The probability that fewer than 22 customers in the sample buy coffee during their visit is 0.7764.
What is a normal approximation to the binomial?
When we utilize a continuous distribution (the normal distribution) to approximate a discrete distribution, we use the normal approximation to the binomial (the binomial distribution). The Central Limit Theorem states that if the sample size is high enough, the sampling distribution of the sample means approximates normality.
In a normal distribution with mean and standard deviation, the z-score of a measure X is given by:
[tex]Z=\frac{X-\mu}{\sigma}[/tex]
Given, 55% of the customers buy coffee, p = 0.55
Sample of 35 customers, n = 35
mean [tex]\mu[/tex] = np = 35*0.55 = 19.25
standard deviation, [tex]\sigma = \sqrt{np(1-p)}[/tex] = [tex]\sqrt{35*0.55*0.45}[/tex] = 2.94
So, the probability that fewer than 23 customers in the sample buy coffee is
P(X < 22 - 0.5) = P(X < 21.5)
= [tex]P(\frac{X-\mu}{\sigma} < \frac{21.5-19.25}{2.94})[/tex]
= P(Z<0.765) = 0.7764
Hence, the probability that fewer than 22 customers in the sample buy coffee during their visit is 0.7764.
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How to solve 3(1+p)=-5(p+1)
Step-by-step explanation:
3(1+p)=-5(p+1)
here is your answer
I hope this helpful for u
The interior angles formed by the sides of a hexagon have measures that sum to 720°.
What is the measure of angle F?
Enter your answer in the box.
m∠F=
Answer:
Step-by-step explanation:
(x-60)+(x-20)+(x-40)+130+120+110=720
3X -120 + 360=720
3x +240= 720
3x= 720-240
3x=480
x= 480/3 = 160
x=160
angle F = (x-20)
angle F = 160-20=140
angle F = 140
the length of a rectangle is four times its width. if the perimeter is at most 130 centimeters, what is the greatest possible value for the width? question 3 options: 2w + 2 • (4w) < 130 2w + 2 • (4w) > 130 2w + 2 • (4w) ≤ 130 2w + 2 • (4w) ≥ 130
Answer:
Step-by-step explanation:
Let L be the Length and W be the Width of a rectangle.
We are told that: L = 4W [the length of a rectangle is four times its width]
Perimeter = 2L + 2W
We learn that P ≤ 130 cm
2L + 2W ≤ 130 cm
Substitute L = 4W:
2L + 2W ≤ 130 cm
2(4W) + 2W ≤ 130 cm
10W ≤ 130 cm
W ≤ 13 cm
Options:
2w + 2 • (4w) < 130 Not correct since the < sign does not allow for the "at most 130 cm.")
2w + 2 • (4w) > 130 Must be ≤, not >
2w + 2 • (4w) ≤ 130 This option works since the ≤ sign is correct.
a multiple regression model has . select one: a. more than one dependent variable b. only one independent variable c. at least two dependent variables d. more than one independent variable
The multiple regression model represented by y = a₀ + a₁x + a₂x + ... has one independent variable.
Explanation:
Simple or linear regression model represents one dependent and one independent variable.Multiple regression model represents one dependent and more than one independent variable.Simple regression model represent by y = mx + b , here y is dependent variable where as 'x' independent variable.Multiple regression model represented by y = a₀ + a₁x + a₂x + ... Multiple regression model is expanded form of linear regression model where more than one independent variables are included.Therefore, the multiple regression model has more than one independent variable that is option d.
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HLP PLLSSSSSS!!! TYSM!!!
Solve 2(3m + 1) − 2m = −14.
m = −4
m equals negative 14 over 3
m equals negative 16 over 6
m = −0.06
Answer:
m = -4
Step-by-step explanation:
2(3m + 1) - 2m = -14
Use distributive property.
6m + 2 - 2m = -14
Combine like terms.
4m + 2 = -14
Subtract 2
4m = -16
Divide by 4.
m = -4
Find the differences between 3,428 and 8,254
Answer: 4826
Step-by-step explanation: 8254 - 3248 = 4826
if a researcher analyzed data using linear regression correlating a performance test and gpa and calculated a slope of 0.028 and y intercept of 0.63. what would be the predicted student's gpa if she scored 63 on the performance test?
The GPA of the student who scored 63 in the performance test is 2.394.
Given, a researcher analyzed data using linear regression correlating a performance test and GPA and calculated a slope of 0.028 and y-intercept of 0.63.
we have find the GPA of a student who scored 63 in the performance test.
Let the score of the student in performance test be, x
and the GPA of the student be, y
So, y = mx + c
as, m = 0.028 and c = 0.63
y = 0.028x + 0.63
at x = 63
y = 0.028×63 + 0.63
y = 2.394
So, the GPA of the student who scored 63 in the performance test is 2.394.
Hence, the GPA of the student who scored 63 in the performance test is 2.394.
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a population of 10,000 people has an annual growth rate of 6.5%. use the exponential growth equation to determine the size of this population after five years if the growth rate stays the same. the size of the population after five years if the growth rate stays the same is closest to:
The Total Population after five years will be 13,700 people
What is Compound Interest?
Compound interest is the adding of interest to the principle sum of a loan or deposit, or interest on interest plus interest. It is the outcome of reinvesting interest, or adding it to the lent capital, rather than paying it out or requesting payment from the borrower, so that interest is received on the principle sum plus previously accrued interest in the next month. In finance and economics, compound interest is the norm.
Solution:
To solve the problem mentioned we need to use the concept of compound interest:
Principal = 10,000
Annual Growth Rate = 6.5%
Time = 5 years
Amount = Principal * ((100+Rate)/100)^Time
Total Population after 5 years = 10,000 * (106.5/100)^5
= 10,000 * (1.065)^5
= 10,000 * 1.37008
= 13,700
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a frog starts at location a and wants to get to location b that is 500 meters away. starting at a, it sits at a given spot on the path from a to b for a time that is exponen- tially distributed with parameter 1 (minute). after that, it jumps 1 meter towards b, sits in the new spot for an exponentially distributed time, etc. all the times are independent. what is the probability (approximately) that it will get to b within 7 hours?
The probability that it will get to b within 7 hours is approximately 0.014.
Probability:
In math, the favorable way of happening the event is known as probability.
Given,
A frog starts at location a and wants to get to location b that is 500 meters away. starting at a, it sits at a given spot on the path from a to b for a time that is exponentially distributed with parameter 1 (minute). after that, it jumps 1 meter towards b, sits in the new spot for an exponentially distributed time, etc. all the times are independent.
Here we need to find the the probability (approximately) that it will get to b within 7 hours.
While we looking at the given question we have identified that,
starting point = a
ending point = b ( 500 meters)
Time take for one jump = 1 minute
Distance covered in one jump = 1 meter.
Here they also said that the time is independent but the distance remains constant.
So, the probability that it will get to b within 7 hours is calculated as,
=> 7/500
=> 0.014
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what is the probability of these events when we randomly select a permutation of {1, 2, 3, 4}? a) 1 precedes 4. b) 4 precedes 1. c) 4 precedes 1 and 4 precedes 2. d) 4 precedes 1, 4 precedes 2, and 4 precedes 3. e) 4 precedes 3 and 2 precedes 1.
The probability that these events when we randomly select a permutation is 24, 1/2, 1/2, 1/3, 1/4, 1/4
What is a probability simple definition?A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to express probabilities.
What is the probability formula?P(A) = n(A)/n (S)
The probability of an event "A" is P(A). The number of successful outcomes is n(A). The total number of events in the sample space is denoted by n(S).
1) From the set we can select 4*3*2*1=24 permutations.
2) There are six permutations that begin with 1, three that begin with 2, three that begin with 3, and no permutations that begin with 4 when 1 comes before 4. So, P1 ={ 6+3+3+0}/{24} = 1/2
3) No permutations begin with 1, three permutations begin with 2, three permutations begin with 3, and six permutations begin with 4, where 4 comes before 1. P2=1/2
4) There are no permutations that begin with 1, no permutations that begin with 2, no permutations that begin with 2, no permutations that begin with 3, and six permutations that begin with 4, where 4 comes before both 1 and 2. Therefore, P 3 = 1/3
5) No permutations begin with 1, no permutations begin with 2, no permutations begin with 3, and there are six permutations that begin with 4, where 4 comes before 1, 2, and 3. So, P4= 1/4
6) There are no combinations that begin with 1, three combinations that begin with 2, no combinations that begin with 3, and three combinations that begin with 4, where 4 comes before 3 and 2 comes before 1. So, P5= 1/4
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Which set of ordered pairs represents a function?
O {(-6,-4), (2, -1), (-6, 0), (-9, 8)}
O {(7,-7), (8,9), (7, 7), (-4,9)}
O {(-4,-1), (-6, -7), (7,6), (-8,6)}
O {(8,-8), (2, -7), (9,-4), (8,-5)}
Submit Answer
Answer:Answer:
D.
{(-9,8), (-5,-8), (-7,8), (-6,-8)}
Step-by-step explanation:
I don’t understand this question , it’s so confusing
the length of a rectanglar photograph is 7 inches more than the width. if the are is 78 inches squared, what are the dimensions of the photograph
The dimensions of the photograph are found as 13 in and 6 in.
Explain the term rectangle?An enclosed 2-D shape called a rectangle has four sides, four corners, and four right angles (90°). A rectangle has equal and parallel opposite sides.Let length = x.
So, width = x - 7
Area = length x width
A = x (x -7)
and A = 78 inches squared.
Thus,
78 = x (x -7)
On solving.
x² - 7x - 78 = 0
Find the factors of the quadratic equation,
x² - 7x - 78 = 0
(x - 13)(x + 6) = 0
Thus,
x = 13 and x = -6 but (x > 0)
Thus, when x = 13 in,
Width = x + 7
Width = 13 - 7
Width = 6 in
Thus, the dimensions of the photograph are found as 13 in and 6 in.
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A book sold 32,100 copies in its first month of release. Suppose this represents 8.2% of the number of copies sold to date. How many copies have
been sold to date?
Round your answer to the nearest whole number.
Answer:
2,632 copies
Step-by-step explanation:
32100× 0.082= 2632.2
About 2,632
Caculate the simple interest earned on $5000 at 5% for 3.5 years
Answer:
56.0
Step-by-step explanation:
the following data were collected for a two-factor anova with two treatments and three blocks. treatment block 1 2 a 46 31 b 37 26 c 44 35 using the 0.05 significance level conduct a test of hypothesis to determine whether the block or the treatment means differ. required: a. state the null and alternate hypotheses for treatments. b. state the decision rule for treatments. (round your answer to 1 decimal place.) c. state the null and alternate hypotheses for blocks. also, state the decision rule for blocks. (round your answer to 1 decimal place.)
The test hypothesis using 0.05 significance level has the following results:The treatment means differ, The block means do not differ.
What is hypothesis testing?A poll or study's findings can be tested using the statistical procedure known as hypothesis testing to see if the findings are significant. By calculating the likelihood that the findings happened by chance, you are basically evaluating if the findings are genuine. If it's possible that your results were a coincidence, the experiment won't be reproducible and won't be of much help.
Hypothesis testing may be one of the most perplexing components for students, mostly because you must first determine what your null is so that you can conduct a test. These challenging word problems that you encounter might sometimes be challenging to understand.
Make a plan for your null hypothesis.
Write down your null hypothesis
Determine the type of test you must do,
How to solve?
Describe the null and alternate treatment hypotheses:
Null hypothesis: No difference in treatment means
Alternative interpretation: The means differ
Indicate the treatment decision-making process:
F(1,2)=18.51 as seen in the table
Reject the null hypothesis if the estimated F exceeds 18.51.
Treatments Calculated F=43.75 > 18.51; hence, the null hypothesis is rejected.
As a result, we find that the treatment means differ.
Write out the null and alternative hypotheses for blocks.
Block means are not different under the null hypothesis.
A different theory There exists at least one pair of distinct meanings.
State the block decision rule as well:
Table F(2,2)=19.0 value
If the estimated F is greater than 19, reject the null hypothesis.
Blocks determined that F=8.14 19.0, thus we did not reject the null hypothesis.
Our conclusion is that the block means are equivalent.
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Suppose that 14 inches of wire costs 84 cents.
At the same rate, how much (in cents) will 37
inches of wire cost?
Answer: 222 cents
Step-by-step explanation: 84/14 = 6 This is the unit rate.
6 x 37 = 222
3,635 nearest thousand
Answer:
4000
Step-by-step explanation:
If we were to take the number 3,635 and round it to the nearest thousand, we can do it like this.
Start with 5. (Ones place)
3,635
5 is rounded to 10.
Now work on the number 4. (Tenths place)
3,640
4 is rounded to 0.
And now we can do the number 6. (Hundreds place)
3600
6 is rounded to 10.
If we look at the number now, it is
4000
3.635 rounded to the nearest thousand is 4000.
The vertices of a rectangle are located at the coordinates (1, 4), (1, 5), (6, 5), and (6, 4).
Find the length of the sides of the rectangle and its perimeter.
Check the picture below.
Enter an equation of the line (in slope-intercept form) that passes through the point (20, −7) and is perpendicular to the line y = −5x + 9. Express any numeric values as integers or simplified fractions.
Answer:
y = 1/5x -11
Step-by-step explanation:
You want the slope-intercept equation of the line perpendicular to y=-5x+9 that goes through the point (20, -7).
Slope-intercept formThe slope-intercept form of the equation for a line is ...
y = mx +b . . . . . . . . where m is the slope and b is the y-intercept
This can be solved to find the y-intercept from a point on the line:
b = y -mx
Comparing this form to the given equation, you see the given line has a slope of m = -5.
Perpendicular lineThe perpendicular line will have a slope that is the opposite reciprocal of the slope of the given line:
slope = -1/(-5) = 1/5
Y-interceptThe y-intercept of the desired line can be found using the equation for b above. The y-intercept of the line with slope 1/5 through point (x, y) = (20, -7) is ...
b = y -mx = (-7) -1/5(20) = -7 -4
b = -11
Now, we have the slope and intercept of the desired line, so we can write its equation:
y = 1/5x -11
Azlyn had $25. She went to lunch and spent $15 what percentage of her money did Azlyn spend on lunch
Answer: 60%
Step-by-step explanation:
15 divided by 25 = 0.6
0.6 x 100 = 60%
:)
The table shows the proportional relationship between the price for a certain number of buckets of golf balls at a driving range.
Buckets 3 5 7
Price (dollars) 28. 50 47. 50 66. 50
Determine the constant of proportionality.
9. 5
10. 5
18. 25
28. 5
The constant of proportionality is 9.5.
The correct option is (a)
Given,
In the question:
The proportional relationship between the price for a certain number of buckets of golf balls at a driving range.
Buckets 3 5 7
Price (dollars) 28. 50 47. 50 66. 50
To determine the constant of proportionality.
Now, According to the question:
We know that:
Proportional relationship equation:
y = kx, where k-constant of proportionality
In the given table, number of buckets represent input values (x) and the price represents output values (y).
We have for the first column:
x = 3, y = 28.50
Find the value of k by plugging in the values of x and y:
28.50 = 3k
k = 28.50/3
k = 9.5
The options are:
a) 9. 5
b) 10. 5
c) 18. 25
d) 28. 5
Hence, The constant of proportionality is 9.5.
So, The correct option is (a).
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The graph of a linear function is shown on the grid.
#6. Find the slope
#7. Find the y-intercept:
#8. Equation: y=
The slope and y-intercept of the given linear equation are [tex]-\frac{5}{4}[/tex] and [tex]5[/tex] respectively. The equation of the given graph is [tex]y=-\frac{5}{4} x+5[/tex]
What is the Slope of a graph?
The ratio of rise to run is known as a line's slope.When given a line's graph and asked to determine its equation, the first step is to determine the slope.The slope formula is used in the procedure for determining the slope from a graph.If there are two points [tex](x_{1} , y_{1} )[/tex] and [tex](x_{2} , y_{2} )[/tex] on the line, then the equation for the slope (m) is given as, [tex]m=\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]What is a y-intercept?
The location where a graph crosses the y-axis is known as the y-intercept (c). Or to put it another way, it is the value of y when x=0.Here, from the graph, we can find a line passing through the two points, [tex](4,0)[/tex] and [tex](0,5)[/tex].
The equation for the slope formula is given as, [tex]m=\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
Using the slope formula, we get the slope of the given graph as,
[tex]m=\frac{ 5-0 }{0-4 }\\\implies m=-\frac{5}{4}[/tex]
The y-intercept (c) is the value of y when x equals zero.
The line is passing through the point [tex](0,5)[/tex]
Here, the value of x is equal to 0 and the value of y is equal to 5.
So, the y-intercept of the given graph, [tex]c=5[/tex]
We know that the equation of a straight line is expressed as, [tex]y=mx+c[/tex]
Substituting the values of m and c in the straight line equation form, we get the equation of the given line as,
[tex]y=-\frac{5}{4} x+5[/tex]
Therefore, the slope of the given graph, [tex]m=-\frac{5}{4}[/tex] and the y-intercept, [tex]c=5[/tex].
Also, the equation of the given line is [tex]y=-\frac{5}{4} x+5[/tex]
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Write an inequality and use substitution to solve the following problem:
Janet plans on mowing lawns for 12 weeks in the summer. Her goal for the summer is to earn more than $500. Which of the following rates of weekly earning would allow her to reach her goal?
The rates of weekly earning would allow her to reach her goal will be 12x > 500.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
Janet anticipates cutting yards for quite a long time in the late spring. Her objective for the late spring is to acquire more than $500.
Let 'x' be the weekly rate. Then the inequality is written as,
12x > 500
The rates of weekly earning would allow her to reach her goal will be 12x > 500.
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when determining the pooled population variance estimate for a t test for independent means with unequal sample sizes,: group of answer choices the variance of both of the original populations must be known (as opposed to estimated) the scores from both samples are combined to form a single sample, and the estimated variance is figured in the usual way, but using this combined sample the estimates based on each of the samples are averaged in such a way as to give more influence to the estimate based on more participants the variance of at least one of the original populations must be known (as opposed to estimated), but the other can be estimated from sample scores
The estimates based on each of the samples are averaged in such a way as to give more influence to the estimate based on more participants.
What is population variance?
Each data point's distance from the population mean is quantified by the population variance, which is a measure of dispersion. The average of the squares of the deviations from the data's mean value is known as population variance.
Hence, when determining the pooled population variance estimate for a t test for independent means with unequal sample sizes, the estimates based on each of the samples are averaged in such a way as to give more influence to the estimate based on more participants.
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ohnny is a sophomore in college and has a 1.5 cumulative grade point average (gpa). johnny's cumulative gpa will fall even further next semester if he performs worse than (i) his cumulative gpa. (ii) he ever performed before. (iii) he did last semester.
The value of the solution is B i.e., his cumulative gpa (i), he ever performed before (ii)
What do you mean by statistics?The science of statistics focuses on creating and researching strategies for gathering, analyzing, interpreting, and presenting empirical data.
What are types of statistics?The two types of statistics are: Descriptive and inferential.
With the alternatives available, Johnny can only do worse if his performance falls short of both his lifetime GPA and his previous best performance. It's possible that the last scenario, in which Johnny performed worse than last semester, won't necessarily have an impact on his GPA. A cumulative GPA represents Johnny's overall GPA since he first began attending school. Considering that his most recent semester may have been one of his best and had a solid outcome, earning a result somewhat below that of his previous semester may not necessarily result in a drop in his cumulative GPA. Therefore, choice B is right.
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need help working this problem
Find the missing angle values
a) ∠a = 35
b) ∠b = 40
c) ∠c = 35
d) ∠d = 70
e) When we add all the angles together we get an angle of 360°.
What is meant by an angle?In Euclidean geometry, an angle is the figure formed by two rays, known as the sides of the angle, that have a common termination, known as the vertex of the angle. These are referred to as dihedral angles. An angle can also be defined by two intersecting curves, which is the angle of the rays lying tangent to the respective curves at their point of intersection.
Given, ∠b = 40
∠d = 70
∠1 = ∠ a
∠2 = ∠c
∠1 = ∠2
So, ∠1 =∠2 = ∠a = ∠c
70 + 40 + ∠a + ∠2 = 180
110 + 2∠a = 180
2∠a = 180 - 110
∠a = 70/2
∠a = 35
∠1 =∠2 = ∠a = ∠c = 35
When we add all the angles together we get an angle of 360°
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an individual is teaching a class on excel macros. the individual plans to break the class up into groups of 4 and wants each group to have a different exercise to practice on. write an equation that expresses the situation, let x be the independent variable and y be the dependent variable.
The required relation between independent and dependent variables is y = x/4.
Explain dependent and independent variables?A simple method for considering independent and dependent variables is, the point at which you're leading an examination, the free factor is what you change, and the reliant variable changes hence. You can likewise consider the autonomous variable the reason and the reliant variable as the impact
According to question:The independent variable x is the total number of students in the class.
And the dependent variable y is number of students in each group.
Therefore,
y = x / 4
Here, when we change the value of x then value of y automatically changed.
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how do i do Write the prime factorization of 6. Use exponents when appropriate and order the factors from least to greatest (for example, 2235).
Answer:
2*3
Step-by-step explanation:
divide by smallest number possible
6/2=3
3/3=1
2*3=6
so 2*3
The question is attached on the image below. Help is needed urgently please help!