Answer:
[tex]a_n = a_o +(n-1) d[/tex]
[tex] 22.5 = 15 +(2-1) d[/tex]
[tex] d = 22.5-15 =7.5[/tex]
The general expression is:
[tex] a_n = 15+ (n-1)*7.5 , n \geq 1[/tex]
Step-by-step explanation:
For this case we have the following arithmetic sequence given:
15, 22.5, 30,37.5
In order to fidn the recursive rule for this sequence we need to take in count that the general formula for an arithmetic sequence is given by:
[tex]a_n = a_o +(n-1) d[/tex]
Where [tex]a_n[/tex] is the nth term [tex]a_o[/tex] the initial value for the sequence and d the common difference. For this case we have that [tex]a_o =15[/tex]
And for the first term we have:
[tex] 15= 15 +(1-1)d[/tex]
For the second term we have this:
[tex] 22.5 = 15 +(2-1) d[/tex]
And solving for the value of d we got:
[tex] d = 22.5-15 =7.5[/tex]
And for the 3th term we have:
[tex] a_3= 15 +(3-1)*7.5 =30[/tex]
And for the 4th term
[tex]a_4 =15 +(4-1)*7.5 =37.5[/tex]
So then our expression is correct and would be given by:
[tex] a_n = 15+ (n-1)*7.5 , n \geq 1[/tex]
What is the rate of change of the following function?
Answer:
You did not provide any function...therefore, i cant give you a proper answer.
Step-by-step explanation:
It cost Jodi $44.88 to buy 12 gallons of gas.what was the cost per gallon of gas?
Answer: $3.74
Step-by-step explanation: 44.88/12=3.74
Answer:
Jodi paid $3.74 for each gallon of gas
Step-by-step explanation:
x ^2 +y ^2 −4x+12y−24=0 What is the center of this circle ?
(2, -6) is the center of the circle.
To find the center of the circle, we need to rewrite the given equation in standard form:
[tex]x^2 - 4x + y^2 + 12y = 24[/tex]
We can complete the square to put it into the standard form:
[tex]x^2 - 4x + 4 + y^2 + 12y + 36 = 24 + 4 + 36\\\\(x - 2)^2 + (y + 6)^2 = 64[/tex]
Now we can see that the center of the circle is (2, -6).
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The center of the circle represented by the equation x^2 + y^2 −4x +12y−24=0 is (2, -6), which is determined by completing the square for both x and y terms.
To determine the center of a circle given by the equation x^2 + y^2 −4x +12y−24=0, we need to complete the square for both the x and y terms.
Step 1: Rearrange the equation by grouping x terms and y terms together: x^2 −4x + y^2 +12y = 24.
Step 2: Complete the square for the x terms and y terms: (x^2 −4x + 4) + (y^2 +12y + 36) = 24 + 4 + 36.
Step 3: Simplify the equation: (x − 2)^2 + (y + 6)^2 = 64.
Step 4: In the standard form of a circle equation, (x − h)^2 + (y − k)^2 = r^2, the center is at (h, k). Therefore, the center of the given circle is (2, -6).
Halla el lafo de un cuadrado tal que la suma de su área más su perímetro es numéricamente igual a 252
We analyzed the relationship between the budgets (in millions of dollars) and the U.S. Box Office Sales (in millions of dollars) for 75 popular movies. The scatterplot showed a weak positive association with a linear form. Here are the StatCrunch linear regression results:
Simple linear regression results:
Dependent Variable: US_Box_Office
Independent Variable: Budget US_Box_Office
IMDb_Rating Rotten Tomatoes = -57.599288 + 17.919209 IMDb_Rating Sample size: 75
R(correlation coefficient) = 0.79786226
R-sq = 0.63658418
Estimate of error standard deviation: 12.916488
Which number describes the percentage of variability in Rotten Tomato ratings that is explained by the changes in IMDb ratings as described by the regression line? This is the slope of the regression line. It describes the predicted change in Rotten Tomato ratings when IMDb ratings increase by one.
a. 0.80
b. 0.64
c. 12.9
d. 17.9
Answer:
According to the information from the exercise, we can deduce that the regression technique is the method of analysis for IMDb ratings and Rotten tomato ratings, so we have a dependent variable such as rotten tomatoes and the independent one that is IMDb-rating. We can say that in this analysis that the variation of the dependent variable is explained by the coefficient of determination, we observe that the coefficient of determination is 0.63 if we convert it into a percentage we obtain that it is equal to 63.65% and we approach 64%, with which which we affirm that it is equal to 64, so this value is the influence that the IMDb ratings generated on the ratings of rotten tomatoes
The percentage of variability in Rotten Tomato ratings explained by the changes in IMDb ratings is represented by the R-squared value of 0.64. Therefore, the correct answer is B. 0.64.
To determine the percentage of variability in Rotten Tomatoes ratings that is explained by the changes in IMDb ratings as described by the regression line, we need to look at the [tex]\( R^2 \)[/tex] value (coefficient of determination).
In the results provided:
[tex]\[R^2 = 0.63658418\][/tex]
This [tex]\( R^2 \)[/tex] value represents the proportion of variability in the dependent variable (Rotten Tomatoes ratings) that can be explained by the independent variable (IMDb ratings) in the regression model.
So, the percentage of variability in Rotten Tomato ratings that is explained by changes in IMDb ratings is:
[tex]\[R^2 = 0.63658418 = 0.64 \text{ or} 64%)\][/tex]
Therefore, the correct answer is:
b. 0.64
Which letter labels a vertex?
NEED URGENT ANSWER!
Answer:
C.
Step-by-step explanation:
In geometry, a vertex is the point where three or more edges meet on a shape (a 3-dimensional one of course). The other letters label sides or faces of the shape.
Answer:
C
Step-by-step explanation:
The easiest way to explain it is that A,B, and D are all labeling lines. A vertex is like a corner, with at least three lines protruding from it. A vertex is each angular point in a shape.
hope this helps :)
Kirby ran three-fourths of a half mile and dropped out of the 800 meter race. Her
pace was 12 miles an hour until the point she dropped out of the race. About how
many minutes did she run approximately?
Answer:
1.88 minutes
Step-by-step explanation:
This question can be solved using speed, distance and time concept along-with use of computing fractions.
Given
Distance ran by Kirby = 3/4 of half mile
= 3/4 of 1/2 mile = 3/4 * 1/2 mile = 3/8 mile.
Speed of Kirby until she dropped out of race = 12 miles/hour
Formula to calculate time = Distance/Time
substituting value of speed of Kirby and distance covered by Kirby
Time = [tex](3/8) / 12 = 3/(8*12) = 1/32 \ hour[/tex]
Since one hour has 60 minutes 1/32 hour = (1/32) * 60 minutes = 1.88 minutes
Simplify 64 x 3 y 3 z 2 24 x y 4 z 4
Answer:
88x+4y+7z+6
Step-by-step explanation:
depends on how u write it take a pic next time please
A research firm supplies manufacturers with estimates of the sales of their products from samples of stores. Marketing managers often look at the sales estimates and ignore sampling error. An SRS of 50 stores this month shows mean sales of 41 units of a particular appliance with a standard deviation of 11 units. During the same month last year, an SRS of 52 stores gave mean sales of 38 units of the same appliances with a standard deviation of 13 units. An increase from 38 to 41 is a rise of 7.9 % . The marketing manager is happy because sales are up 7.9 % . (a) Give a 95 % confidence interval for the difference in mean number of units of the appliance sold at all retail stores. (Enter your answer rounded to three decimal places.)
Answer:
lower interval = -1.715
upper interval = 7.715
Step-by-step explanation:
The 95% confidence interval for the difference in mean number of units of the appliance sold at all retail stores for this case is [-1.667, 7.667]
How to find the confidence interval for difference in mean?Supposing the samples are large, let we're given that:
For first sample:
[tex]n_1[/tex] =sample size[tex]s_1[/tex] = sample standard devation[tex]\overline{x}_1[/tex] = sample meanFor second sample:
[tex]n_2[/tex] =sample size[tex]s_2[/tex] = sample standard devation[tex]\overline{x}_2[/tex] = sample meanSuppose the confidence level be p% = p/100 in decimal, then the level of significance would be [tex]\alpha = 1 - p/100[/tex]
Then, the margin of error would be:
[tex]MOE = Z_{\alpha/2}\sqrt{\dfrac{s_1^2}{n_1} + \dfrac{s_2^2}{n_2}}[/tex]
where [tex]Z_{\alpha/2}[/tex] is the critical value of Z at level of significance [tex]\alpha[/tex]
The confidence interval would be:
[tex]CI = \overline{x}_1 - \overline{x}_2 \pm MOE[/tex]
Thus, for this case, we're specified that:
For first sample (SRS this month):
[tex]n_1[/tex] =sample size = 50[tex]s_1[/tex] = sample standard devation = 11[tex]\overline{x}_1[/tex] = sample mean = 41For first sample(SRS last month):
[tex]n_2[/tex] =sample size = 52[tex]s_2[/tex] = sample standard devation = 13[tex]\overline{x}_2[/tex] = sample mean = 38Level of significance = 1 - 95/100 = 0.05
The critical value of z at 0.05 level of significance (from the tables of critical value of Z) is: [tex]Z_{0.05/2} = 1.96[/tex]
Thus, the margin of error would be:
[tex]MOE = Z_{\alpha/2}\sqrt{\dfrac{s_1^2}{n_1} + \dfrac{s_2^2}{n_2}}\\\\\\MOE = 1.96\sqrt{\dfrac{11^2}{50} + \dfrac{13^2}{52}}\\\\MOE \approx 4.667[/tex]
Thus, the confidence interval would be:
[tex]CI = \overline{x}_1 - \overline{x}_2 \pm MOE\\CI \approx 41 - 38 \pm 4.667\\CI \approx 3 \pm 4.667\\CI \approx [3 - 4.667, 3 + 4.667] = [-1.667, 7.667][/tex]
Thus, the 95% confidence interval for the difference in mean number of units of the appliance sold at all retail stores for this case is [-1.667, 7.667]
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State the type of hypothesis test to be used in the following situation: Researchers hoped to determine whether time spent watching television is associated with cardiovascular fitness. Subjects were asked how many hours per day they watch television and were classified as physically fit if they scored in the excellent or very good category on a step test. The data obtained is as follows: Physically Fit Not Physically Fit 0 hours 35 147 1-2 hours 101 629 3-4 hours 28 222 5 or more hours 4 34 Determine if the association the researchers were interested in exists or not.
Answer:
t-test for difference in slopes
no association exists
Step-by-step explanation:
t-test can be used to determine signifiance in difference in slopes of of fit vs time and not fit vs time graph
The data shows that as number of hours spent watchnig television increases, there is no increasing or decreasing trend in number of people fit or not fit. The number of people fit or not fit seems to be distributed around 629 for 1-2 hours of watching television. There trend is not consistent in both cases with increasing number of hours
If Miranda flips a coin twice, what is the probability that both coins will land heads up?
The probability that the first coin will land heads up is
The probability that the second coin will land heads up is
The probability that both coins will land heads up is
Answer: The probability that the first coin will land heads up is : 50
The probability that the second coin will land heads up is
The probability that both coins will land heads up is : 25
Step-by-step explanation:
Answer: Both coins 1/4
First coin 1/2
Second coin 1/2
I. Red help pls bros
Answer:
the 3rd one
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
because it has too many on one side
A trapezoid on a square. The square has side lengths of 12 feet. The trapezoid has a base of 6 feet, height of 3 feet, and top side length of 4 feet. Tariq is a swimming-pool designer. He is known for his irregular-shaped swimming pools. The bottom of this pool will be covered in tile. The area of the pool that is covered in tile is ft2.
Answer:
159
Step-by-step explanation:
Answer:
159
Step-by-step explanation:
Suppose that the function g is defined for all real numbers as follows
Answer:
-9
0
3
Step-by-step explanation:
-(-2-1)^2
-(1-1)^2
x>2 , so g(x) = 3
Three points of a function are graphed.
Which statement describes the function through the points?
The function is a direct variation function with a constant
of variation of 1.5.
The function is a direct variation function with a constant
of variation of 1.8.
The function is linear but is not a direct variation
function.
The function is not a linear function,
. (18, 30)
. (14, 24)
• (10, 18)
4
8
12
16 20 24 28 32 36
x
Answer:
The answer is C.
Step-by-step explanation:
I just took the test on edg and got a 100
The function is linear but is not a direct variation.
What is Direct Variation?Direct variations are defined as the functions of the form y = kx, where k is a constant.
Here when y increases, x increases and if y decreases, x also decreases.
Given is a function that passes through three points (18, 30), (14, 24) and (10, 18).
If the function is linear, the the slope must be constant.
Slope = Change in y coordinates / Change in x coordinates
Consider (18, 30) and (14, 24).
Slope = (24 - 30) / (14 - 18) = -6 / -4 = 3/2
Consider (14, 24) and (10, 18).
Slope = (18 - 24) / (10 - 14) = 3/2
Since slope is constant, function is linear.
Let y = mx + c be the equation of the function, where m is the slope and c is the y intercept.
If the function is direct variation, c = 0.
Substitute (10, 18) in to the equation.
18 = (3/2 × 10) + c
⇒ c = 3
It is not direct variation.
Hence the function is linear but is not a direct variation.
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Select the correct answer,
Why are online payment services necessary?
OAIndividuals who sell items online cannot afford
OB. It is too risky to use credit cards online, and on
C. Government regulations require all online tran
OD
Online payment services are the only payment
Answer:
B. It is too risky to use credit cards online, and online payment services have better security because of the increasing number of hackers that may steal money from your bank account.
Step-by-step explanation:
There are 20 flowers. I have 10 how many are there
Answer: 10
Step-by-step explanation: because you subtract it by 10
20-10= 10
What is the length of the radius of a circle whose area is 100 pie(3.14)?
Help? Question are above. 15 points
Answer:
1).
7, rational
2).
2.36 (repeating), irrational
3).
[tex]Simplify:\frac{734}{1000} / \frac{2}{2} = \frac{367}{500}[/tex]
4).
[tex]Simplify: \frac{2588}{1000} /\frac{4}{4} =\frac{647}{250} \\If.you.want.to.convert.it.to.a.mixed.fraction: 2\frac{147}{250}[/tex]
Put the fraction in order from least to greatest 1/8, 1/3, 1/6
Answer:
You have to make them equal first. Start with that.
1/8 --> 3/24
1/6 ---> 4/24
1/3 --> 8/24
Now, order them.
1/8, 1/6. 1,3
A bucket of water is one quarter full. You add 3.6L to the bucket. Now it has 18L in it. How much water will the bucket hold?
Answer:
57.6 Liters
Step-by-step explanation:
18 - 3.6 to find what 1 quarter is
14.4 * 4 to find the total amount it can hold
= 57.6
As a salesperson, you are paid $52 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.
Answer:
s≥16
Step-by-step explanation:
3s+52≥100
3s≥100-52
3s≥48
s≥48/3
s≥16
The solution to the inequality is x ≥ 16.
What is inequality?It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal = ≤
Greater than and equal = ≥
We have,
Let x be the number of sales you need to make.
The total pay you receive will be $52 + $3x.
Since you want your pay to be at least $100, we can write the inequality:
52 + 3x ≥ 100
Solving for x, we get:
3x ≥ 48
x ≥ 16
Therefore,
The solution to the inequality is x ≥ 16.
This means that you need to make at least 16 sales to earn at least $100 this week.
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» A cylinder has a height of 13 millimeters and a radius of 11 millimeters. What is its
volume? Use a 3.14 and round your answer to the nearest hundredth.
Answer:
V =4939.22 mm^3
Step-by-step explanation:
The volume of a cylinder is given by
V = pi r^2 h
where r is the radius and h is the height
V = 3.14 (11)^2 *13
V =4939.22 mm^3
The recycling bin in the shape of a rectangular prism is 15.5 inches long, 8 inches wide and 7 inches high. The recycling bins need to be emptied when it is 80% full. What is the total amount needed, to the nearest cubic inch, before the recycle bin is ready to empty?
Answer:
694 cubic inches
Step-by-step explanation:
Dimension of prism
Length = 15.5 inches
width = 8 inches
height = 7 inches
Volume of regular prism is given by area of base * height
area of base = length * width ( as bin is rectangular)
area of base = 15.5 * 8 square inches = 124 square inches
Volume of regular prism = area of base * height
= 124 * 7 cubic inches = 868 cubic inches
_________________________________________________
868 cubic inches is the full capacity of the recycling bin
it is given that recycling bins need to be emptied when it is 80% full
so we need to find the 80% capacity of recycling bin
80% capacity of recycling bin = 80/100 * full capacity of the recycling bin
= 0.8 * 868 cubic inches = 694.4 cubic inches
694.4 cubic inches is the amount needed before the recycle bin is ready to empty .
But question says answer should in nearest cubic inch
hence answer is 694 cubic inches
What is the length of segment TV?
Answer:
38 units
Step-by-step explanation:
VS = TS
39 = 6x – 3
39 + 3 = 6x
42 = 6x
X = 7
TV = 2(VR)
TV = 2 ( 2(7) + 5)
TV = 38 units
Brainiest please?
Find 6% of $5.65 and round the product to the nearest cent.
Answer:
$0.34
Step-by-step explanation:
a = p*w
a = .06*5.65
a = 0.339
rounded = 0.34
hope this helps :)
Using the traditional formula, a 95% CI for p1 − p2 is to be constructed based on equal sample sizes from the two populations. For what value n (= m) will the resulting interval have width at most 0.4 irrespective of the results of the sampling? (Round your answer up to the nearest whole number.)
Answer:
The minimum sample size required is 49.
Step-by-step explanation:
The (1 - α)% confidence interval for the difference between two proportions is:
[tex]CI=(\hat p_{1}-\hat p_{2})\pm z_{\alpha/2}\ \sqrt{\frac{\hat p_{1}(1-\hat p_{1})+\hat p_{2}(1-\hat p_{2})}{n}}[/tex]
*The sample size is considered equal in this case.
The width of the interval is at most 0.40.
Then the margin of error of the interval will be:
MOE = Width ÷ 2 = 0.20
The formula of the margin of error is:
[tex]MOE= z_{\alpha/2}\ \sqrt{\frac{\hat p_{1}(1-\hat p_{1})+\hat p_{2}(1-\hat p_{2})}{n}}[/tex]
Assume that the two sample proportion values are 0.50.
The critical value of z for 95% confidence level is:
[tex]z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96[/tex]
Compute the sample size required as follows:
[tex]MOE= z_{\alpha/2}\ \sqrt{\frac{\hat p_{1}(1-\hat p_{1})+\hat p_{2}(1-\hat p_{2})}{n}}[/tex]
[tex]n=[\frac{z_{\alpha/2}\times \sqrt{\hat p_{1}(1-\hat p_{1})+\hat p_{2}(1-\hat p_{2})}}{MOE}]^{2}[/tex]
[tex]=[\frac{1.96\times \sqrt{0.50(1-0.50)+0.50(1-0.50)}}{0.20}]^{2}\\\\=48.02\\\\\approx 49[/tex]
Thus, the minimum sample size required is 49.
If you bought a camera in good condition from a friend, would you pay the same as you would if you bought the same item from a stranger? A researcher at Cornell University want to know how friendship might affect simple sales such as this. She randomly divided 15 subjects into two groups and gave each group the same description of a used camera. One group was told to imagine buying from a friend whom they expected to see again. The other group was told to imagine buying from a stranger. The researcher recorded the price each person was willing to pay for the camera.
Final answer:
The degree of imperfect information varies depending on the transaction type. Buying apples or dinner locally involves relatively low imperfect information because of the immediate availability of visual or experiential information, whereas buying a used laptop or ordering flowers online involves higher imperfect information due to the lack of direct product interaction.
Explanation:
Imperfect Information in Economic Transactions
The concept of imperfect information refers to a situation where one or both parties in a transaction do not have all the necessary information to make an entirely informed decision. When assessing the degree of imperfect information in various scenarios, it is essential to consider the transparency and availability of information about the product or service, as well as the trustworthiness of the source providing it.
Buying apples at a roadside stand: The degree of imperfect information is expected to be relatively low as the buyer can visually inspect the apples and assess their quality on the spot.
Buying dinner at the neighborhood restaurant: Imperfect information is also expected to be relatively low since, through prior experience or reputation, one usually has an idea about the quality of food and service.
Buying a used laptop computer at a garage sale: Imperfect information would be relatively high as the buyer may not have the expertise to thoroughly check the laptop's condition or know its history.
Ordering flowers over the internet for a friend in a different city: The degree of imperfect information could be high since the buyer cannot see the actual flowers being sent and must rely on the vendor's description and reputation.
These situations highlight how different market transactions harbor varying levels of imperfect information, which can influence a buyer's willingness to pay and overall decision-making process, according to the principles of behavioral economics. Unlike mainstream economics, which assumes rational actors with perfect information, behavioral economics acknowledges that decisions are often made based on relative outcomes and perceived value rather than absolute savings.
What is the covariance for the number of times a head appears for each coin? Suppose you have two unfair coins. Coin 1, denoted as C1, has a probability of landing heads with probability 2/5 and tails with probability 3/5. Coin 2, denoted as C2, has a probability of landing heads with probability 1/3 and tails with probability 2/3. Toss coin 1 first. If coin 1 lands heads, toss coin 1 again. If coin 1 lands tails, then toss coin 2.
Answer:
Check the explanation
Step-by-step explanation:
Kindly check the attached images below to see the step by step explanation to the question above.
if a pack of 24 pencils cost $2.35 how much does a single pencil cost
Answer:
Just divide dollar amount by unit count
2.35/24 =$ ______ per pencil
so each= =0.097917
so 97 cents
The amount that a single pencil cost is $0.10 per pencil.
Using this formula
Cost per pencil=Cost of pencil per pack/Number of pencil per pack
Where:
Cost of pencil per pack=$2.35
Number of pencil per pack=24 pencil
Let plug in the formula
Cost per pencil=$2.35/24
Cost per pencil=$0.098
Cost per pencil=$0.10 (Approximately)
Inconclusion the amount that a single pencil cost is $0.10 per pencil.
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