9514 1404 393
Answer:
common ratio: -2first term -3/4sum of 11 terms: -2049/4Step-by-step explanation:
The formula for the generic term can be solved to find the first term and the common ratio.
an = a1·r^(n-1)
For the given terms, we have ...
a4 = 6 = a1·r^(4 -1)
a7 = -48 = a1·r^(7-1)
Dividing the second equation by the first gives ...
a7/a4 = -48/6 = r^(6 -3)
r = (-8)^(1/3)
r = -2 . . . . . . . . . . the common ratio
Then the first term is ...
6 = a1·(-2)^(3) = -8a1
-6/8 = a1 = -3/4 . . . . . the first term
__
The sum of N terms is ...
Sn = a1·(r^n -1)/(r -1)
Then the sum of 11 terms is ...
S11 = (-3/4)((-2)^11 -1)/(-2-1) = (-1/4)(2^11 +1)
S11 = -2049/4 . . . . . the sum of 11 terms
Two alloys A and B are being used to manufacture a certain steel product. An experiment needs to be designed to compare the two in terms of maximum load capacity in tons (the maximum weight that can be tolerated without breaking). It is known that the two standard deviations in load capacity are equal at 5 tons each. An experiment is conducted in which 30 specimens of each alloy (A and B) are tested and the results recorded as follows:
x¯A = 49.5, x¯B = 45.5, x¯A − x¯B = 4
The manufacturers of alloy A are convinced that this evidence shows conclusively that muA & muB and strongly supports the claim that their alloy is superior. Manufacturers of alloy BB claim that the experiment could easily have given x¯A − x¯B = 4 even if the two population means are equal. In other words, "the results are inconclusive!"
(a) Make an argument that manufacturers of alloy B are wrong. Do it by computing
P(x¯A − x¯B > 4 | muA - muB
(b) Do you think these data strongly support alloy A?
Answer:
Step-by-step explanation:
From the given information, we can compute the table showing the summarized statistics of the two alloys A & B:
Alloy A Alloy B
Sample mean [tex]\bar {x} _A = 49.5[/tex] [tex]\bar {x} _B = 45.5[/tex]
Equal standard deviation [tex]\sigma_A = 5[/tex] [tex]\sigma_B= 5[/tex]
Sample size [tex]n_A = 30[/tex] [tex]n_{B}= 30[/tex]
Mean of the sampling distribution is :
[tex]\mu_{\bar{X_1}-\bar{X_2}}= 49.5-45.5 \\ \\ = 4.0[/tex]
Standard deviation of sampling distribution:
[tex]\sigma_{\bar{x_1}-\bar{x_2} }= \sqrt{\sigma^2_{\bar{x_1}-\bar{x_2} }} \\ \\ = \sqrt{\dfrac{\sigma_1^2}{n_1} + \dfrac{\sigma^2_2}{n_2} } \\ \\ =\sqrt{\dfrac{25}{30}+\dfrac{25}{30}} \\\\=\sqrt{1.667} \\ \\ =1.2909[/tex]
Hypothesis testing.
Null hypothesis: [tex]H_o: \mu_A -\mu_B = 0[/tex]
Alternative hypothesis: [tex]H_A:\mu_A -\mu_B > 4[/tex]
The required probability is:
[tex]P(\overline X_A - \overline X_B>4|\mu_A - \mu_B) = P\Big (\dfrac{(\overline X_A - \overline X_B)-\mu_{X_A-X_B}}{\sigma_{\overline x_A -\overline x_B}} > \dfrac{4 - \mu_{X_A-\overline X_B}}{\sigma _{\overline x_A - \overline X_B}} \Big) \\ \\ = P \Big( z > \dfrac{4-0}{1.2909}\Big) \\ \\ = P(z \ge 3.10)\\ \\ = 1 - P(z < 3.10) \\ \\ \text{Using EXCEL Function:} \\ \\ = 1 - [NORMDIST(3.10)] \\ \\ = 1- 0.999032 \\ \\ 0.000968 \\ \\ \simeq 0.0010[/tex]
This implies that a minimal chance of probability shows that the difference of 4 is not likely, provided that the two population means are the same.
b)
Since the P-value is very small which is lower than any level of significance.
Then, we reject [tex]H_o[/tex] and conclude that there is enough evidence to fully support alloy A.
Sale price decreased from $22 to $17 percent of change
Answer:
22%
Step-by-step explanation:
Two investments totaling $15,500 produce an annual income of $1450. One investment yields 10% per year, while the other yields 5% per year. How much is invested at each rate?
Answer:10% rate:
Principal = p
Rate = 0.10
Interest = 0.10p
5% rate:
Principal = 15500 - p
Rate = 0.05
Interest = 0.05(15500 - p) = 775 - 0.05p
0.10p + (775 - 0.05p) = 1450
0.05p + 775 = 1450
0.05p = 675
p = 13500
10% rate:
Principal = p = $13,500
5% rate:
Principal = 15500 - p = 15500 - 13500 = $2000
Step-by-step explanation:
hope it helps
what is 2/5 * 2 3/4 equal to
Answer:
1 1/10
Step-by-step explanation:
Hope this helps
Happy Easter!
May the Lord bless you
Have a nice day!
:)
Let 2_3/4 be 11/4.
We now have 2/5 * 11/4.
(numerator times numerator)/(denominator times denominator).
(2 * 11)/(5 * 4)
22/20
We can now reduce this fraction to the lowest terms.
The greatest factor of 22 and 20 is 2.
22 divided by 2 = 11.
20 divided by 2 = 10.
Answer: 11/10
For the given scenario, determine the type of error that was made, if any.
A new whitening toothpaste advertises four shades as the mean number of shades the toothpaste whitens your teeth. One user claims that the mean number of shades the toothpaste whitens your teeth is less than four shades. The user conducts a hypothesis test and fails to reject the null hypothesis. Assume that in reality, the mean number of shades the toothpaste whitens your teeth is three shades. Was an error made? If so, what type?
a. yes type I error
b. yes type II error
c. no correct decison
Answer:
b. yes type II error
Step-by-step explanation:
When the null hypothesis is false as is in this case and it is accepted so the decision made is wrong. This is a type II error.
When we accept the null hypothesis when actually it is false it is called a type II error.
In reality, the mean number of shades the toothpaste that whitens the teeth is three shades.
Where as the null hypothesis was that the four shades are taken as the mean number of shades the toothpaste whitens the teeth.
Therefore as the null hypothesis which is actually false is accepted so a wrong decision is made a type II error is made.
During an economic downturn, 11 companies were sampled and asked whether they were planning to increase their workforce. Only 2 of the 11 companies were planning to increase their workforce. Use the small-sample method to construct an 80% confidence interval for the proportion of companies that are planning to increase their workforce. Round the answers to at least three decimal places.
An 80% confidence interval for the proportion of companies that are planning to increase their workforce is _______ < p< ________
Answer:
An 80% confidence interval for the proportion of companies that are planning to increase their workforce is 0.033 < p < 0.331.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
Only 2 of the 11 companies were planning to increase their workforce
This means that [tex]n = 11, \pi = \frac{2}{11} = 0.182[/tex]
80% confidence level
So [tex]\alpha = 0.2[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.2}{2} = 0.9[/tex], so [tex]Z = 1.28[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.182 - 1.28\sqrt{\frac{0.182*0.818}{11}} = 0.033[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.182 + 1.28\sqrt{\frac{0.182*0.818}{11}} = 0.331[/tex]
An 80% confidence interval for the proportion of companies that are planning to increase their workforce is 0.033 < p < 0.331.
Nikola buys a bouquet of 8 sunflowers for $18.
What is the cost of 1 sunflower?
1 sunflower costs $2.25 because 18/8=2.25
Enlarge the triangle by scale fador 3 using the blue det
as the centre of enlargement
Answer:
Step-by-step explanation:
Let the blue point is located at the origin.
Therefore, coordinates of the vertices of the given triangle ABC will be,
A(2, 1), B(2, -1) and C(3, -1)
Rule for the dilation of a point (x, y) by a scale factor 'k' will be,
(x, y) → (kx, ky)
By applying this rule, coordinates of the image points of the vertices will be,
A(2, 1) → A'(2k, k)
→ A'(6, 3) for (k = 3)
B(2, -1) → B'(6, -3)
C(3, -1) →C'(9, -3)
Answer:
So this is the right answer.....
Step-by-step explanation:
Please help! What is the Area of the Triangle?
Answer and explanation please! <3
Answer:
5
Step-by-step explanation:
A1 = (h*b)/2
= ( (8-1)*(3-1) ) /2
= 7
A2 = (h*b)/2
= (2*2) /2
= 2
Ablue = A1 - A2
= 7 - 2
= 5
When working with a sample of size 25, find the area under a t-curve:
(a) Above 2.
(b) Below -1.6
(c) Between -0.9 and 1.9.
Answer:
YUH SHAWTY BAE SHAWTY BAD SHAWTY GAYYY
Step-by-step explanation:
CALL ME WHEN U WANT CALL ME WHEN U NEED CALL ME IN THE MORNING ILL BE ON THE WAYYYYY
Answer:
C
Step-by-step explanation:
Mark me brainllest
You randomly draw twice from this deck of cards
What is the probability of drawing a 3, then drawing an even number without replacing the first card?
Answer:
probability: 1/10 or 10%
Which equation best describes the graph?
8
2
-8
-6
-4
-2
2
2
8
-2
4
-6
-8
С
A y = 2x + 4
y = -2x +
Dy=-3x+4
B
y = 3x + 4
Answer:
b i think
Step-by-step explanation:
Answer:
b...................
PALEEZE Help Me!! The ceiling of Katie’s living room is a square that is 16 ft long on each side. To decorate for a party, she plans to hang crepe paper around the perimeter of the ceiling and then from each corner to the opposite corner. Katie can buy rolls that each contain 28 ft of crepe paper. What is the minimum number of rolls she should buy? Show your work and draw a diagram to support your answer.
Answer:
At least 4
Step-by-step explanation:
Photo of my work and where I got the equation from
Write the fractions as BOTH percentages and decimals.
74/89
Answer:
0.83 in decimal
83% in percentage
Find the perimeter of the figure to the nearest hundredth.
6 cm
10 cm
8 cm
12 cm
Answer:
36 cm
Step-by-step explanation:
Perimeter = sum of lenght of all sides
Perimeter = 6 + 10 + 8 + 12
Perimeter = 36 cm
find the volume round to the nearest 10
Answer:
Volume of triangular pyramid = 56 mi³
Step-by-step explanation:
Given:
Height of base = 6 mi
Base of triangular base = 8 mi
Height of triangular pyramid = 7 mi
Find:
Volume of triangular pyramid
Computation:
Area of triangular pyramid = (1/2)(b)(h)
Area of triangular pyramid = (1/2)(6)(8)
Area of triangular pyramid = 24 mi
Volume of triangular pyramid = (1/3)(A)(H)
Volume of triangular pyramid = (1/3)(24)(7)
Volume of triangular pyramid = 56 mi³
What are the first four terms of the sequence modeled by the recursive formula a n =a n-1 +5, when a1 = -3?
Answer:2,7,12,19
Step-by-step explanation:
a2=a2-1+5=-3+5=2
a3=a3-1+5=a2+5=2+5=7
a4=a3+5=12 and continue so on
how to find a slope of a line
Answer:
The slope of a line characterizes the direction of a line. To find the slope, you divide the difference of the y-coordinates of 2 points on a line by the difference of the x-coordinates of those same 2 points
A researcher is interested in estimating the mean weight of a semi tracker tractor truck to determine the potential load capacity. She takes a random sample of 17 trucks and computes a sample mean of 20,000 pounds with sample standard deviation of 1,500. The 95% confidence interval for the population mean weight of a semi tracker tractor truck is ______________.
Answer:
(19228.737 ; 20771.263)
Step-by-step explanation:
Given that:
Sample size, n = 17
Sample mean, m = 20,000
Sample standard deviation, s = 1500
α = 95%
The confidence interval,
Mean ± margin of error
Margin of Error : Tcritical * s/sqrt(n)
Tcritical at α = 0.05 ; df = n-1 = 17 - 1 = 16 ; 2 - tailed test = 2.120
Margin of Error = 2.120 * 1500/sqrt(17) = 771.263
Lower boundary :
20,000 - 771.263 = 19228.737
Upper boundary :
20,000 + 771.263 = 20771.263
Confidence interval :
(19228.737 ; 20771.263)
Of the 16 children in the park, seven-eighths are wearing a red shirt. How many children in the park are wearing a red shirt?
Answer:
14 children are wearing a red shirt in the park.
Step-by-step explanation:
The fraction 7/8 is 7 out of 8 but your total kids is 16 so we can go ahead and multiply by 2.
(7*2)/(8*2)
14/16
So now it's 14 out of 16 kids which is the total you have.
Conclusion: 14 Children are wearing a red shirt in the park.
One of the following is a regression example for which Entity and Time Fixed Effects could be used: ________
a. minimum wages on teenage employment using annual data from the 48 contiguous states in 2006.
b. various performance statistics on the (log of) salaries of baseball pitchers in the American League and the National League in 2005 and 2006.
c. inflation and inflationary expectations on unemployment rates in the United States, using quarterly data from 1960-2006.
d. drinking alcohol on the GPA of 150 students at your university, controlling for incoming SAT scores.
Answer:
b
Step-by-step explanation:
The regression which comprises of both entity & time effect can be expressed as;
[tex]Y_{it} = B_1X_{it} + \alpha_i + \lambda_i + \mu_{it}[/tex]
Where;
take charge of the state-explicit qualities that don't change over the long run
controls the variables that differ after some time yet not across substances,
[tex]u_{it}[/tex] controls state-specific qualities which shift after some time.
Thus, from the options given above:
The first option lacks or does not involve the time effect as we are only looking for a particular year.
The second option comprises only 2 years of data which implies that we have a time effect involved. In addition to that, there exist a few variables in executing measurements that join fixed effects. In this case, we can utilize regression with time and fixed effect.
(c) The information here is quarterly over an extended period of time. Hence, it would prefer a period arrangement information than a fixed and time impact information. Thus, this is incorrect.
(d) Since no time variable is associated, we reject the option.
Can someone help meeee plz and no link plz is due in 9 minutes
Answer:
A (4,3)
Step-by-step explanation:
J is inside the parallelogram.
K is indside a trapezium.
So we want to find the coordinates of point J.
Reading from the scales, point J is x = 4 and y = 3.
Writing our answer in the form (x, y) coordinates of J are: (4,3)
Please help quickly what's the answer Ill give u brainlest
Richard deposits $193.67 every month into his mortgage. At the end of 30 years, he has a balance of $120,182.07. What interest has accrued (been earned) over 30 years?
Please help!
Center:_____
Radius:_____
# of radi:____
Diameter:_____
# of Diameters:_____
Circumference:_____
Answer:
Center = P
Radius = 12 cm
Diameter = 2(radius) = 2(12) = 24 cm
Circumference = 2πr = 2(3.14)(12) =75.36 cm
There are infinite radii and diameters in a circle.
Hi please help me with this asap.
Answer:
Step-by-step explanation:
Top question
150000-(150000*.15Take 150000*.15 and get 22500, Then 150000-22500=127500
Question two
A- 3000Take 1/3*9000=3000
B-60009000-(9000*1/3)
From a train station, one train heads north, and another heads east. Some time later, the northbound train has traveled 12 miles, and the eastbound train has traveled 16 miles. How far apart are the two trains, measured in a straight line?
9514 1404 393
Answer:
20 miles
Step-by-step explanation:
The north and east distances form the legs of a right triangle. The straight-line distance between the trains is the hypotenuse of that triangle. The Pythagorean theorem can be used to find the length of the hypotenuse (d).
d² = 12² +16²
d² = 144 +256 = 400
d = √400 = 20
The two trains are 20 miles apart.
__
Additional comment
You may recognize the given distances are in the ratio 3 : 4. You may recall that side ratios of 3 : 4 : 5 make a right triangle. If so, you recognize that the straight-line distance is (4 miles)×5 = 20 miles. (3:4:5 right triangles show up often in algebra and geometry problems, so might be something you want to look for.)
A class photo is being taken of six students, sitting in a row. Three of the students are Jamie, Marshall, and Susan, and Jamie wants to sit between Marshall and Susan. (This also means that Jamie is next to both Marshall and Susan.) How many arrangements are possible?
Answer:
2 different arrangments
HELP ASAP PLSS
Given the following diagram, find the trigonometric ratios.
Leave answers as reduced fractions (improper fractions are fine).
11
C
8
B
sin A =
COS A =
tanA=
Answer:
Sin A = 8/17
Cos A = 15/17
Tan A = 8/15
Step-by-step explanation:
Recall: SOHCAHTOA
Reference angle = <A
Opposite = 8
Hypotenuse = 17
Adjacent = 15
Therefore,
Sin A = Opp/Hyp = 8/17
Cos A = Adj/Hyp = 15/17
Tan A = Opp/Adj = 8/15
Part three of me suffering because of my math homework. ( last part)
Answer:
3 sides
180 degrees
Yes
False
60 degrees
Extending to the side or moving to the side
Rhombus, Square, Rectangle
Acute
Sides
Angles
Find the area of the trapezoid. Round your answer to the nearest hundredth.
Answer:
42.50 units²
Step-by-step explanation:
Area of the trapezoid = ½(AB + DC)×AD
AB = 6
DC = 11
AD = ?
Use trigonometric function, TOA to find AD:
Tan 45 = Opp/Adj
Opp = AD
Adj = 11 - 6 = 5
Tan 45 = AD/5
5 × tan 45 = AD
AD = 5
✔️Find Area of trapezoid.
Area = ½(AB + DC)×AD
= ½(11 + 6)×5
= 42.50 units²