Given the equation 4x - 3y = 12
1. Write the equation in slope-intercept form.
2. Identify the slope and y-intercept.
3. Graph the line.
4. Identify if it is a positive or negative slope.
Answers
Answer:
see below
Step-by-step explanation:
Slope intercept form is y = mx+b where m is the slope and b is the y intercept
4x - 3y = 12
Solve for y
Subtract 4x from each side
4x-4x - 3y =-4x+ 12
-3y = -4x+12
Divide by -3
-3y/-3 = -4x/-3 + 12/-3
y = 4/3x -4
The slope is 4/3 and the y intercept is -4
The slope is Positive
Related Questions
What percent of this grid is unshaded?
The grid has 10 columns and 10 rows making 100 equal sized squares 5 rows are
unshaded. The sixth row has 6 squares unshaded.
Answers
As 5 rows= 50 squares
And 6 are unshaded in the sixth row
So 50+6=56
So 56/100
So 56%
Hope it helps
Plz rate
And don’t forget to mark as brainliest
Answer:
56% shaded
Step-by-step explanation:
if there are 100 boxes, then every box it 1%
5 rows (50%) + 6 extra boxes (6%) = 56%
Chocolate chip cookies have a distribution that is approximately normal with a mean of 24.7 chocolate chips per cookie and a standard deviation of 2.1 chocolate chips per cookie. Find Upper P 10 and Upper P 90. How might those values be helpful to the producer of the chocolate chip cookies?
Answers
Answer:
P10 = 27.4
P90 = 22.0
It helps the producer to know the higher (P10) and lower estimates (P90) for the amount of chocolate chips per cookie.
Step-by-step explanation:
In P10 and P90 the P stands for "percentile".
In the case of P10, indicates the value X of the random variable for which 10% of the observed values will be above this value X.
In the case of P90, this percentage is 90%.
In this case, we can calculate from the z-values for each of the percentiles in the standard normal distribution.
For P10 we have:
[tex]P(z>z_{P10})=0.1\\\\z_{P10}=1.2816[/tex]
For P90 we have:
[tex]P(z>z_{P90})=0.9\\\\z_{P90}=-1.2816[/tex]
Then, we can convert this values to our normal distribution as:
[tex]P10=\mu+z\cdot\sigma=24.7+1.2816\cdot 2.1=24.7+2.7=27.4 \\\\P90=\mu+z\cdot\sigma=24.7-1.2816\cdot 2.1=24.7-2.7=22.0[/tex]
Find the surface area of the solid shown or described. If necessary, round to the nearest tenth. A.348m^2 B.484m^2 C.180.7m^2 D.262m^2
Answers
Answer: 484m²
Step-by-step explanation: This is a question on solid shape.
The surface area of a cone is the same thing as the perimeter of the cone ie, the materials required to construct the cone.
Formula for the surface area of the cone = πrl + πr², ( the circular base )
From.the diagram,
r = 7.1m , l = 14.6m, π = 3.142
Now substitute for those values in.the formula above
SA = πrl + πr²
= 3.142 × 7.1 × 14.6 + 3.142 × 7.1²
= 325.6997 + 158.388
= 484.09
Now to the nearest tenth meter,
SA = 484m²
A sample of 26 offshore oil workers took part in a simulated escape exercise, and their escape time (unit: second) were observed. The sample mean and sample standard deviation are 370.69 and 24.36, respectively. Suppose the investigators had believed a priori that true average escape time would be at most 6 minutes. Does the data contradict this prior belief? Assuming normality, test the appropriate hypotheses using the rejection region method at a significance level of 0.05.
Answers
Answer:
Yes, it contradict this prior belief as there is enough evidence to support the claim that the true average escape time is significantly higher than 6 minutes.
Test statistic t=2.238>tc=1.708.
The null hypothesis is rejected.
Step-by-step explanation:
This is a hypothesis test for the population mean.
The claim is that the true average escape time is significantly higher than 6 minutes (360 seconds).
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=360\\\\H_a:\mu> 360[/tex]
The significance level is 0.05.
The sample has a size n=26.
The sample mean is M=370.69.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=24.36.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{24.36}{\sqrt{26}}=4.777[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{370.69-360}{4.777}=\dfrac{10.69}{4.777}=2.238[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=26-1=25[/tex]
The critical value for a right-tailed test with a significance level of 0.05 and 25 degrees of freedom is tc=1.708. If the test statistic is bigger than 1.708, it falls in the rejection region and the null hypothesis is rejected.
As the test statistic t=2.238 is bigger than the critical value t=1.708, the effect is significant. The null hypothesis is rejected.
There is enough evidence to support the claim that the true average escape time is significantly higher than 6 minutes (360 seconds).
In a plane, if a line is perpendicular to one of two blank lines, then it is also perpendicular to the other
Answers
Answer:
ParallelStep-by-step explanation:
The complete statement would be "if a line is perpendicular to one of two parallel lines, then it is also perpendicular to the other".
The reason for this is because parallel lines have the same slope, that's the condition. On the other hand, parallel lines have opposite and reciprocal slopes.
So, if you think this through, if a line is perpendicular to another, then it's going to be perpendicular to all different lines which are parallel to the first one, because all their slopes are equivalent, and they will fulfill the perpendicularity condition.
Answer:
Parallel line
Step-by-step explanation:
Hope It Helps
Identify the axis of symmetry of the given quadratic
y= -3x^2 - 12
Answers
Answer:
[tex]\frac{d}{dy}(-3x^{2} -12) = -6x[/tex]
0 = -6x
0 = x
[tex]-3(0)^{2} -12 = -12[/tex]
(0,-12)
Step-by-step explanation:
The straight line L has equation y = 1/2x+7 The straight line M is parallel to L and passes through the point (0, 3). Write down an equation for the line M.
Answers
Answer:
y = [tex]\frac{1}{2}[/tex] x + 3
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = [tex]\frac{1}{2}[/tex] x + 7 ← is in slope- intercept form
with slope m = [tex]\frac{1}{2}[/tex]
Parallel lines have equal slopes
line M crosses the y- axis at (0, 3) ⇒ c = 3
y = [tex]\frac{1}{2}[/tex] x + 3 ← equation of line M
Use the properties of logarithms to prove log81000= log210.
Answers
Answer:
Step-by-step explanation:
Given the expression [tex]log_81000 = log_210[/tex], to prove this expression is true using the properties of logarithm, we will follow the following steps.
Starting from the Left Hand Side:
[tex]log_81000\\[/tex]= log₈ 10³= log_ 2^3 (10³)= log₂10a. dashed line, shade below
b. dashed line, shaded above
c. solid line, shade above
d. solid line, shade below
Answers
Answer:
the answer is A
Step-by-step explanation:
Find the mass and center of mass of the lamina that occupies the region D and has the given density function rho. D is the triangular region with vertices (0, 0), (2, 1), (0, 3); rho(x, y) = 2(x + y)
Answers
The mass of the lamina is 6 units.
The center of mass of the lamina is (X,Y) = (-3/2, 9/2).
Here,
To find the mass and center of mass of the lamina, we need to integrate the density function ρ(x, y) over the triangular region D.
The mass (M) of the lamina is given by the double integral of the density function over the region D:
M = ∬_D ρ(x, y) dA
where dA represents the differential area element.
The center of mass (X,Y) of the lamina can be calculated using the following formulas:
X = (1/M) ∬_D xρ(x, y) dA
Y = (1/M) ∬_D yρ(x, y) dA
Now, let's proceed with the calculations:
The triangular region D has vertices (0, 0), (2, 1), and (0, 3). We can define the limits of integration for x and y as follows:
0 ≤ x ≤ 2
0 ≤ y ≤ 3 - (3/2)x
Now, let's calculate the mass (M):
M = ∬_D ρ(x, y) dA
M = ∬_D 2(x + y) dA
We need to set up the double integral over the region D:
M = ∫[0 to 2] ∫[0 to 3 - (3/2)x] 2(x + y) dy dx
Now, integrate with respect to y first:
M = ∫[0 to 2] [x(y²/2 + y)] | [0 to 3 - (3/2)x] dx
M = ∫[0 to 2] [x((3 - (3/2)x)²/2 + (3 - (3/2)x))] dx
M = ∫[0 to 2] [(3x - (3/2)x²)²/2 + (3x - (3/2)x²)] dx
Now, integrate with respect to x:
[tex]M = [(x^3 - (1/2)x^4)^2/6 + (3/2)x^2 - (1/4)x^3)] | [0 to 2]\\M = [(2^3 - (1/2)(2^4))^2/6 + (3/2)(2^2) - (1/4)(2^3)] - [(0^3 - (1/2)(0^4))^2/6 + (3/2)(0^2) - (1/4)(0^3)]\\M = [(8 - 8)^2/6 + 6 - 0] - [0]\\M = 6[/tex]
So, the mass of the lamina is 6 units.
Next, let's calculate the center of mass (X,Y):
X = (1/M) ∬_D xρ(x, y) dA
X = (1/6) ∬_D x * 2(x + y) dA
We need to set up the double integral over the region D:
X = (1/6) ∫[0 to 2] ∫[0 to 3 - (3/2)x] x * 2(x + y) dy dx
Now, integrate with respect to y first:
X = (1/6) ∫[0 to 2] [x(y² + 2xy)] | [0 to 3 - (3/2)x] dx
X = (1/6) ∫[0 to 2] [x((3 - (3/2)x)² + 2x(3 - (3/2)x))] dx
X = (1/6) ∫[0 to 2] [x(9 - 9x + (9/4)x² + 6x - (3/2)x²)] dx
X = (1/6) ∫[0 to 2] [(9/4)x³ - (3/2)x⁴ + 15x - (3/2)x³] dx
Now, integrate with respect to x:
[tex]X = [(9/16)x^4 - (3/8)x^5 + (15/2)x^2 - (3/8)x^4] | [0 to 2]\\X = [(9/16)(2)^4 - (3/8)(2)^5 + (15/2)(2)^2 - (3/8)(2)^4] - [(9/16)(0)^4 - (3/8)(0)^5 + (15/2)(0)^2 - (3/8)(0)^4]\\X = [9/2 - 12 + 15 - 0] - [0]\\X = 15/2 - 12\\X = -3/2[/tex]
Next, let's calculate Y:
Y = (1/M) ∬_D yρ(x, y) dA
Y = (1/6) ∬_D y * 2(x + y) dA
We need to set up the double integral over the region D:
Y = (1/6) ∫[0 to 2] ∫[0 to 3 - (3/2)x] y * 2(x + y) dy dx
Now, integrate with respect to y first:
Y = (1/6) ∫[0 to 2] [(xy² + 2y²)] | [0 to 3 - (3/2)x] dx
Y = (1/6) ∫[0 to 2] [x((3 - (3/2)x)²) + 2((3 - (3/2)x)²)] dx
Y= (1/6) ∫[0 to 2] [x(9 - 9x + (9/4)x²) + 2(9 - 9x + (9/4)x²)] dx
Y = (1/6) ∫[0 to 2] [(9x - 9x² + (9/4)x³) + (18 - 18x + (9/2)x²)] dx
Now, integrate with respect to x:
[tex]Y= [(9/2)x^2 - 3x^3 + (9/16)x^4) + (18x - 9x^2 + (9/6)x^3)] | [0 to 2]\\Y = [(9/2)(2)^2 - 3(2)^3 + (9/16)(2)^4) + (18(2) - 9(2)^2 + (9/6)(2)^3)] - [(9/2)(0)^2 - 3(0)^3 + (9/16)(0)^4) + (18(0) - 9(0)^2 + (9/6)(0)^3)]\\Y = [18 - 24 + 9/2 + 36 - 36 + 12] - [0]\\Y= 9/2[/tex]
So, the center of mass of the lamina is (X,Y) = (-3/2, 9/2).
Learn more about mass here
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E = { x l x is a perfect square <36}
Answers
Answer:
E = { x l x is a perfect square <36}
And we can rewrite it taking in count the list of all the perfect squares less than 36 and we have:
1= 1*1
4= 2*2
9 = 3*3
16 =4*4
25= 5*5
And we can rewrite the set on this way:
E= {1,4,9,16,25}
Step-by-step explanation:
For this problem we have the following set:
E = { x l x is a perfect square <36}
And we can rewrite it taking in count the list of all the perfect squares less than 36 and we have:
1= 1*1
4= 2*2
9 = 3*3
16 =4*4
25= 5*5
And we can rewrite the set on this way:
E= {1,4,9,16,25}
Select the correct answer.
The function RX) = 2x + 3x + 5, when evaluated, gives a value of 19. What is the function's input value?
A. 1
B. -1
C. 2
D. -2
E. -3
Answers
Answer:
Correct option: C.
Step-by-step explanation:
(Assuming the correct function is R(x) = 2x^2 + 3x + 5)
To find the input value that gives the value of R(x) = 19, we just need to use this output value (R(x) = 19) in the equation and then find the value of x:
[tex]R(x) = 2x^2 + 3x + 5[/tex]
[tex]19 = 2x^2 + 3x + 5[/tex]
[tex]2x^2 + 3x -14 = 0[/tex]
Solving this quadratic function using the Bhaskara's formula (a = 2, b = 3 and c = -14), we have:
[tex]\Delta = b^2 - 4ac = 9 + 112 = 121[/tex]
[tex]x_1 = (-b + \sqrt{\Delta})/2a = (-3 + 11)/4 = 2[/tex]
[tex]x_2 = (-b - \sqrt{\Delta})/2a = (-3 - 11)/4 = -3.5[/tex]
So looking at the options, the input to the function is x = 2
Correct option: C.
What is the next number in the sequence.
1,121,12321, 1234321
The next number in the sequence is _____
Answers
Answer:
123454321
Step-by-step explanation:
it's a palendrome, made out of a number of numbers in the sqquence.
What is the difference?
StartFraction x Over x squared + 3 x + 2 EndFraction minus StartFraction 1 Over (x + 2) (x + 1) EndFraction
StartFraction x minus 1 Over 6 x + 4 EndFraction
StartFraction negative 1 Over 4 x + 2 EndFraction
StartFraction 1 Over x + 2 EndFraction
StartFraction x minus 1 Over x squared + 3 x + 2 EndFraction
Answers
Answer:
The answer is option D.Step-by-step explanation:
First we must first find the LCM
The LCM of x² + 3x + 2 and (x + 2)(x + 1 ) is
x² + 3x + 2
So we have
[tex] \frac{x}{ {x}^{2} + 3x + 2 } - \frac{1}{(x + 2)(x + 1)} \\ \\ = \frac{x - 1}{ {x}^{2} + 3x + 2 } [/tex]
Hope this helps you
Answer:
The answer is OPTION D!
Step-by-step explanation:
HoPe ThIs HeLpS!
the table shows the time it took a group of students to complete a puzzle
Answers
Answer:
Where is the table because I dont see it up here?
Given the equation y = 7 sec(6x– 30)
The period is:
The horizontal shift is:
Answers
Answer:
The period is of [tex]\frac{\pi}{3}[/tex] units.
The horizontal shift is of 30 units to the left.
Step-by-step explanation:
The secant function has the following general format:
[tex]y = A\sec{(Bx + C)}[/tex]
A represents the vertical shift.
C represents the horizontal shift. If C is positive, the shift is to the right. If it is negative, it is to the left.
The period is [tex]P = \frac{2\pi}{B}[/tex]
In this question:
[tex]y = 7\sec{6x - 30}[/tex]
So [tex]B = 6, C = -30[/tex]
Then [tex]P = \frac{2\pi}{6} = \frac{\pi}{3}[/tex]
The period is of [tex]\frac{\pi}{3}[/tex] units.
The horizontal shift is of 30 units to the left.
mohsin is writing a 2400 words essay for his school project he writes 1/5 of the essay on the first day 2/3 of the remainder on the second day 220 words on third day now he has to write the conclusion how long was his conclusion
Answers
Answer: 420 words
Step-by-step explanation:
First find how much he did the first day by doing 1/5*2400=480.
Then find out how much he did the second day by doing 2400-480=1920, then doing 1920*(2/3)=1280.
Then, because he did 220 words the third day, simply do 2400-480-1280-220=420.
Hope it helps <3
Ans420 words per min
Step-by-step explanation:
C equals 2 pi r; Cequals62.8 (Circumference of a circle)
Answers
Answer:
about 10
Step-by-step explanation:
62.8 = 2 pi r/2
62.8/2 = pi r
31.4/pi = pi r/pi
about 10 = r
The U.S. Department of Agriculture guarantees dairy producers that they will receive at least $1.00 per pound of butter they supply to the market. Below is the current monthly demand and supply schedule for wholesale butter (in millions of pounds per month). Wholesale Butter Market
Price (dollars per pound) Quantity of Butter Demanded Quantity of Butter Supplied
(millions of pounds) (millions of pounds)
$0.80 107 63 0
.90 104 71
1.00 101 79
1.10 98 87
1.20 95 95
1.30 92 103
1.40 89 111
1.50 86 119
1.60 83 127
1.70 80 135
1.80 77 143
a. In the butter market, the monthly equilibrium quantity is million pounds and the equilibrium price is $ per pound.
b. What is the monthly surplus created in the wholesale butter market due to the price support (price floor) program? 22 million pounds 79 million pounds Zero 11 million pounds Suppose that a decrease in the cost of feeding cows shifts the supply schedule to the right by 40 million pounds at every price.
Answers
Answer:
a. In the butter market, the monthly equilibrium quantity is 95 million pounds and the equilibrium price is $1.2 per pound.
b. The correct option is zero.
c. See the attached excel file for the new supply schedule.
d. The monthly surplus created by the price support program is 18 million pounds given the new supply of butter.
Step-by-step explanation:
Note: This question is not complete. A complete question is therefore provided in the attached Microsoft word file.
a. In the butter market, the monthly equilibrium quantity is million pounds and the equilibrium price is $ per pound.
At equilibrium, quantity demanded must be equal with the quantity supplied.
In this question, equilibrium occurs at the price of $1.20 per pound and quantity of 95 million pounds.
Therefore, in the butter market, the monthly equilibrium quantity is 95 million pounds and the equilibrium price is $1.2 per pound.
b. What is the monthly surplus created in the wholesale butter market due to the price support (price floor) program?
Price floor refers to a government price control on the lowest price that can be charged for a commodity.
It should be noted that for a price floor to be binding, it has to be fixed above the equilibrium price.
Since the price floor of $1 per pound is lower than the equilibrium price of $1.2 per pound, the price floor will therefore not be binding. As a result, the market will still be at the equilibrium point and the monthly surplus created in the wholesale butter market due to the price support (price floor) program will be zero.
Therefore, the correct option is zero.
c. Fill in the new supply schedule given the change in the cost of feeding cows.
Since a decrease in the cost of feeding cows shifts the supply schedule to the right by 40 million pounds at every price, this implies that there will be an increase in supply by 40 million at each price.
Note: Find attached the excel file for the new supply schedule.
d. Given the new supply of butter, what is the monthly surplus of butter created by the price support program?
Since the price floor has been fixed at $1 per pound by the price support program, we can observe that the quantity demanded is 101 million pounds and quantity supplied is 119 million pounds at this price floor of $1. The surplus created is then the difference between the quantity demanded and quantity supplied as follows:
Surplus created = Quantity supplied - Quantity demanded = 119 - 101 = 18 million pounds
Therefore, the monthly surplus created by the price support program is 18 million pounds given the new supply of butter.
The larger of two numbers is 33 more than the smaller. When added together, the sum of the larger number and five times the smaller number is 129. What are the two numbers? larger number = ___ smaller number = ____ Please Help!
Answers
Step-by-step explanation:
let the larger number be x and smaller number be y
according to this question
x=y+33----------(1)
y+33+5y=129----------(2)
6y+33=129
y=16
x=16+33(takimg equation (1)
x=49
Answer:
Larger number: 49.
Smaller number: 16.
Step-by-step explanation:
Let's say that the larger number is represented by y, and the smaller is represented by x.
y = 33 + x
y + 5 * x = 129
(33 + x) + 5x = 129
6x + 33 = 129
6x = 96
x = 16
y = 33 + 16
y = 49
Check our work...
49 + 5 * 16 = 49 + 80 = 129
49 = 33 + 16 = 49
Since it all works out, the larger number is 49 and the smaller number is 16.
Hope this helps!
4b • 0.5a 2ab 2a2b 2ab2 2a2b2
Answers
Answer:
(4b)•(0.5a) = (4•0.5)(a)(b) = 2ab
Step-by-step explanation:
A department store finds that in a random sample of 200 customers, 60% of the sampled customers had browsed its website prior to visiting the store. Based on this data, a 90% confidence interval for the population proportion of customers that browse the store’s website prior to visiting the store will be between
Answers
Answer:
between 108-110?
Step-by-step explanation:
60% or 200 = 120 people
90% of 120 = 108
question doesnt look complete so this is the best I could come up with...♀️
List price is 45$ if the sales tax rate is 7% how much is the sales tax in dollars
Answers
Answer:
3.15 dollars
Step-by-step explanation:
The sales tax rate is 7% = 0.07
So, we need to multiply the listed price and the sales tax rate.
= 45 * 0.07 = 3.150 (3.15)
Hope this helps and please mark as the brainliest
The Rocky Mountain district sales manager of Rath Publishing Inc., a college textbook publishing company, claims that the sales representatives make an average of 41 sales calls per week on professors. Several reps say that this estimate is too low. To investigate, a random sample of 38 sales representatives reveals that the mean number of calls made last week was 42. The standard deviation of the sample is 3.9 calls. Using the 0.025 significance level, can we conclude that the mean number of calls per salesperson per week is more than 41?H0 : µ = 40
H1 : µ > 401. Compute the value of the test statistic. 2. What is your decision regarding H0?
Answers
Answer:
1. Test statistic t=1.581.
2. The null hypothesis H0 failed to be rejected.
There is not enough evidence to support the claim that the mean number of calls per salesperson per week is significantly more than 41.
NOTE: if the null hypothesis is µ = 40, there is enough evidence to support the claim that the mean number of calls per salesperson per week is significantly more than 40 (test statistic t=3.161).
Step-by-step explanation:
This is a hypothesis test for the population mean.
The claim is that the mean number of calls per salesperson per week is significantly more than 41.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=41\\\\H_a:\mu> 41[/tex]
The significance level is 0.025.
The sample has a size n=38.
The sample mean is M=42.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=3.9.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{3.9}{\sqrt{38}}=0.633[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{42-41}{0.633}=\dfrac{1}{0.633}=1.581[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=38-1=37[/tex]
This test is a right-tailed test, with 37 degrees of freedom and t=1.581, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=P(t>1.581)=0.061[/tex]
As the P-value (0.061) is bigger than the significance level (0.025), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the mean number of calls per salesperson per week is significantly more than 41.
For µ = 40:
This is a hypothesis test for the population mean.
The claim is that the mean number of calls per salesperson per week is significantly more than 40.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=40\\\\H_a:\mu> 40[/tex]
The significance level is 0.025.
The sample has a size n=38.
The sample mean is M=42.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=3.9.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{3.9}{\sqrt{38}}=0.633[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{42-40}{0.633}=\dfrac{2}{0.633}=3.161[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=38-1=37[/tex]
This test is a right-tailed test, with 37 degrees of freedom and t=3.161, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=P(t>3.161)=0.002[/tex]
As the P-value (0.002) is smaller than the significance level (0.025), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that the mean number of calls per salesperson per week is significantly more than 40.
My question is probably obvious but I don't know it. What is the z axis
Answers
Answer:
z-Axis. The axis in three-dimensional Cartesian coordinates which is usually oriented vertically. Cylindrical coordinates are defined such that the -axis is the axis about which the azimuth coordinate. is measured.
Step-by-step explanation:
Divide and answer in simplest form: 1/5 ÷ 7
Answers
Answer: 1/35
Step-by-step explanation:
1/5 = 0.2
0.2/7= 1/35
Answer:
[tex] \frac{1}{35} [/tex]Step by step explanation
[tex] \frac{1}{5} \div 7[/tex]
Dividing is equivalent to multiplying with the reciprocal:
[tex] \frac{1}{5} \times \frac{1}{7} [/tex]
Multiply the fraction
[tex] \frac{1 \times 1}{5 \times 7} [/tex]
[tex] = \frac{1}{35} [/tex]
Hope this helps...
Good luck on your assignment.
When individuals in a sample of 150 were asked whether or not they supported capital punishment, the following information was obtained. Do you support capital punishment? Number of individuals Yes 40 No 60 No Opinion 50 We are interested in determining whether or not the opinions of the individuals (as to Yes, No, and No Opinion) are uniformly distributed. The calculated value for the test statistic equals a. 20. b. 4. c. 2. d. -2.
Answers
Answer:
[tex]\chi^2 = \sum_{i=1}^n \frac{(O_i -E_i)^2}{E_i}[/tex]
The expected values for all the categories is :
[tex] E_i =\frac{150}{3}=50[/tex]
And then the statistic would be given by:
[tex]\chi^2 = \frac{(40-50)^2}{50}+\frac{(60-50)^2}{50}+\frac{(50-50)^2}{50}=4[/tex]
And the best option would be:
b. 4
Step-by-step explanation:
For this problem we have the following observed values:
Yes 40 No 60 No Opinion 50
And we want to test the following hypothesis:
Null hypothesis: All the opinions are uniformly distributed
Alternative hypothesis: Not All the opinions are uniformly distributed
And for this case the statistic would be given by:
[tex]\chi^2 = \sum_{i=1}^n \frac{(O_i -E_i)^2}{E_i}[/tex]
The expected values for all the categories is :
[tex] E_i =\frac{150}{3}=50[/tex]
And then the statistic would be given by:
[tex]\chi^2 = \frac{(40-50)^2}{50}+\frac{(60-50)^2}{50}+\frac{(50-50)^2}{50}=4[/tex]
And the best option would be:
b. 4
Assume that the random variable X is normally distributed, with mean 60 and standard deviation 16. Compute the probability P(X < 80). Group of answer choices
Answers
Answer:
P(X < 80) = 0.89435.
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
[tex]\mu = 60, \sigma = 16[/tex]
P(X < 80)
This is the pvalue of Z when X = 80. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{80 - 60}{16}[/tex]
[tex]Z = 1.25[/tex]
[tex]Z = 1.25[/tex] has a pvalue of 0.89435.
So
P(X < 80) = 0.89435.
Will give brainliest answer
Answers
Answer:
9π or 28.3 units²
Step-by-step explanation:
A = πr²
A = π(3)²
A = 9π
or
A= 28.3 units²
Hope this helps. :)
Which of the following statements must be true about this diagram? Check all that apply.
Answers
Answer:
Options (D), (E) and (F) are the correct options.
Step-by-step explanation:
From the figure attached,
1). Angle 4 is the exterior angle of the given triangle having interior angles 1, 2 and 3.
Therefore, by the property of exterior angle,
∠4 = ∠1 + ∠2
2). Since ∠4 = ∠1 + ∠2,
Therefore, ∠4 will be greater than ∠1
Similarly, ∠4 will be greater than ∠2
Therefore, Options (D), (E) and (F) are the correct options.