Answer:
pi is the ratio if the circumference over the diameter
Step-by-step explanation:
My locker combination has three digits. None of the digits are 0. What is the probability that the first digit of my locker combination is less than 3? A. 1/3 B. 1/2 C. 2/9 D. 3/10
The probability that the first digit of a three-digit locker combination is less than 3 is 2/9, because there are 2 favorable digits (1 and 2) out of 9 possible non-zero digits, option C.
The question is asking about the probability that the first digit of a three-digit locker combination is less than 3, given that none of the digits can be 0. Since the digits can range from 1 to 9 (inclusive), there are a total of 9 possible digits for the first position. We are interested in the digits 1 and 2, which are the only digits less than 3. Therefore, there are 2 favorable outcomes.
To calculate the probability, we use the formula:
Probability = Number of favorable outcomes / Total number of possible outcomes
In this case, the probability is 2 (favorable outcomes) divided by 9 (possible outcomes), which simplifies to:
Probability = 2/9, option C.
The x-intercept and y-intercept
Answer:
x intercept = (1.2 , 0)
y intercept = (0 , 0.75)
Step-by-step explanation:
You wan to get it into whatever formula makes it easiest for you to understand. I put it into standard slope formula ax + by = c
5x +8y = 6
6/5 = x
x= 1.2
6/8 = y
y = 0.75
A candidate for one of Ohio's two U.S. Senate seats wishes to compare her support among registered voters in the northern half of the state with her support among registered voters in the southern half of the state. A random sample of 2000 registered voters in the northern half of the state is selected, of which 1062 support the candidate. Additionally, a random sample of 2000 registered voters in the southern half of the state is selected, of which 900 support the candidate.
A 95% confidence interval for the difference in proportion of registered voters that support this candidate between the northern and southern halves of the state is
A. 0.050 to 0.112.
B. 0.035 to 0.127.
C. 0.040 to 0.122.
D. 0.037 to 0.119.
Answer:
[tex](0.531-0.45) - 1.96 \sqrt{\frac{0.531(1-0.531)}{2000} +\frac{0.45(1-0.45)}{2000}}=0.050[/tex]
[tex](0.531-0.45) + 1.96 \sqrt{\frac{0.531(1-0.531)}{2000} +\frac{0.45(1-0.45)}{2000}}=0.112[/tex]
And the best option for this case would be:
A. 0.050 to 0.112.
Step-by-step explanation:
Data given
[tex]p_A[/tex] represent the real population proportion of who support the cnadite for the northern half state
[tex]\hat p_A =\frac{1062}{2000}=0.531[/tex] represent the estimated proportion of who support the candidate for the northern half state
[tex]n_A=2000[/tex] is the sample size required the northern half state
[tex]p_B[/tex] represent the real population proportion of who support the candidate for the southern half state
[tex]\hat p_B =\frac{900}{2000}=0.45[/tex] represent the estimated proportion of people who support the candidate for the southern half state
[tex]n_B=2000[/tex] is the sample size for the northern half state
[tex]z[/tex] represent the critical value
The confidence interval for the difference of two proportions would be given by this formula
[tex](\hat p_A -\hat p_B) \pm z_{\alpha/2} \sqrt{\frac{\hat p_A(1-\hat p_A)}{n_A} +\frac{\hat p_B (1-\hat p_B)}{n_B}}[/tex]
For the 95% confidence interval the value of [tex]\alpha=1-0.95=0.05[/tex] and [tex]\alpha/2=0.025[/tex], with that value we can find the quantile in the normal standard distribution and we got.
[tex]z_{\alpha/2}=1.96[/tex]
Replacing into the formula we got:
[tex](0.531-0.45) - 1.96 \sqrt{\frac{0.531(1-0.531)}{2000} +\frac{0.45(1-0.45)}{2000}}=0.050[/tex]
[tex](0.531-0.45) + 1.96 \sqrt{\frac{0.531(1-0.531)}{2000} +\frac{0.45(1-0.45)}{2000}}=0.112[/tex]
And the best option for this case would be:
A. 0.050 to 0.112.
Suppose that the population of the scores of all high school seniors that took the SAT-M (SAT math) test this year follows a Normal distribution, with mean μ and standard deviation σ = 100. You read a report that says, "On the basis of a simple random sample of 100 high school seniors that took the SAT-M test this year, a confidence interval for μ is 512.00 ± 25.76." The confidence level for this interval is
Answer:
The confidence level for this interval is 99%.
Step-by-step explanation:
The margin of error M has the following equation.
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
z is related to the confidence level.
In this problem:
[tex]M = 25.76, \sigma = 100, n = 100[/tex]
So
[tex]25.76 = z*\frac{100}{\sqrt{100}}[/tex]
[tex]10z = 25.76[/tex]
[tex]z = 2.576[/tex]
Looking at the z table, [tex]z = 2.576[/tex] has a pvalue of 0.995.
So the confidence level is:
[tex]1 - 2(1 - 0.995) = 1 - 0.01 = 0.99[/tex]
The confidence level for this interval is 99%.
12. Find the perimeter of the triangle below:
please help show steps thank you :)
Given:
The lengths of the three sides of the triangle are [tex]\frac{3}{x-4}[/tex], [tex]\frac{16-x}{x^{2}-2 x-8}[/tex] and [tex]\frac{x+5}{x+2}[/tex]
We need to determine the perimeter of the triangle.
Perimeter of the triangle:
The perimeter of the triangle can be determined by adding all the three sides.
Thus, we have;
[tex]Perimeter=\frac{3}{x-4}+\frac{16-x}{x^{2}-2 x-8}+\frac{x+5}{x+2}[/tex]
Factoring the term [tex]x^2-2x-8[/tex], we get, [tex](x-4)(x+2)[/tex]
Substituting, we get;
[tex]Perimeter=\frac{3}{x-4}+\frac{16-x}{(x-4)(x+2)}+\frac{x+5}{x+2}[/tex]
Taking LCM , we have;
[tex]Perimeter=\frac{3(x+2)+16-x+(x+5)(x-4)}{(x-4)(x+2)}[/tex]
Simplifying the numerator, we get;
[tex]Perimeter=\frac{3x+6+16-x+x^2-4x+5x-20}{(x-4)(x+2)}[/tex]
Adding the like terms in the numerator, we get;
[tex]Perimeter=\frac{x^2+3x+2}{(x-4)(x+2)}[/tex]
Factoring the numerator, we get;
[tex]Perimeter=\frac{(x+2)(x+1)}{(x-4)(x+2)}[/tex]
Cancelling the common terms, we have;
[tex]Perimeter=\frac{x+1}{x-4}[/tex]
Thus, the perimeter of the triangle is [tex]\frac{x+1}{x-4}[/tex]
Time taken by a randomly selected applicant for a mortgage to fill out a certain form has a normal distribution with mean value 9 min and standard deviation 4 min. If five individuals fill out a form on one day and six on another, what is the probability that the sample average amount of time taken on each day is at most 11 min? (Round your answer to four decimal places.)
Answer:
u know this carol
Step-by-step explanation:
On the standard coordinate grid at initial moment, ship Tiger is at the position (0, 795), ship Lion is at the position (985, 0). Tiger sails along the straight line to the position (1229, 0). At the same time, Lion sails along the straight line to the position (0, 1039). Lion will reach her destination in one hour, Tiger – in two hours.
a) Find the point of intersection of the paths of the ships.
b) At what time from the moment of departure each of the ships will pass the point of intersection of the paths.
c) At what time (in minutes after departure) the distance between Lion and Tiger will be the shortest?
d) What is the shortest distance between Lion and Tiger?
e) What will be the positions of both ships at the moment when the distance between them is the shortest?
Answer:
A) (380, 640)
B) ship Tiger: Time = 0.96 hours
Ship Lion: Time = 0.62 hours
C) Ship Tiger = 57.6 minute
Ship Lion = 37.2 minutes
D) Distance = 533 metres
E) Ship Tiger (0, 795)
Ship Lion (1039,0)
Step-by-step explanation:
From the question, we can form the equation of the straight line from the initial and final position of the two ships. Using the general linear equation Y = mx + c. that is
Ship Tiger
Initial position (0, 795)
Final position (1229, 0)
M = (0 - 1229)/795
M = - 1.55
1229 = -1.55(0) + C
C = 1229
Hence the equation of the line for ship Tiger will be
Y = - 1.55x + 1229 ...... (1)
Ship Lion
Initial position (985, 0).
Final position (0, 1039).
M = 1039/ -985 = - 1.05
0 = -1.05(985) + C
0 = - 1039 + C
C = 1039
The equation of the line for ship Lion will be
Y = - 1.05(x) + 1039..... (2)
At the point of intersection of the paths of the ships, they will have common Y and X. Hence equation 1 is equal to equation 2
- 1.55x + 1229 = -1.05(x) + 1039
1.55(x) - 1.05(x) = 1229 - 1039
0.5x = 190
X = 190/0.5 = 380
Substitute x in equation 1
Y = -1.55(380) + 1229
Y = -589 + 1229
Y = 640
Therefore the point of intersection of the paths of the ships is (380, 640)
B) given that Lion will reach her destination in one hour, Tiger – in two hours.
Ship Tiger
distance = root(795^2 + 1229^2)
Distance = 1463.7
Speed = distance/time
Speed = 1463.7/2 = 731.9 m/s
Distance at the point of intersection will be
Distance = root(380^2 + (640-1229)^2)
Distance = root(144400 + 346921)
Distance = 700.9
Speed = distance/time
Time = distance /speed
Time = 700.9/731.9
Time = 0.96 hours
Ship Lion
distance = root(985^2 + 1039^2)
Distance = 1431.69
Speed = distance/time
Speed = 1431.69/1 = 1431.69
Distance at the point of intersection will be
Distance = root((380 - 985)^2 + (640)^2)
Distance = root(775625)
Distance = 880.7 meters
Speed = distance/time
Time = distance /speed
Time = 880.7/1431.69
Time = 0.615 hours
C) the time in minute the distance between Lion and Tiger will be the shortest will be
Ship Tiger: 0.96 × 60 = 57.6 minute
Ship Lion: 0.62 × 60 = 36.9 minutes
D) The shortest distance between Lion and Tiger will be achieved by using pythagorean theorem for the the distances at the point of intersection
Root (880.7^2 - 700.9^2)
Distance = 533 metres
E) the positions of both ships at the moment when the distance between them is the shortest will be the initial position of both ships
That is
Ship Tiger
Initial position (0, 795)
Ship Lion
Initial position (985, 0).
Find the equation of the regression line for the given data. Then construct a scatter plot of the data and draw the regression line. The pair of variables have a significant correlation. Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. The number of hours 6 students spent or a test and their scores on the test are shown below.Hours spend studying, x 1 2 3 3 4 6 (a) x = 2 hours (B) x = 3.5 hrsTest score, y 37 41 51 48 65 69 (c) x = 12 hours (d) x = 1.5 hrsFind the regression equation : Y (hat) = _____x +(_____) round to 3 decimal placesPlot the grapha. predict the value of y for x = 2b. predict the value of y for x = 3.5c. Predict the value of y for x = 12d. predict the value of y for x = 1.5
Answer:
(a)
x = 2
y = 42.019
(b)
x = 3.5
y = 51.833
(c)
x = 12
y = 107.447
(d)
x = 1.5
y = 38.747
Step-by-step explanation:
If you use a regressor calculator you will find that
y = 6.542x + 28.933
then for (a)
x = 2
y = 42.019
(b)
x = 3.5
y = 51.833
(c)
x = 12
y = 107.447
(d)
x = 1.5
y = 38.747
Regression equations are used to represent scatter plots
The regression equation is [tex]\^y = 6.54\^x + 28.94[/tex]The predicted values when x = 2, 3.5, 12 and 1.5 are 42.02, 51.83, 107.42 and 38.75The table is given as:
x | 1 2 3 3 4 6
y | 37 41 51 48 65 69
To determine the regression equation, we make use of an graphing calculator.
From the graphing calculator, we have:
Sum of X = 21 Sum of Y = 311 Mean X = 3.5 Mean Y = 51.8333 Sum of squares (SSX) = 17.5 Sum of products (SP) = 114.5The regression equation is represented as:
[tex]\^y =b\^x + a[/tex]
Where:
[tex]b = \frac{SP}{SS_x}[/tex] and [tex]a = M_y - bM_x[/tex]
So, we have:
[tex]b = \frac{SP}{SS_x}[/tex]
[tex]b = \frac{17.5}{114.5}[/tex]
[tex]b = 6.54[/tex]
[tex]a = M_y - bM_x[/tex]
[tex]a = 51.83 - (6.54*3.5)[/tex]
[tex]a = 28.94[/tex]
Substitute values for (a) and (b) in [tex]\^y =b\^x + a[/tex]
[tex]\^y = 6.54\^x + 28.94[/tex]
The predicted values when x = 2, 3.5, 12 and 1.5 are:
[tex]\^y = 6.54 \times 2 + 28.94 = 42.02[/tex]
[tex]\^y = 6.54 \times 3.5 + 28.94 = 51.83[/tex]
[tex]\^y = 6.54 \times 12 + 28.94 = 107.42[/tex]
[tex]\^y = 6.54 \times 1.5 + 28.94 = 38.75[/tex]
Hence, the predicted values when x = 2, 3.5, 12 and 1.5 are 42.02, 51.83, 107.42 and 38.75
Read more about regressions equations at:
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A player pays $2 to randomly draw a card from a standard deck of playing cards. He wins $10 if he draws a black 2, and $5 if a 10 or ace is picked. Determine the probability of each possible value of X (the amount won or lost) to complete the probability distribution for the game. Give each value as a fraction with a denominator of 52.
Answer:
1/52
2/52
4/52
Step-by-step explanation:
If you randomly draw a card from the standard deck the drawing an specific card will have a probability of 1/52
If you draw a black 2 it can be from Spades 2, or Clubs 2, therefore you have only two options, and the probability is 2/52
If you draw an ace it can be spades, clubs, hearts or diamonds, so the probability would be 4/52
how many 2/3s are in 3/8
Final answer:
To determine how many 2/3s fit into 3/8, multiply 3/8 by the reciprocal of 2/3, resulting in 9/16, which is less than 1. Thus, there are around 0.5625 of 2/3 in 3/8.
Explanation:
To find how many 2/3s are in 3/8, we're essentially asking how to divide 3/8 by 2/3. This is done by multiplying 3/8 by the reciprocal of 2/3, which is 3/2:
Dividing fractions: (3/8) ÷ (2/3) = (3/8) × (3/2)
Multiplying fractions: (3 × 3) / (8 × 2) = 9/16
To simplify this and understand the proportion, we need to compare the fraction 9/16 to a whole number. Since 9/16 is definitely less than 1, there is less than one 'whole' 2/3 in 3/8. Therefore, there are somewhat around 0.5625 of 2/3 in 3/8 (since 9 divided by 16 equals 0.5625).
Newberg is 5 miles due north of the airport, and Rockport is 12 miles due east of the airport. How far apart are Newberg and Rockport?
Step-by-step explanation:
No of miles Newberg is north of airport = 5
No of miles Rockport is east of the airport = 12
No of miles Newberg and Rockport are apart = 12+5 =17
Answer:
I did this now and was not 12 it was 13
PLEASE HURRY!! The pictures Please!!!
Which inequality is represented by this graph?
A. 0>x
B. x>0
C.0>_x
D. 0>_0
X > 0
sdjkfgsdjfjkdfnejnwsfjdnsk it made me write more
Since the blue line points to numbers more positive then 0, it would be a greater then. Since the dot is open it would be greater then and not equal to.
Therefore the answer is B, x > 0
Richie Rich started his day with 12 bucks. Richie Rich ended his day with a dozen bucks. A. How many bucks did Richie Rich share today? B. Explain your answer.
Answers and Step-by-step explanations:
A. He shared $0.
B. Richie Rich started out with $12. He ended his day with a dozen bucks. However, notice that a dozen is the same as 12, so he still has $12. In other words, he didn't share any money today, so he shared $0.
Hope this helps!
Answer:
A. 0
B. No difference in starting and ending amounts
Step-by-step explanation:
12 = 1 dozen
12 bucks is equal to 1 dozen bucks, which means he didn't spend/share any
Over the interval [-3, 0], the local minimum is
Over the interval [0, 3], the local maximum is
Over the interval [0, 3] the local minimum is
Answer: 1. -16.18
2. 3.75
3. -3
Step-by-step explanation:
The value of the local minimum, maximum, and minimum will be -16, 4, and -1.5.
What is local minima and local maxima?The larger than the critical value of a set are really the highest and lowest items in the set, as described by mathematics.
From the graph, the conclusion are given below.
Over the interval [-3, 0], the local minimum is approximately -16.
Over the interval [0, 3], the local maximum is approximately 4.
Over the interval [0, 3] the local minimum is approximately -1.5.
The complete question is attached below.
More about the local minima and local maxima link is given below.
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Simplify the expression.
Answer:
(2x)(-2x+5)(x+2)
Step-by-step explanation:
Crash testing is a highly expensive procedure to evaluate the ability of an automobile to withstand a serious accident. A simple random sample of 12 small cars were subjected to a head-on collision at 40 miles per hour. Of them 8 were "totaled," meaning that the cost of repairs is greater than the value of the car. Another sample of 15 large cars were subjected to the same test, and 5 of them were totaled. Find a 95% confidence interval for the difference in the prop
Answer:
95% confidence interval for the difference in the proportion is [-0.017 , 0.697].
Step-by-step explanation:
We are given that a simple random sample of 12 small cars were subjected to a head-on collision at 40 miles per hour. Of them 8 were "totaled," meaning that the cost of repairs is greater than the value of the car.
Another sample of 15 large cars were subjected to the same test, and 5 of them were totaled.
Firstly, the pivotal quantity for 95% confidence interval for the difference between population proportion is given by;
P.Q. = [tex]\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} } }[/tex] ~ N(0,1)
where, [tex]\hat p_1[/tex] = sample proportion of small cars that were totaled = [tex]\frac{8}{12}[/tex] = 0.67
[tex]\hat p_2[/tex] = sample proportion of large cars that were totaled = [tex]\frac{5}{15}[/tex] = 0.33
[tex]n_1[/tex] = sample of small cars = 12
[tex]n_2[/tex] = sample of large cars = 15
[tex]p_1[/tex] = population proportion of small cars that are totaled
[tex]p_2[/tex] = population proportion of large cars that were totaled
Here for constructing 95% confidence interval we have used Two-sample z proportion statistics.
So, 95% confidence interval for the difference between population population, ([tex]p_1-p_2[/tex]) is ;
P(-1.96 < N(0,1) < 1.96) = 0.95 {As the critical value of z at 2.5% level
of significance are -1.96 & 1.96}
P(-1.96 < [tex]\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} } }[/tex] < 1.96) = 0.95
P( [tex]-1.96 \times {\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} } }[/tex] < [tex]{(\hat p_1-\hat p_2)-(p_1-p_2)}[/tex] < [tex]1.96 \times {\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} } }[/tex] ) = 0.95
P( [tex](\hat p_1-\hat p_2)-1.96 \times {\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} } }[/tex] < [tex]p_1-p_2[/tex] < [tex](\hat p_1-\hat p_2)+1.96 \times {\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} } }[/tex] ) = 0.95
95% confidence interval for [tex]p_1-p_2[/tex] = [[tex](\hat p_1-\hat p_2)-1.96 \times {\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} } }[/tex] , [tex](\hat p_1-\hat p_2)+1.96 \times {\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} } }[/tex]]
= [[tex](0.67-0.33)-1.96 \times {\sqrt{\frac{0.67(1-0.67)}{12}+\frac{0.33(1-0.33)}{15} } }[/tex] , [tex](0.67-0.33)+1.96 \times {\sqrt{\frac{0.67(1-0.67)}{12}+\frac{0.33(1-0.33)}{15} } }[/tex]]
= [-0.017 , 0.697]
Therefore, 95% confidence interval for the difference between proportions l and 2 is [-0.017 , 0.697].
A regular heptagon has a side of 13.9 and an apothem of 14.4. Find the area of the heptagon. Round your answer to the nearest WHOLE NUMBER.
Answer:
Step-by-step explanation:
Given that,
A regular heptagon, a heptagon has 7 sides and since it is a regular heptagon, then, it has equal sides
n = 7, number of sides
Each sides of the heptagon has a length of 13.9
s= 13.9
The apothem is 14.4
Apothem is a line from the centre of a regular polygon at right angles to any of its sides.
r = 14.4
The area of a regular heptagon can be calculated using
Area = ½ n•s•r
Where n is the number of sides
s- is the length of the sides
r Is the apothem
Then,
A = ½ × 7 × 13.9 × 14.4
A = 700.56 square units
To the nearest whole number, I.e no decimal points
A = 701 Square units
This cake was sliced parallel to the base. What shape will the cross-section make?
The shape of the cross-section of the cake is a square.
What is cross-section?In geometry and science, a cross section is the non-empty intersection of a solid body in three-dimensional space with a plane, or the analog in higher- dimensional spaces. Cutting an object into slices creates many parallel cross-sections.
Given that, a cake was sliced parallel to the base, we need to find the shape of the cross section,
we see that the shape of the cake is a square base pyramid,
That means if we cut it horizontally parallel to its base, we will always find a square,
Therefore, the cross-section is a square.
Hence, the shape of the cross-section of the cake is a square.
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When slicing a cake parallel to its base, the resulting cross-section will be a circle, mirroring the shape of the base of the cake.
The question pertains to the shape of the cross-section resulting from slicing a cake parallel to its base. When you slice a three-dimensional object like a cake in this way, the cross-section will mirror the shape of the object's base. As the base of a cake is typically a circle, the cross-section in this case will be a circular shape. To understand this better, imagine a cylinder, which is similar to a circular cake. When you slice a cylinder parallel to its base, you always obtain a circular cross-section. This concept is consistent across different objects, given that the slice is parallel to the base, such as slicing a cylindrical polony or cutting a slice of brick-shaped bread.
More on the Leaning Tower of Pisa. Refer to the previous exercise. (a) In 1918 the lean was 2.9071 meters. (The coded value is 71.) Using the least-squares equation for the years 1975 to 1987, calculate a predicted value for the lean in 1918. (Note that you must use the coded value 18 for year.)
Answer:
2.9106
Step-by-step explanation:
According to the information of the problem
Year 75 76 77 78 79 80 81 82 83 84 85 86 87
Lean 642 644 656 667 673 688 696 698 713 717 725 742 757
If you use a linear regressor calculator you find that approximately
[tex]y = 9.318 x - 61.123[/tex]
so you just find [tex]x = 18[/tex] and then the predicted value would be 106mm
therefore the predicted value for the lean in 1918 was 2.9106
How many minutes does it take 7people to paint 4 walls ?
Bruh. More information is needed to answer that question. We need to know the rate of change.
. If $200 is invested at the end of each month into an account that has an APR of 3.4% compounded monthly, what will the balance be after 15 years?
Answer:
$332.82
Step-by-step explanation:
We will use the compound interest formula provided to solve this:
[tex]A=P(1+\frac{r}{n} )^{nt}[/tex]
P = initial balance
r = interest rate (decimal)
n = number of times compounded annually
t = time
First, we change 3.4% into a decimal:
3.4% -> [tex]\frac{3.4}{100}[/tex] -> 0.034
Since the interest is compounded monthly, we will use 12 for n. Lets plug in the values now:
[tex]A=200(1+\frac{0.034}{12})^{12(15)}[/tex]
[tex]A=332.82[/tex]
Your balance after 15 years will be $332.82
Miguel buys textbook with a listed price of $81. Miguel uses
a discount that provides 10% off. What is the total final
price Miguel pays?
Answer:
$72
Step-by-step explanation:
Answer:
72.9 (mark me brainleist pls )
Step-by-step explanation:
81 x 0.10 = 8.1
81 - 8.1 = 72.9
UCF believes that the average time someone spends in the gym is 56 minutes. The university statistician takes a random sample of 32 gym goers and finds the average time of the sample was 50 minutes. Assume it is known the standard deviation of time all people spend in the gym is 8 minutes. What conclusion can the university statistician make?
Answer:
We conclude that the average time someone spends in the gym is different from 56 minutes.
Step-by-step explanation:
We are given that UCF believes that the average time someone spends in the gym is 56 minutes.
The university statistician takes a random sample of 32 gym goers and finds the average time of the sample was 50 minutes. Assume it is known the standard deviation of time all people spend in the gym is 8 minutes.
Let [tex]\mu[/tex] = population average time someone spends in the gym
SO, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 56 minutes {means that the average time someone spends in the gym is 56 minutes}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu\neq[/tex] 56 minutes {means that the average time someone spends in the gym is different from 56 minutes}
The test statistics that will be used here is One-sample z test statistics as we know about the population standard deviation;
T.S. = [tex]\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
where, [tex]\bar X[/tex] = sample average time someone takes in the gym = 50 min
[tex]\sigma[/tex] = population standard deviation = 8 minutes
n = sample of gym goers = 32
So, test statistics = [tex]\frac{50-56}{\frac{8}{\sqrt{32} } }[/tex]
= -4.243
Since in the question we are not given the level of significance so we assume it to b 5%. Now at 5% significance level, the z table gives critical value between -1.96 and 1.96 for two-tailed test. Since our test statistics does not lie within the range of critical values of z so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.
Therefore, we conclude that the average time someone spends in the gym is different from 56 minutes.
5. Which of the following statements is true? (A) Histograms have gaps between each bar. (B) Dotplots do not provide enough information to determine if there are outliers in the data. (C) Bar graphs can display both quantitative and categorical data. (D) Stemplots are the best graphs for displaying data sets with two variables. (E) Boxplots clearly show the five-number summary of a data set.
Boxplots clearly show the five-number summary of a data set. Therefore, option D and E are the correct answer.
What is histogram?A histogram is a visual representation of statistical data that makes use of rectangles to illustrate the frequency of data items in a series of equal-sized numerical intervals. The independent variable is represented along the horizontal axis and the dependent variable is plotted along the vertical axis in the most popular type of histogram.
A) A histogram has an appearance similar to a vertical bar chart, but there are no gaps between the bars.
B) Both dot plots and stem plots can show symmetry, gaps, clusters, and outliers.
C) A bar chart or pie chart is often used to display categorical data. These types of displays, however, are not appropriate for quantitative data. Quantitative data is often displayed using either a histogram, dot plot, or a stem-and-leaf plot.
D) The advantage of a stem leaf diagram is it gives a concise representation of data. The advantage of a frequency histogram is, that it is visually strong. Histograms are usually preferable to stem and leaf diagrams in large data sets.
E) A box and whisker plot—also called a box plot—displays the five-number summary of a set of data. The five-number summary is the minimum, first quartile, median, third quartile, and maximum. In a box plot, we draw a box from the first quartile to the third quartile.
Therefore, option D and E are the correct answer.
Learn more about the histogram here:
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Among the listed statements, options C and E are true. Other statements about histograms, dotplots, and stemplots have inaccuracies.
Explanation:Let's go through each of the statements:
(A) Histograms have gaps between each bar: This statement is false as histograms present continuous data where the bars are adjacent to each other with no gaps. It's used for displaying large, continuous, quantitative datasets.
(B) Dotplots do not provide enough information to determine if there are outliers in the data: We can't completely conclude this as it would depend on the nature of the data and how it's presented. Dotplots can sometimes show outliers but they are not the most efficient graph for this purpose.
(C) Bar graphs can display both quantitative and categorical data: This is true. Bar graphs are very versatile and can represent both types of data. They compare categories of data with either horizontal or vertical bars.
(D) Stemplots are the best graphs for displaying data sets with two variables: This is false. Stemplots are good for displaying a single variable and summarizing the shape of the dataset.
(E) Boxplots clearly show the five-number summary of a data set: This is true. Boxplots are an excellent way to display the minimum, first quartile, median, third quartile and maximum values of a data set.
Learn more about Graphs in Statistics here:
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Consider the following least squares specification between test scores and the student - teacher ratio: TestScore = 557.8 + 36.42 In (Income). According to this equation, a 1% increase income is associated with an increase in test scores of :A. 36.42 points B. cannot be determined from the information given here C. 0.36 points D. 557.8 points
Answer:
[tex] Test score_i= 557.8 +36.42 Income[/tex]
If we increase the income by 1% that means that the new income would be 1.01 the before one and if we replace this we got:
[tex] Test score_f = 557.8 + (36.42* 1.01 Income)= 557.8 +36.7842 Income[/tex]
And the net increase can be founded like this:
[tex] Test score_f -Tet score_i = 557.8 +36.7842 Income- [557.8 +36.42 Income] = 36.7842 Income -36.42 Income = 0.3642[/tex]
So then the net increase would be:
C. 0.36 points
Step-by-step explanation:
For this case we have the following linear relationship obtained from least squares between test scores and the student-teacher ratio:
[tex] Test score_i= 557.8 +36.42 Income[/tex]
If we increase the income by 1% that means that the new income would be 1.01 the before one and if we replace this we got:
[tex] Test score_f = 557.8 + (36.42* 1.01 Income)= 557.8 +36.7842 Income[/tex]
And the net increase can be founded like this:
[tex] Test score_f -Tet score_i = 557.8 +36.7842 Income- [557.8 +36.42 Income] = 36.7842 Income -36.42 Income = 0.3642[/tex]
So then the net increase would be:
C. 0.36 points
For a 1% increase in income, the test scores would increase by approximately 0.36 points based on the given regression equation. This is calculated by multiplying the coefficient of the natural logarithm of income, 36.42, with the decimal value of the percent change in income, which is 0.01.
Explanation:The equation provided is a linear regression equation where the dependent variable, TestScore, is predicted based on the natural logarithm of the independent variable, Income. The coefficient of 36.42 in front of the natural logarithm indicates how much the dependent variable changes for a 1% change in the independent variable. To find the contribution to the test scores for a 1% increase in income, we need to use the fact that the derivative of the natural logarithm, Ln(x), with respect to x is 1/x, which means a change in income translates directly to the change in test score when multiplied by the coefficient.
So, for a small percentage change in income, approximately 1%, the corresponding change in TestScore is 36.42 multiplied by the percentage change in decimal form. Specifically, 0.01 × 36.42 = 0.3642 or approximately 0.36 points.
free round trip tickets Hawaii were given to 0.4% of the people staying at a hotel. Larry says that tickets were given to 4/10 of the people at the hotel.
Answer: He is badly mistaken! It's 4/1000
Larry needs to learn how to read percentages!
Step-by-step explanation:
4/10 would be 40% For every 100 guests, 40 free tickets would be given away. A very popular offer, but the hotel will soon be out money, and out of business!
0.4% is less than 1% . As a decimal it is 0.004. That is Four thousandths!
Only 4 out of every 1000 people were given free round trip tickets to Hawaii.
What does our base tell us about the exponent
The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took the customers in the sample to check out was 3.1 minutes. The population standard deviation is known to be 0.5 minute. We want to test to determine whether or not the mean waiting time of all customers is significantly more than 3 minutes.
Answer:
The mean waiting time of all customers is significantly more than 3 minutes, at 0.05 significant level
Step-by-step explanation:
Step 1: State the hypothesis and identify the claim.
[tex]H_0:\mu=3\\H_1:\mu\:>\:3(claim)[/tex]
Step 2: We calculate the critical value. Since we were not given any significant level, we assume [tex]\alpha=0.05[/tex], and since this is a right tailed test, the critical value is z=1.65
Step 3: Calculate the test statistic.
[tex]Z=\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }=\frac{3.1-3}{\frac{0.5}{\sqrt{100} } }=2[/tex]
Step 4:Decide. Since the test statistic , 2 s greater than the critical value, 1.65, and it is in the critical region, the decision is to reject the null hypothesis.
Step 5: Conclusion, there is enough evidence to support the claim that the mean is greater than 3
Nielsen ratings are based on televisions in 50005000 households. Nielsen estimates that 12 comma 00012,000 people live in these households. Suppose Nielsen reports that American Idol had 6565% of the TV audience. Interpret this result with a 95% confidence interval, based on a sample size of 12 comma 00012,000 people.
Answer:
We are 95% confident that the true proportion of TV audience is between 65.15% and 65.85%
Step-by-step explanation:
-From the given information, [tex]\hat p=0.65[/tex].
-We calculate the confidence interval using this value at 95% confidence level:
[tex]CI=\hat p\pm z \sqrt{\frac{\hat p(1-\hat p)}{n}}\\\\\\=0.65\pm 1.96\times \sqrt{\frac{0.65\times 0.35}{12000}}\\\\\\=0.65\pm 0.0085\\\\\\=[0.6415,0.6585][/tex]
So, the 95% confidence interval is (0.6515,0.6585).
Hence, we are 95% confident that the true proportion of TV audience is between 65.15% and 65.85%.
Just the distributive property to write an expression that is equivalent to 10 + 15x
Answer:
5 ( 2 + 3x )
Step-by-step explanation:
1st step: Take the GCF of the equation 10+15x
2nd step: GCF means, taking the Greatest Common Factor out of BOTH the numbers in an equation. (GCF is 5 in this case.)
3rd step: Divide by the GCF that you got. (In this case, you have 10 +15x. You need to do 10/5, and 15x /5. (Note that ANYTHING multiplied by "x" can also be divided just like a regular number.)
4th step: Put the the number that you divided with for both numbers OUTSIDE parentheses. (Note in this case it is common.)
5th step: Check your work. PLEASE DO THIS STEP.
Check: 5( 2 + 3x )
5 x 2 = 10
5 x '3x' = 15x
So, the answer for this problem is: 5 ( 2 +3x )
Answer: 5( 2 + 3x)
Hope this helped you understand the basics of disributive property. And if you have another problem just like this, you can use the same rule as shown above. :)
Final answer:
Use the distributive property to factor out a common factor in 10 + 15x to get an equivalent expression.
Explanation:
To write an expression equivalent to 10 + 15x using the distributive property, you can factor out a common factor. Here’s how:
Factor out 5 from 10 and 15x: 10 + 15x = 5(2 + 3x)
Apply the distributive property to get the equivalent expression: 5(2 + 3x) = 5*2 + 5*3x = 10 + 15x