×3 = 18, add 3 to get 21, write down 21. Then the product is 21504.
__
When doing mental calculation, or using an abacus or soroban, it often works better to do the multiplication left to right, as shown in the answer above.
What are the coordinates of the pre-image of B'?
O (2, -8)
O (-8, -2)
O (-2, 8)
O (8,2)
Answer:
b. (-8, -2)
Step-by-step explanation:
Reflection across the x-axis
(x, y) ---> (x, -y)
B'(- 8, 2) ---> B( - 8, -2)
The coordinates of the pre image of B is (-8,-2) by studying the given graph.
How to find reflected coordinates of B'The given figure ABCD is reflected across the x-axis to create the figure A'B'C'D'.
By referring the graph we can say that the coordinate of B' is (-8,2)
The reflected point will have y coordinate's sign changed as the figure is reflected across x-axis.
Thus the pre image of B' will be (-8,-2)
Hence the coordinates of the pre image of B' is (-8,-2)
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A car is traveling at a speed of 63 kilometers per hour. What is the car's speed in kilometers per minute? How many kilometers will travel in 5 minutes?
Answer:
5.25 kilometers
Step-by-step explanation:
63k/60 = 1.05k
1.05k x 5 = 5.25k
A team of 5 IT specialists is to be selected to attend a lecture from 16 IT specialists. In how
many different ways can the team be formed?
124
4368
480
2880
Answer:
[tex] 16C5= \frac{16!}{5! (16-5)!}= \frac{16!}{5! 11!}= \frac{16*15*14*13*12*11!}{5! 11!}[/tex]
If we simplify we got:
[tex] 16C5 = \frac{16*15*14*13*12}{5*4*3*2*1}=4368[/tex]
And the best option would be:
4368
Step-by-step explanation:
For this case we have a total of 16 IT specialists and we want to select 5 IT specialists from the total of 16 so we can use the combination formula given by:
[tex] nC x= \frac{n!}{x! (n-x)!}[/tex]
And replacing we got:
[tex] 16C5= \frac{16!}{5! (16-5)!}= \frac{16!}{5! 11!}= \frac{16*15*14*13*12*11!}{5! 11!}[/tex]
If we simplify we got:
[tex] 16C5 = \frac{16*15*14*13*12}{5*4*3*2*1}=4368[/tex]
And the best option would be:
4368
Find the distance between the points (1,7) and ( 5, 10).
Answer:
Step-by-step explanation:
[tex]\sqrt{(5-1)^{2} +(10-7)^{2}\\\\\sqrt{4^{2} + 3^{2} \\\\\sqrt{16+9} = \sqrt{25} = 5[/tex]
In the equation 52y = 104, what is the next step in the equation solving sequence?
Solve for the variable.
Isolate the variable using inverse operations.
Combine like terms.
Move all numbers without a variable.
Answer:
Isolate the variable using inverse operations.
You would divide each side by 52.
The profit a company makes from producing x tabletops is modeled by the equation p(x) = 480x minus 2x squared. For what number of tabletops does the company need to make a profit of zero dollars?
Answer:
240 table tops or none
Step-by-step explanation:
p(x) = 480x- 2x^2
For profit to be 0, it means;
p(x)= 0
Therefore 480x- 2x^2 = 0
Dividing through by 2 we have ;
240x - x^2 = 0
By factorisation of x we have ;
(240-x) x = 0
x = 0 or 240-x= 0; x= 240( by moving x to the right of the expression:240-x= 0; we have 240=x => x=240).
So the company needs to produce 240 table tops or none in order not to make a profit.
The company need to make a profit of zero dollars will be 240.
What is a profit?A monetary profit, particularly the distinction between the amount gained and the actual cost of purchasing, running or creating anything.
The profit a company makes from producing x tabletops is modeled by the equation is given as,
p(x) = 480x – 2x²
Then the company need to make a profit of zero dollars will be
p(x) = 0
480x – 2x² = 0
2x(240 – x) = 0
x = 0, 240
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The US Department of Agriculture reports that the mean cost of raising a child from birth to age 2 in a rural area is $10,460. A team of economists believes this value is incorrect, so they select a random sample of 900 children (age 2) and find that the sample mean cost is $10,345 with a sample standard deviation of $1540. Is this significantly different than the US Department of Agriculture reports
Answer:
[tex]t=\frac{10345-10460}{\frac{1540}{\sqrt{900}}}=-2.24[/tex]
The degrees of freedom are given by:
[tex]df=n-1=900-1=899[/tex]
The p value for this case would be given by:
[tex]p_v =2*P(t_{(899)}<-2.24)=0.0127[/tex]
The p value is low and if we use a significance level of 0.05 we can reject the null hypothesis and we can conclude tha the true mean is different from 10460
Step-by-step explanation:
Information given
[tex]\bar X=10345[/tex] represent the mean height for the sample
[tex]s=1540[/tex] represent the sample standard deviation for the sample
[tex]n=900[/tex] sample size
[tex]\mu_o =10460[/tex] represent the value to verify
t would represent the statistic
[tex]p_v[/tex] represent the p value for the test
Hypothesis to test
We want to verify if the true mean is equal to 10460, the system of hypothesis would be:
Null hypothesis:[tex]\mu = 10460[/tex]
Alternative hypothesis:[tex]\mu \neq 10460[/tex]
The statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing the info given we got:
[tex]t=\frac{10345-10460}{\frac{1540}{\sqrt{900}}}=-2.24[/tex]
The degrees of freedom are given by:
[tex]df=n-1=900-1=899[/tex]
The p value for this case would be given by:
[tex]p_v =2*P(t_{(899)}<-2.24)=0.0127[/tex]
The p value is low and if we use a significance level of 0.05 we can reject the null hypothesis and we can conclude tha the true mean is different from 10460
Solve the inequality 7x ≥ –7
Answer:
x ≥ -1
Step-by-step explanation:
Divide everything by 7 to isolate x and you have your answer!
Answer:
x ≥ –1
Step-by-step explanation:
7x ≥ –7
Divide by 7
7x /7≥ –7/7
x ≥ –1