Answer:
We know that:
The original price was $515
and
It was $125 off
so we need to find the price of the sofa after the discount.
$515 - $125 = $390
The sale price of the sofa after the discount was $390
hope This helps and pls mark me brainliest if it did :)
Peggy had four times as many quarters as nickels. She had $2.10 in all. How many nickels and how many quarters did she have?
If the variable n represents the number of nickels, then which of the following expressions represents the number of quarters?
Answer:
2 nickels8 quartersStep-by-step explanation:
If n represents the number of nickels, and the number of quarters is 4 times the number of nickels, then the number of quarters is represented by 4n.
The total value of the coins in cents is ...
5(n) +25(4n) = 210
105n = 210 . . . . . . . . collect terms
n = 210/105 = 2 . . . . number of nickels
4n = 4(2) = 8 . . . . . . number of quarters
Peggy has 2 nickels and 8 quarters.
. Suppose that only 20% of all drivers come to a complete stop at an intersection having flashing lights in all directions when no other cars are visible. What is the probability that, of 15 randomly chosen drivers coming to an intersection under these conditions,
Answer:
a. P(x≤9)=0.9999
b. P(x=6)=0.0430
c. P(x≥6)=0.0611
Step-by-step explanation:
The question is incomplete:
a.At most 9 will come to a complete stop?
b.Exactly 6 will come to a complete stop?
c.At least 6 will come to a complete stop?
d.How many of the next 20 drivers do you expect to come to a complete stop?
The amount of drivers from the sample that will come to a complete stop can be modeled by a binomial random variable with n=15 and p=0.2.
The probability that exactly k drivers from the sample come to a complete stop is:
[tex]P(x=k) = \dbinom{n}{k} p^{k}q^{n-k}[/tex]
a. We have to calculate the probability that at most 9 come to a complete stop:
[tex]P(x\leq9)=\sum_{k=0}^9P(x=k)\\\\\\P(x=0) = \dbinom{15}{0} p^{0}q^{15}=1*1*0.0352=0.0352\\\\\\P(x=1) = \dbinom{15}{1} p^{1}q^{14}=15*0.2*0.044=0.1319\\\\\\P(x=2) = \dbinom{15}{2} p^{2}q^{13}=105*0.04*0.055=0.2309\\\\\\P(x=3) = \dbinom{15}{3} p^{3}q^{12}=455*0.008*0.0687=0.2501\\\\\\P(x=4) = \dbinom{15}{4} p^{4}q^{11}=1365*0.0016*0.0859=0.1876\\\\\\P(x=5) = \dbinom{15}{5} p^{5}q^{10}=3003*0.0003*0.1074=0.1032\\\\\\P(x=6) = \dbinom{15}{6} p^{6}q^{9}=5005*0.0001*0.1342=0.043\\\\\\[/tex]
[tex]P(x=7) = \dbinom{15}{7} p^{7}q^{8}=6435*0*0.1678=0.0138\\\\\\P(x=8) = \dbinom{15}{8} p^{8}q^{7}=6435*0*0.2097=0.0035\\\\\\P(x=9) = \dbinom{15}{9} p^{9}q^{6}=5005*0*0.2621=0.0007\\\\\\P(x\leq9)=0.0352+0.1319+0.2309+0.2501+0.1876+0.1032+0.043+0.0138+0.0035+0.0007\\\\P(x\leq9)=0.9999[/tex]
b. We have to calculate the probability that exactly 6 will come to a complete stop:
[tex]P(x=6) = \dbinom{15}{6} p^{6}q^{9}=5005*0.0001*0.1342=0.043\\\\\\[/tex]
c. We have to calculate the probability that at least 6 will come to a complete stop:
[tex]P(x\geq6)=\sum_{k=6}^{15}P(x=k)\\\\\\P(x=6) = \dbinom{15}{6} p^{6}q^{9}=5005*0.0001*0.1342=0.043\\\\\\P(x=7) = \dbinom{15}{7} p^{7}q^{8}=6435*0*0.1678=0.0138\\\\\\P(x=8) = \dbinom{15}{8} p^{8}q^{7}=6435*0*0.2097=0.0035\\\\\\P(x=9) = \dbinom{15}{9} p^{9}q^{6}=5005*0*0.2621=0.0007\\\\\\P(x=10) = \dbinom{15}{10} p^{10}q^{5}=3003*0*0.3277=0.0001\\\\\\P(x=11) = \dbinom{15}{11} p^{11}q^{4}=1365*0*0.4096=0\\\\\\P(x=12) = \dbinom{15}{12} p^{12}q^{3}=455*0*0.512=0\\\\\\[/tex]
[tex]P(x=13) = \dbinom{15}{13} p^{13}q^{2}=105*0*0.64=0\\\\\\P(x=14) = \dbinom{15}{14} p^{14}q^{1}=15*0*0.8=0\\\\\\P(x=15) = \dbinom{15}{15} p^{15}q^{0}=1*0*1=0\\\\\\P(x\geq6)=0.043+0.0138+0.0035+0.0007+0.0001+0+0+0+0\\\\P(x\geq6)=0.0611[/tex]
Reflect on the concept of function. What concepts (only the names) did you need to accommodate the concept of function in your mind? What is the simplest function you can imagine? In your day to day, is there any occurring fact that can be interpreted as a function? Is it possible to view a function? What strategy are you using to get the graph of a function?
Answer:
Step-by-step explanation:
For this kind of question you'd be better off if you'd write down and share your own answers to these conceptual questions and then ask for Brainly feedback on what you have written. You'll need to understand the concept of "function" often in algebra and beyond.
What concepts (only the names) did you need to accommodate the concept of function in your mind? input, output, rule, domain, range, mapping, variation (direct and inverse)
Simplest function: y = c (there's only one x-value and y equals that value)
In your day to day, is there any occurring fact that can be interpreted as a function? An electronic parking meter: the amount of time you can park at the meter without risking getting a ticket is dependent upon the number of quarters you insert into the meter, e. g, 15 minutes for 25 centers, 30 minutes for 50 cents, and so on.
Is it possible to view a function? Sure. Graph the function.
What strategy are you using to get the graph of a function? Set up a coordinate plane. Label the horizontal axis "x" and the vertical axis "y". Choose x (input) values that are included in the domain of the function. If the domain includes '0' you will be finding the 'y-intercept' of the function. Write the input and output as a point: (x, y). Plot that point. Choose other x values within the domain and calculate the corresponding y value for each. Plot several more points and draw a line or a curve through them. Of course there are more sophisticated strategies for graphing functions. Remember: If you're working with a function, there is never more than one output or y value for any particular input value.
2x^3-3x^2-11x+6 divide by x-3
Answer: [tex]2x^2+3x-2[/tex]
Step-by-step explanation:
You can do long division, which is very very hard to show with typing on a keyboard. You essentially want to divide the leading coefficient for each term. Ill try my best to explain it.
Do [tex]\frac{2x^3}{x}=2x^2[/tex]. Write 2x^2 down. Now multiply (x - 3) by it. Then subtract it from the trinomial.
[tex]2x^2*(x-3)=2x^3 -6x^2\\(2x^3 -3x^2-11x+6)-(2x^3-6x^2) = 3x^2-11x+6[/tex]
Now do [tex]\frac{3x^2}{x} =3x[/tex]. Write that down next to your 2x^2. Multiply 3x by (x - 3) to get:
[tex]3x(x-3)=3x^2-9x\\(3x^2-11x+6)-(3x^2-9x)=-2x+6[/tex]
Your final step is to do [tex]\frac{-2x}{x} =-2[/tex]. Write this -2 next to your other two parts
Multiply -2 by (x - 3) to get:
[tex]-2(x-3)=-2x+6\\(-2x+6)-(-2x+6)=0[/tex]
Our remainder is 0 so that means (x - 3) goes into that trinomial exactly:
[tex]2x^2+3x-2[/tex] times
Answer:
2x² + 3x -2
Step-by-step explanation:
2x³ - 3x² - 11x + 6 : (x - 3)
2x³ - 6x² from (x - 3) * 2x²
-------------------------- —
3x² - 11x + 6
3x² - 9x from (x - 3) * 3x
-------------------------- —
- 2x + 6
- 2x + 6 from (x - 3) * (-2)
-------------------------- —
0
so 2x³ - 3x² - 11x + 6 : (x - 3) = 2x² + 3x -2
There is a clothing store in Bartlesville. The owner has devised his own method of pricing items. A vest costs $20, socks cost $25, a tie costs $15 and a blouse costs $30. Using the method, how much would underwear cost?
Answer:
25
Step-by-step explanation:
I'm going with $25 since socks should cost as much as underwear, you wear them underneath and they're an essential.
Running times for 400 meters are Normally distributed for young men between 18 and 30 years of age with a mean of 93 seconds and a standard deviation of 16 seconds. How fast does a man have to run to be in the top 1% of runners?
Answer:
To be in the top 1% of the runners, the man has to run the 400 meters in at most 55.768 seconds.
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 = 93, \sigma = 16[/tex]
How fast does a man have to run to be in the top 1% of runners?
The lower the time, the faster they are. So the man has to be at most in the 1st percentile, which is X when Z has a pvalue of 0.01. So he has to run in at most X seconds, and X is found when Z = -2.327. Then
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-2.327 = \frac{X - 93}{16}[/tex]
[tex]X - 93 = -2.327*16[/tex]
[tex]X = 55.768[/tex]
To be in the top 1% of the runners, the man has to run the 400 meters in at most 55.768 seconds.
You have budgeted 2/5 of your monthly income for rent and utilities. Your monthly income is $2100.
a) What amount have you budgeted for rent and utilities?
b) What amount is left over for expenditures during the month?
Answer:
a. $840
b. $1,260
Step-by-step explanation:
a. 2/5 x 2100 = 840
b. 2100 - 840 = 1,260
which transformations are non ridged transformations pick two options (dialation, reflection, rotation, stretch, translation)
Determine whether the results appear to have statistical significance, and also determine whether the results appear to have practical significance. In a study of a gender selection method used to increase the likelihood of a baby being born a girl, 1936 users of the method gave birth to 950 boys and 986 girls. There is about a 21% chance of getting that many girls if the method had no effect.
Answer:
Due to the fact that there is 21% chance of getting that many girls by chance and also In conjunction to that; there is no test involved as well , we can conclude that the method does not have statistical significance.
The result does not appear to have a practical significance.
Step-by-step explanation:
Given that:
In a random selection 1936 users, we observed that the method gave birth to 950 boys and 986 girls
There is about a 21% chance of getting that many girls if the method had no effect.
Due to the fact that there is 21% chance of getting that many girls by chance and also In conjunction to that; there is no test involved as well , we can conclude that the method does not have statistical significance.
Given that:
The number of girls = 986
Number of boys = 950
Number of babies born = 1936
The percentage of girls = number of girls born/ number of babies born
The percentage of girls = 986 /1936
The percentage of girls = 0.5093
The percentage of girls = 50.93%
We can infer that this method does not have a practical significance because most couples would not prefer to use a method that raise the likelihood of a girl from the approximately 50% rate expected by chance to the 50.93% .
Zia is building a plastic model rocket that has the combined shape of a cone and a cylinder as shown. additionally, the cylinder has a hemisphere hollowed out of its bottom. the plastic for the cone weighs 1.4 grams per cubic centimeter and the plastic for the cylinder weights only 0.8 grams per cubic centimeter.
(a) the volume of plastic that remains in the cylinder after it has been hollowed out to the nearest cubic centimeter.
(b) what has a greater total weight, the plastic that makes up the cone or the plastic that makes up the cylinder after it has been hollowed out?
Answer:
226 cm^3
The mass of plastic used to make cylinder is greater
Step-by-step explanation:
Given:-
- The density of cone material, ρc = 1.4 g / cm^3
- The density of cylinder material, ρl = 0.8 g / cm^3
Solution:-
- To determine the volume of plastic that remains in the cylinder after gouging out a hemispherical amount of material.
- We will first consider a solid cylinder with length ( L = 10 cm ) and diameter ( d = 6 cm ). The volume of a cylinder is expressed as follows:
[tex]V_L =\pi \frac{d^2}{4} * L[/tex]
- Determine the volume of complete cylindrical body as follows:
[tex]V_L = \pi \frac{(6)^2}{4} * 10\\\\V_L = 90\pi cm^3\\[/tex]
- Where the volume of hemisphere with diameter ( d = 6 cm ) is given by:
[tex]V_h = \frac{\pi }{12}*d^3[/tex]
- Determine the volume of hemisphere gouged out as follows:
[tex]V_h = \frac{\pi }{12}*6^3\\\\V_h = 18\pi cm^3[/tex]
- Apply the principle of super-position and subtract the volume of hemisphere from the cylinder as follows to the nearest ( cm^3 ):
[tex]V = V_L - V_h\\\\V = 90\pi - 18\pi \\\\V = 226 cm^3[/tex]
Answer: The amount of volume that remains in the cylinder is 226 cm^3
- The volume of cone with base diameter ( d = 6 cm ) and height ( h = 5 cm ) is expressed as follows:
[tex]V_c = \frac{\pi }{12} *d^2 * h[/tex]
- Determine the volume of cone:
[tex]V_c = \frac{\pi }{12} *6^2 * 5\\\\V_c = 15\pi cm^3[/tex]
- The mass of plastic for the cylinder and the cone can be evaluated using their respective densities and volumes as follows:
[tex]m_i = p_i * V_i[/tex]
- The mass of plastic used to make the cylinder ( after removing hemispherical amount ) is:
[tex]m_L = p_L * V\\\\m_L = 0.8 * 226\\\\m_L = 180.8 g[/tex]
- Similarly the mass of plastic used to make the cone would be:
[tex]m_c = p_c * V_c\\\\m_c = 1.4 * 15\pi \\\\m_c = 65.973 g[/tex]
Answer: The total weight of the cylinder ( m_l = 180.8 g ) is greater than the total weight of the cone ( m_c = 66 g ).
The volume of the remaining plastic in the cylinder is large, which
makes the weight much larger than the weight of the cone.
Responses:
(a) Volume of the remaining plastic in the cylinder is 226 cm³(b) The weight of the cylinder is greater than the weight of the cone.How can the weight and volume be evaluated?Density of the plastic for the cone = 1.4 g/cm³
Density of the plastic used for the cylinder = 0.8 g/cm³
From a similar question, we have;
Height of the cylinder = 10 cm
Diameter of the cylinder = 6 cm
Height of the cone = 5 cm
(a) Radius of the cylinder, r = 6 cm ÷ 2 = 3 cm
Volume of a cylinder = π·r²·h
Volume of a hemisphere = [tex]\mathbf{\frac{2}{3}}[/tex] × π× r³
Volume of the cylinder after it has been hollowed out, V, is therefore;
[tex]V = \mathbf{\pi \times r^2 \times h - \frac{2}{3} \times \pi \times r^3}[/tex]Which gives;
[tex]V = \pi \times 3^2 \times 10 - \frac{2}{3} \times \pi \times 3^3 \approx \mathbf{ 226}[/tex]
Volume of the cylinder after it has been hollowed out, V ≈ 226 cm³(b) Volume of the cone = [tex]\mathbf{\frac{1}{3}}[/tex] × π × 3² × 5 ≈ 47.1
Mass of the cone = 47.1 cm³ × 1.4 g/cm³ ≈ 66 g
Mass of the hollowed cylinder ≈ 226 cm³ × 0.8 g/cm³ = 180.8 g
The mass and therefore, the weight of the plastic that makes up the hollowed cylinder is greater than the weight of the plastic that makes up the cone.Learn more about volume and density of solids here:
https://brainly.com/question/4773953
Item 5 Item 5
You are earning an average of $47,400 and will retire in 10 years. If you put 20% of your gross average income in an ordinary annuity compounded at 7% annually, what will be the value of the annuity when you retire?
Answer: the value of the annuity when you retire is $130919
Step-by-step explanation:
We would apply the future value which is expressed as
FV = C × [{(1 + r)^n - 1}/r]
Where
C represents the yearly payments.
FV represents the amount of money
in your account at the end of 10 years.
r represents the annual rate.
n represents number of years or period.
From the information given,
r = 7% = 7/100 = 0.07
C = 20/100 × 47400 = $9480
n = 10 years
Therefore,
FV = 9480 × [{(1 + 0.07)^10 - 1}/0.07]
FV = 9480 × [{1.967 - 1}/0.07]
FV = 9480 × 13.81
FV = $130919
The HCF of two numbers is 11, and their L.C.M is 368. If one number is 64, then the other number is ….
Answer:
63.45
Step-by-step explanation:
First, it should be noted that the question is incorrect because 64 can't be divided by 11 but assuming that the question is correct, the solution is as follows
Given
LCM = 368
HCF = 11
One number = 64
Required
The other number
Let both numbers be represented by m and n, such that
[tex]m = 64[/tex]
From laws of HCF and LCM
The product of both numbers = Product of HCF and LCM
i.e.
[tex]m * n = HCF * LCM[/tex]
By substituting 68 for m; 368 for LCM and 11 for HCF
[tex]m * n = HCF * LCM[/tex] becomes
[tex]64 * n = 368 * 11[/tex]
[tex]64n = 4048[/tex]
Divide both sides by 64
[tex]\frac{64n}{64} = \frac{4048}{64}[/tex]
[tex]n = \frac{4048}{64}[/tex]
[tex]n = 63.25[/tex]
PLEASE HELP
In two or more complete sentences, compare the number of x-intercepts in the graph of f(x) = x2 to the number of x-intercepts in the graph of g(x) = (x-2)2 -3. Be sure to include the transformations that occurred between the parent function f(x) and its image g(x).
Answer:
Ok, for f(x) = x^2 we have only one x-intercept (actually, two equal x-intercepts) at x = 0.
Now, for g(x) = (x - 2)^2 - 3
First, let's analyze the transformations.
When we have g(x) = f(x - a) this means that we moved "a" units to the right (if a is positive)
When we have g(x) = f(x) + a, this means that (if a > 0) we move the graph "a" units up.
In this case we have both those transformations:
g(x) = f(x - 2) - 3
this means that we move 2 units to the right, and 3 units down (because the number is negative)
now we can find the roots of g(x) as:
g(x) = (x - 2)^2 - 3 = x^2 - 4x + 4 - 3 = x^2 - 4x + 1 = 0
using the Bhaskara's equation:
[tex]x = \frac{4 +-\sqrt{4^2 - 4*1*1} }{2*1} = \frac{4 +- 3.5}{2}[/tex]
then the roots are:
x = (4 + 3.5)/2 = 3.75
x = (4 - 3.5)/2 = 0.25
Here we have two different x-intercepts
A, B, and C are collinear points. B is between A and C. AB = 5x + 8 BC = 6x - 1 AC = 12x - 11 Find AC.
Answer:
AC = 198
Step-by-step explanation:
Since all these points are collinear, we know that the addition of AB plus BC should give the same as AC. We can then set an equation that addresses this identity:
AB + BC = AC
5x +8 +6x - 1 = 12x - 11
Now re-arranging like terms in order to combine them:
8 - 1 + 11 = 12x - 5x - 6x
19 - 1 = 12x - 11x
18 = x
Now that we know the value of 'x", we can determine the value of AC:
AC = 12x - 11
AC = 12 (18) - 11
AC = 216 - 18
AC = 198
You received your monthly bank statement and you are reconciling your account balance using the information below. What is the true balance of your checking account? Check Register Balance $314.97 Bank Statement Balance $423.68 Outstanding Checks $123.71 Service Charge $15.00
Answer:
299.97 is the actual answer
Step-by-step explanation:
I took the test.
What is the quotient of (x3-x2-17x-15) / (x-5)
Answer:
Step-by-step explanation:
x
2
+
4
x
+
3
x
2
+
4
x
+
3
On his way out to meet a friend for lunch, David realized that his financial record was not up to date. He notices that he forgot to record three transactions. The first transaction was on August 2nd in the amount of $12.32, another transaction on that same day in the amount or $52.34, and finally a transaction on August 8th in the amount of $85.35. Determine David's balance carried forward for the 8th of August using the table below and the information provided. A check register. The Balance on August fifth is 1,049 dollars and 16 cents. a. $975.32 b. $899.15 c. $1,049.16 d. $848.84
Answer:
b
Step-by-step explanation:
add the three numbers together then minus from the main total
Answer:
B. $899.15
Step-by-step explanation:
I need help!!!! I don’t understand and it’s very confusing
Answer:
C
Step-by-step explanation:
I explained in my last answer but someone deleted it
The relationship between ttt and rrr is expressed by the equation 2t+3r+6=02t+3r+6=02, t, plus, 3, r, plus, 6, equals, 0. If rrr increases by 444, which of the following statements about ttt must be true?
Question:
The relationship between t and r is expressed by the equation 2t+3r+6 = 0. If r increases by 4, which of the following statements about t must be true?
Answer:
The value of t is reduced by 6 when the value of r is increased by 4
Step-by-step explanation:
Given
[tex]2t + 3r + 6 = 0[/tex]
Required
What happens when r is increased by 4
[tex]2t + 3r + 6 = 0[/tex] -------- Equation 1
Subtract 2t from both sides
[tex]2t + 3r + 6 - 2t = 0 - 2t[/tex]
[tex]3r + 6 = - 2t[/tex] --- Equation 2
When r is increased by 4, equation 1 becomes
[tex]2T + 3(r+4) + 6 = 0[/tex]
Note that the increment of r also affects the value of t; hence, the new value of t is represented by T
Open bracket
[tex]2T + 3r+12 + 6 = 0[/tex]
Rearrange
[tex]2T + 3r+6 +12 = 0[/tex]
Substitutr -2t for 3r + 6 [From equation 2]
[tex]2T -2t +12 = 0[/tex]
Make T the subject of formula
[tex]2T = 2t - 12[/tex]
Divide both sides by 2
[tex]\frac{2T}{2} = \frac{2t - 12}{2}[/tex]
[tex]T = t - 6[/tex]
This means that the value of t is reduced by 6 when the value of r is increased by 4
Simplify the expression and then evaluate it for the given value of the variable: (6−2x)+(15−3x) for x=−0.2
PLEASE HELP!!!!!!
Answer:
20
Step-by-step explanation:
The simplified expression is -5x+21
-5(0.2)+21=
-1+21= 20
Answer:
24
Step-by-step explanation:
f(x)= (6−2x)+(15−3x)
x=-0.2
f(-0.2)=(6−2(-0.2)+(15−3(-0.2))
f(-0.2)=(6+0.4)+(15+0.6)
f(-0.2)=6.4+15.6
f(-0.2)=22
You are on a TV show. You have been asked to either play a dice game five times or accept a $50 bill. The dice game works like this. If you roll a 1, 2 or 3, you win $50. If you roll a 4 or 5, you lose $20. If you roll a 6, you lose $90.
EV= $
Step-by-step explanation:
Take the $50 and quit.
(Each game as outlined by drwls has an expected value of $1.50.
You are playing it 5 times, so the expected return is $7.50.
Your choice was to either accept $50 or play the game)
three friends went to a restraunt and ordered two orders of wings and three soft drinks. their bill totaled $22.50. later that day, five friends went to the same restraunt and ordered three orders of wings and a soft drink each. their bill totaled $34.50. write and solve a system of equations to determine the price of one order of wings.
Answer:
$9
Step-by-step explanation:
Let the price of one order of wings be w.
Let the price for one order of soft drinks be s.
Three friends went to a restaurant and ordered two orders of wings and three soft drinks. Their bill totaled $22.50. This means that:
2w + 3s = 22.50 _____________(1)
Five friends went to the same restaurant and ordered three orders of wings and a soft drink each. Their bill totaled $34.50. This means that:
3w + 5s = 34.50 ______________(2)
We have a system of quadratic equations:
2w + 3s = 22.50 _____________(1)
3w + 5s = 34.50 ______________(2)
Multiply (1) by 5 and (2) by 3:
10w + 15s = 112.50 _______(3)
9w + 15s = 103.50 _______(4)
Subtract (4) from (3):
w = $9
Therefore, the price of one order of wings is $9.
A new post-surgical treatment is being compared with a standard treatment. Seven subjects receive the new treatment, while seven others (the controls) receive the standard treatment. The recovery times, in days, are given below.
Treatment: 12 13 15 19 20 21 24
Control: 18 23 24 30 32 35 39
Required:
Find a 98% confidence interval for the difference in the mean recovery times between treatment and control.
Answer:
[tex] (17.714-28.714) -2.681 \sqrt{\frac{4.461^2}{7} +\frac{7.387^2}{7}}= -19.745[/tex]
[tex] (17.714-28.714) +2.681 \sqrt{\frac{4.461^2}{7} +\frac{7.387^2}{7}}= -2.255[/tex]
Step-by-step explanation:
For this case we have the following info given:
Treatment: 12 13 15 19 20 21 24
Control: 18 23 24 30 32 35 39
We can find the sample mean and deviations with the the following formulas:
[tex] \bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]
[tex] s =\sqrt{\frac{\sum_{i=1}^n (X_i- \bar X)^2}{n-1}}[/tex]
And repaplacing we got:
[tex] \bar X_T = 17.714[/tex] the sample mean for treatment
[tex] \bar X_C = 28.714[/tex] the sample mean for treatment
[tex] s_T= 4.461[/tex] the sample deviation for treatment
[tex] s_C= 7.387[/tex] the sample deviation for control
[tex]n_T= n_C= 7[/tex] the sample size for each sample
The degrees of freedom are given by:
[tex] df= 7+7-2= 12[/tex]
The confidence interval for the difference of means is given by:
[tex] (\bar X_T -\bar X_C) \pm t_{\alpha/2} \sqrt{\frac{s^2_T}{n_T} +\frac{s^2_C}{n_C}}[/tex]
The confidence is 98% so then the significance is [tex]\alpha=0.02[/tex] and [tex] \alpha/2 =0.01[/tex]. Then the critical value would be:
[tex] t_{\alpha/2}=2.681[/tex]
And replacing we got:
[tex] (17.714-28.714) -2.681 \sqrt{\frac{4.461^2}{7} +\frac{7.387^2}{7}}= -19.745[/tex]
[tex] (17.714-28.714) +2.681 \sqrt{\frac{4.461^2}{7} +\frac{7.387^2}{7}}= -2.255[/tex]
11. List and describe three factors that may affect body temperature.
it is age heart rate and weather
You are choosing between two different window washing companies. The first charges $5 per window. The second charges a base fee of $40 plus $3 per window
Answer:
you forgot the rest of the question homie but once there is 20 companies both companies will be equal
Step-by-step explanation:
Answer:
20 windows
Step-by-step explanation:
Which of these shapes have rectangular cross sections when they are cut perpendicular to the base? Select three options.
-rectangular prism
-triangular prism
-cylinder
-cone
-square pyramid
-triangular pyramid
Answer:
A, B, and E
Step-by-step explanation:
Answer:
abe
Step-by-step explanation:
WILL MARK BRAINLIEST !!!
In the given point(-4,b) -4 is the x value.
Locate -4 on the graph and find the y value where the line is located. The y value would be b.
B = 1
Many students brag that they have more than 150 friends on a social media website. For a class project, a group of students asked a random sample of 13 students at their college who used the social media website about their number of friends and got the data available below. Is there strong evidence that the mean number of friends for the student population at the college who use the social media website is larger than 150?
Required:
a. Find and interpret the test statistic value.
b. Report and interpret the P-value and state the conclusion in context. Use a significance level of 0.05.
c. What does the test statistic value represent?
1. The test statistic value is the difference between the sample mean and the null hypothesis value.
2. The test statistic value is the number of standard errors from the null hypothesis value to the sample mean.
3. The test statistic value is the expected mean of the differences between the sample data and the null hypothesis value.
4. The test statistic value is the number of standard deviations from the null hypothesis value to the sample mean.
Answer:
Step-by-step explanation:
The question is incomplete. The missing data is:
30, 155, 205, 235, 180, 235, 70, 250, 135, 145, 225, 230, 30
Solution:
Mean = (30 + 155 + 205 + 235 + 180 + 235 + 70 + 250 + 135 + 145 + 225 + 230 + 30)/13 = 163.5
Standard deviation = √(summation(x - mean)²/n
n = 13
Summation(x - mean)² = (30 - 163.5)^2 + (155 - 163.5)^2 + (205 - 163.5)^2+ (235 - 163.5)^2 + (180 - 163.5)^2 + (235 - 163.5)^2 + (70 - 163.5)^2 + (250 - 163.5)^2 + (135 - 163.5)^2 + (145 - 163.5)^2 + (225 - 163.5)^2 + (230 - 163.5)^2 + (30 - 163.5)^2 = 73519.25
Standard deviation = √(73519.25/13) = 75.2
We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean
For the null hypothesis,
µ ≤ 150
For the alternative hypothesis,
µ > 150
It is a right tailed test.
a) Since the number of samples is small and no population standard deviation is given, the distribution is a student's t.
Since n = 13,
Degrees of freedom, df = n - 1 = 13 - 1 = 12
t = (x - µ)/(s/√n)
Where
x = sample mean = 163.5
µ = population mean = 150
s = samples standard deviation = 75.2
t = (163.5 - 150)/(75.2/√13) = 0.65
The lower the test statistic value, the higher the p value and the higher the possibility of accepting the null hypothesis.
b) We would determine the p value using the t test calculator. It becomes
p = 0.26
Since alpha, 0.05 < than the p value, 0.26, then we would fail to reject the null hypothesis. Therefore, At a 5% level of significance, the sample data does not show significant evidence that the mean number of friends for the student population at the college who use the social media website is larger than 150.
c)
1.The test statistic value is the difference between the sample mean and the null hypothesis value.
How many real solutions does the function shown on the graph have?
Answer:
2 real solutions
Step-by-step explanation:
In a 30-60-90 triangle, the length of the side opposite the 30 degree angle is 8. Find the length of the side opposite the 60 degree angle.
Answer:
The length of the side opposite the 60 degree angle 'c' = 4
Step-by-step explanation:
Step(i):-
Given data ∠A = 90° , ∠B = 60° and ∠C = 30°
Given data the length of the side opposite the 30 degree angle is 8
let 'a' = 8
step(ii):-
By using sine rule formula in properties of triangle
[tex]\frac{a}{Sin A} = \frac{b}{Sin B} = \frac{c}{Sin C} = 2 R[/tex]
[tex]\frac{a}{Sin A} = \frac{c}{Sin C}[/tex]
[tex]\frac{8}{Sin 90} = \frac{c}{Sin 30}[/tex]
cross multiplication , we get
[tex]\frac{8 X sin 30}{Sin 90} = c[/tex]
we know that trigonometry formulas
sin 30° = [tex]\frac{1}{2}[/tex] and sin 90°= 1
C = 8 X 1/2 = 4
conclusion:-
The length of the side opposite the 60 degree angle 'c' = 4
