Answer:If 104° is a measure of one of the vertical angles formed by the intersection of two straight lines, then the measure of the other vertical angle would also be 104°. This is because vertical angles are always congruent, which means they have the same measure.
Step-by-step explanation:
which of the following is true about a normally distributed set of data? (choose one or more) group of answer choices the tails are the same length the right tail is longer than the left tail the tails are asymptotic the left tail is longer than the right tail
Normal distribution is symmetric distribution so mean, median and mode are the same. The tails are the same length.
The left tail of such a distribution is longer than the right tail in negative type of asymmetric distribution. The “extremities” of a distribution are precisely what their name suggests - the extensions on either side of a distribution. While this term can be applied to a set of data, it is more easily observable when the data is represented graphically, as the extremities become readily apparent.
The extension on the left is referred to as the left-extremity, and likewise, the one on the right is called the right-extremity. It's not essential for a distribution to have both of these; it can have just one on either side.
Upper and Lower Extremities: Although it's more common to denote the extremities as being on the "left" or "right," this can be problematic if you're not examining a graph. In other words, if you're dealing with a set of data, it may not be immediately clear which data should be placed on the left or right of a graph. The alternative names for the right and left extremities, which address this problem, are upper extremity and lower extremity.
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Use the table to find ratios that are equivalent to 4:6.
4
8
12
12:
48
18
30
6
12
18
20
30
36
54
Answer:
ratios 2:3, 8:12, 12:18, 16:24, and 20:30 are equivalent to 4:6.
Step-by-step explanation:
To find ratios that are equivalent to 4:6, we can simplify the ratio by dividing both terms by their greatest common factor, which is 2.
| Ratio | Simplified Ratio |
|---------|-----------------|
| 4:6 | 2:3 |
| 8:12 | 4:6 |
| 12:18 | 2:3 |
| 16:24 | 2:3 |
| 20:30 | 2:3 |
Therefore, ratios 2:3, 8:12, 12:18, 16:24, and 20:30 are equivalent to 4:6.
melanie is a researcher who wishes to estimate the mean birthweight of full-term babies in her hospital. what minimum number of babies should she sample if she wishes to be at least 99% confident that the mean birth- weight of the sample is within 150 grams of the mean birthweight of all babies? assume that the distribution of birthweights at her hospital is normal with a standard deviation of 600 g
Melanie is a researcher who wishes to estimate the mean birthweight of full-term babies in her hospital. What minimum number of babies should she sample if she wishes to be at least 99% confident that the mean birth- weight of the sample is within 150 grams of the mean birthweight of all babies? Assume that the distribution of birthweights at her hospital is normal with a standard deviation of 600 g.
The sample size needed is 45.6. The researcher will need a sample size of 46 babies if she wishes to be at least 99 percent confident that the sample's mean birth weight is within 150 grams of the population's mean birth weight. We'll use the formula zα/2 (σ/√n) to solve this issue.Zα/2 = 2.576, σ = 600, and E = 150 are the inputs used in the formula.
The formula for solving for n is rewritten as follows:(Zα/2)^2 (σ^2 )/E^2where Zα/2 is the z-score at the α/2 level of the confidence level (0.005 in this case) and E is the error, which is given as 150 in the question. Zα/2 is 2.576, while σ is 600, which gives us:(Zα/2)^2 (σ^2 )/E^2 = (2.576)^2 (600)^2 /(150)^2 = 45.6.We get a sample size of 46 babies by rounding up to the nearest whole number. Therefore, if Melanie wants to be at least 99 percent confident that the mean birth weight of the sample is within 150 grams of the population mean birth weight, she will require a sample size of 46 babies.
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at one hospital, there were 796 boys and 764 girls born during one particular year. if a delivery from that year at the hospital is chosen at random. what is the probability that the baby is a girl? (round to four decimals like 0.1234)
A delivery from a particular year at the hospital is randomly choose. The probability that the baby is a girl is equals to the 0.4897.
We have provide a data of girl and boy born babies in a particular year.
At hospital, total born boy baby = 796
born baby girls in hospital = 764
total babies in hospital = 796 + 764
= 1560
We have to determine the probability that the baby is a girl. Let the event E be the choose baby is girl. Probability is defined as the ratio of favourable outcomes to the possible outcomes of an event .
So, favourable outcomes for event E
= 764
Total possible outcomes = 1560
So, the probability that the baby is a girl, P( E) = 764/1560
= 0.4897
Hence, required probability value is 0.4897.
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the resultant data are: forty mothers have taken the suspected drug during their pregnancies. of these mothers, 35 have delivered malformed infants. in addition, 10 other infants are born with malfunctions. what type of study design is this?
The study is investigating the relationship between the exposure to the suspected drug during pregnancy and the risk
of delivering a malformed infant. This study design is a case-control study design.
The resultant data are: forty mothers have taken the suspected drug during their pregnancies. Of these mothers, 35
have delivered malformed infants. In addition, 10 other infants are born with malfunctions," then the answer would be
as follows:
The type of study design that is described in this scenario is a case-control study design.
A case-control study design is a type of observational study design that compares people with a particular condition
(cases) to people without that condition (controls) to determine whether there is a relationship between the exposure
to a suspected risk factor and the development of the condition.
In this scenario, the cases are the 35 mothers who delivered malformed infants, and the controls are the 5 mothers
who did not deliver malformed infants. The study is investigating the relationship between the exposure to the
suspected drug during pregnancy and the risk of delivering a malformed infant. Therefore, this study design is a case
control study design.
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find x and y
y = 4x
у=5x - 2
Answer:
x=2, y=8
Step-by-step explanation:
This is a system of equations, so we need to substitute one equation for another one but they are both equal to y.
4x=5x-2
-x=-2
x=2
y=4x
y=4(2)
y=8
last year, 44 of business owners gave a holiday gift to their employees. a survey of business owners conducted this year indicates that planned to provide a holiday gift to their employees. suppose the survey results are based on a sample of business owners. a. how many business owners in the survey planned to provide a holiday gift to their employees this year? round your answer to the nearest whole number.
Number of business owners in the survey planned to provide a holiday gift to their employees this year is 27
We are given that 30% of business owners planned to provide a holiday gift to their employees this year. We can use this percentage to estimate the number of business owners in the sample who planned to provide a gift.
To do this, we can multiply the percentage by the total number of business owners in the sample
30% of 90 business owners = 0.30 x 90 = 27 business owners
Rounding to the nearest whole number, we get:
Approximately 27 business owners planned to provide a holiday gift to their employees this year.
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The given question is incomplete, the complete question is:
Last year 44% of business owners gave a holiday gift to their employees. A survey of business owners conducted this year indicates that 30% planned to provide a holiday gift to their employees. Suppose the survey results are based on a sample of 90 business owners.
How many business owners in the survey planned to provide a holiday gift to their employees this year? Round your answer to the nearest whole number.
Justify the last two steps in the proof.
Thus, by the property of side side side congruence of triangle, ΔRST ≅ ΔUTS .
Explain about the triangle congruency:Both triangles are considered congruent if the three angles and three sides of one triangle match the corresponding angles and sides of the other triangle.
2 triangles are congruent provided their accompanying 3 side lengths are equal, according to the side-side-side rule (SSS).2 triangles are congruent when their accompanying two angles but one included side are equivalent, according to the Angle- Side- Angle rule (ASA).Given :
RS ≅ UTRT ≅ USThe statements are-
RS ≅ UT Given
RT ≅ US Given
St ≅ TS Common
ΔRST ≅ ΔUTS By side side side congruence
Thus, by the property of side side side congruence of triangle, ΔRST ≅ ΔUTS .
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k is a degree 5 polynomial that passes through the origin, has zeros i and 8-i, and k(-4)= - 49300.
Find the equation for k.
Use x for your input. Simplify your answer so that it has only real numbers as coefficients.
the equation for K is K(x) = -20x⁵+ 260x³ - 800x.
How to solve the question?
Since K is a degree 5 polynomial with zeros i and 8-i, it also has two other complex zeros that are conjugates of each other, namely -i and 8+i. Thus, we can express K in factored form as:
K(x) = a(x-i)(x+i)(x-(8-i))(x-(8+i))(x-0)
where a is some constant coefficient. Simplifying the above expression, we get:
K(x) = a(x²+ 1)(x² - 16x + 65)x
Now we can use the fact that K(-4) = -49300 to solve for the coefficient a. Plugging in -4 for x, we get:
K(-4) = a((-4)²+ 1)((-4)²- 16(-4) + 65)(-4) = -49300
Simplifying the expression above, we get:
a(17)(129) = -49300
a = -20
Thus, the equation for K(x) is:
K(x) = -20(x² + 1)(x²- 16x + 65)x
Expanding and simplifying the expression above, we get:
K(x) = -20x⁵ + 260x³ - 800x
Therefore, the equation for K is K(x) = -20x⁵+ 260x³ - 800x.
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PLEASE HELP ME PLEASE PLEASE!!!! SHOW EXPLANATION OR YOU WILL GET REPORTED
Answer:
y = -x² + 5
Step-by-step explanation:
If x = -1
y = -(-1²) + 5
y = 4
If x = 0
y = 0 + 5
y = 5
If x = 1
y = -1² + 5
y = 4
If x = 2
y = -2² + 5
y = 1
If x = 3
y = -3² + 5
y = -4
Hope this helps!
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A checking account has a balance of $350. A customer makes two withdrawals, one $50 more than the other. Then he makes a deposit of $75.
The new balance of the checking account after the two withdrawals and the deposit is $375 - 2x. Note that we do not know the value of x, so we cannot determine the exact new balance without additional information.
What is statistics?
Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data.
After the two withdrawals and the deposit, the new balance of the checking account can be calculated as follows:
First withdrawal: Let x be the amount of the first withdrawal. Then the second withdrawal is x + $50.
Balance after first withdrawal: $350 - x
Balance after second withdrawal: ($350 - x) - (x + $50) = $350 - 2x - $50 = $300 - 2x
Deposit: After the deposit of $75, the new balance is ($300 - 2x) + $75 = $375 - 2x.
Therefore, the new balance of the checking account after the two withdrawals and the deposit is $375 - 2x. Note that we do not know the value of x, so we cannot determine the exact new balance without additional information.
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2) The cost of building a bridge in 1995 was estimated as £24
million. When it was finally completed in 1998 its total cost
amounted to £37.7 million.
13.7
What was the percentage increase?
The percentage increase in the cost of building the bridge was approximately 57.08%.
What is percentage increase?Percentage increase is a measure of the amount of increase or growth expressed as a percentage of the original value. It is calculated by subtracting the original value from the new value, then dividing the result by the original value, and finally multiplying the quotient by 100.
According to question:To find the percentage increase, we need to calculate the difference between the final cost and the initial cost, and then divide that difference by the initial cost and multiply by 100 to get the percentage increase.
The formula for percentage increase is:
Percentage increase = (New value - Old value) / Old value x 100
Difference = Final cost - Initial cost
Difference = £37.7 million - £24 million
Difference = £13.7 million
Percentage increase = (Difference / Initial cost) x 100
Percentage increase = (13.7 / 24) x 100
Percentage increase = 57.08%
Therefore, the percentage increase in the cost of building the bridge was approximately 57.08%.
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Which relationships have the same constant of proportionality between
�
yy and
�
xx as the following graph?
Options A and C have the same constant of proportionality between y and x as the given graph.
What is graph?Rather than using values variable, theoretical physicists assess and illustrate claims using graphs. Typically, a graph point shows the relationship between several distinct objects. A graph is a particular kind of transportation system formed up of both groups and lines. The channels or borders should be fastened with glue. The numbers 1 through 4 and also the characters 2.5, certain individuals.
The graph shows a linear relationship between x and y, where as x increases, y also increases at a constant rate. The slope of the line is positive, which means that y increases as x increases.
To find relationships with the same constant of proportionality between y and x as the given graph, we need to look for equations that represent a straight line with a positive slope.
From the given options, two equations that represent a straight line with a positive slope are:
A) 6y = 8x (or y = 4/3 x)
C) y = 2x + 4
Therefore, options A and C have the same constant of proportionality between y and x as the given graph.
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Question 2(Multiple Choice Worth 2 points)
(Comparing Data MC)
The line plots represent data collected on the travel times to school from two groups of 15 students.
A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 4,6,14, and 28. There are two dots above 10, 12, 18, and 22. There are three dots above 16. The graph is titled Bus 47 Travel Times.
A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 8, 9,18, 20, and 22. There are two dots above 6, 10, 12,14, and 16. The graph is titled Bus 18 Travel Times.
Compare the data and use the correct measure of variability to determine which bus is the most consistent. Explain your answer.
Bus 18, with an IQR of 16
Bus 47, with an IQR of 24
Bus 18, with a range of 16
Bus 47, with a range of 24
Based on the interquartile range values, bus 18 has a lower IQR than bus 47, so we conclude that bus 18 is more stable. This means that the travel times of students on the 18th bus are more clustered around the median and there are fewer outliers in the data.
What is a line graph?A line graph is a type of chart that displays data as points or points along a number line. Each dot or dot represents a single data value and the number line indicates the range of data.
Line grapgs display small to medium-sized data sets and are useful for identifying central trends and variability in your data.
To determine which buses are the most consistent, we need to look at the variability of data. The most appropriate measure of variability for this purpose is the interquartile range (IQR), which is the range of the central 50% of the data.
Given the data, we can calculate the IQR for both buses as follows:
For bus 18:
Lower quartile (Q1) = 8
Upper quartile (Q3) = 24
IQR = Q3 - Q1 = 24 - 8 = 16
For bus 47:
Lower quartile (Q1) = 10
Upper quartile (Q3) = 34
IQR = Q3 - Q1 = 34 - 10 = 24
The range, or the difference between the maximum and minimum values, is not a very good measure of variance for this purpose because it is heavily influenced by outliers. Therefore, range cannot be used to determine data consistency on both buses.
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At the spelling bee finals, sarah correctly spelled two less than three times as many words as christian. Leonard correctly spelled one more than twice the number of words as christian. Altogether, the three students correctly spelled a total of 95 words. How many words did each of the students spell correctly?
By answering the presented question, we may conclude that So Christian equation spelled 16 words correctly, Sarah spelled 3x - 2 = 46 words correctly, and Leonard spelled 2x + 1 = 33 words correctly.
What is equation?
An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x Plus 3" equals the number "9." The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. The variable x is raised to the second power in the equation "x2 + 2x - 3 = 0." Lines are utilized in many different areas of mathematics, such as algebra, calculus, and geometry. Let's start by defining some variables to represent the number of words each student spelled correctly:
Let x be the number of words Christian spelled.
x + (3x - 2) + (2x + 1) = 95
6x - 1 = 95
6x = 96
x = 16
So Christian spelled 16 words correctly, Sarah spelled 3x - 2 = 46 words correctly, and Leonard spelled 2x + 1 = 33 words correctly.
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melissa flipped her lucky coin 13 times and got 6 heads. melissa used these numbers to estimate the probability of getting a head with her lucky coin. find the margin of error for melissa's estimated probability above.
The probability of getting a head with her lucky coin is 0.46 and the margin of error for Melissa's estimated probability is 0.218.
Probability is a way to gauge how likely something is to happen. Several things are difficult to forecast with absolute confidence. With it, we can only make predictions about the likelihood of an event happening, or how likely it is. The range of probability is 0 to 1, with 0 representing impossibility and 1 denoting certainty.
Let X be the "number of heads" in a n=13 trial.
The observed percentage of fortunate coins with heads is,
X= 6
The estimated probability of Josue ‘flipping a head’ with his lucky coin is,
p = X/n
p = 6/13
p = 0.46
A statistic called the margin of error measures the degree of random sampling error in a survey's findings. It indicates a likelihood that the results of a sample will be quite close to the findings that one would arrive at if the full population had been surveyed. The margin of error is obtained by multiplying the critical value by the standard deviation.
The estimated probability calculated using Josue's margin of error (ME) assuming,
α = 1 - 0.95= 0.05 is,
ME= Zc x [tex]\sqrt{{p^(1-p^)/n[/tex]
Here, p = 0.46, Zc= z(0.05/2)= 1.96
ME = 1.96 x √0.46⨉0.55/20
ME = 1.96 x √0.01238
ME = 0.21808≅ 0.218
The margin of error is 0.218.
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What is the perimeter of a pentagon with sides that are each 12 inches long?
[tex]p = 5a[/tex]
Answer
P=60
Step by step explanation
a= 12
so according to the formula
p=5(12)
p=60
The perimeter of a pentagon with sides that are each 12 inches long is 60 inches.
What is Perimeter?The perimeter of a form is the space surrounding its edge.
The whole distance encircling a shape is referred to as its perimeter. It is the length of any two-dimensional geometric shape's boundary or outline. Depending on the size, the perimeter of several figures can be the same.
We have,
Sides of Pentagon = 12 inches
We know that Pentagon have 5 sides.
So, Perimeter of Pentagon
= 5 x side
= 5 x 12
= 60 inches
Thus, the Perimeter is 60 inches.
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in a sample of 400 voters, 320 indicated they favor the incumbent governor. the 95% confidence interval of voters not favoring the incumbent is
The 95% confidence interval for voters not favoring is approximately 16.08% to 23.92%.
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lines c and d are parallel. which statement about the relationship between the angle measures are true?
The statement which is true by the corresponding angles theorem is option (B) ∠2 ≅ ∠6
The corresponding angles theorem states that when a transversal intersects two parallel lines, the pairs of corresponding angles are congruent.
In this case, lines c and d are parallel and transversal p intersects them, creating eight angles: ∠1, ∠2, ∠3, ∠4, ∠5, ∠6, ∠7, and ∠8.
The corresponding angles are
∠1 and ∠5
∠2 and ∠6
∠3 and ∠7
∠4 and ∠8
Since lines c and d are parallel, we know that ∠2 and ∠6 are corresponding angles. Therefore, by the corresponding angles theorem, we can conclude that ∠2 ≅ ∠6
Therefore, the correct option is (B) ∠2 ≅ ∠6
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The given question is incomplete, the complete question is:
Lines c and d are parallel lines cut by transversal p.
Which must be true by the corresponding angles theorem?
A) ∠1 ≅ ∠7
B) ∠2 ≅ ∠6
C) ∠3 ≅ ∠5
D) ∠5 ≅ ∠7
Air currents cause planes to fly faster traveling from west to east than they do from east to west because they are flying with a tailwind at high altitudes. A plane traveling 2500 miles from Los Angeles to New York and 2500 miles back again takes 10 hours of flight time. If the plane's cruising speed is 505 miles per hour, calculate the speed of the air current.
Formulate an equation representing the situation and use it to calculate the speed of the air current.
The speed of the air current is 22.36 mph(rounded to two decimal places).
What is distance?
Distance is the measure of how far apart two objects or locations are from each other. It is usually measured in units such as meters, kilometers, miles, or feet.
Let's assume the speed of the air current as x mph.
When the plane is traveling from Los Angeles to New York, it flies with a tailwind, so its effective speed will be the sum of its cruising speed and the speed of the air current, which is 505 + x mph.
When the plane is traveling from New York to Los Angeles, it flies against the headwind, so its effective speed will be the difference between its cruising speed and the speed of the air current, which is 505 - x mph.
We can use the formula:
time = distance / speed
to set up an equation based on the given information:
2500 / (505 + x) + 2500 / (505 - x) = 10
Multiplying both sides by (505 + x) * (505 - x), we get:
2500(505 - x) + 2500(505 + x) = 10(505 + x)(505 - x)
Simplifying the equation, we get:
505000 - 2500x + 505000 + 2500x = 25502500 - 10x²Simplifying further, we get:
10x² = 5000
x² = 500
x = 22.36 (rounded to two decimal places)
Therefore, the speed of the air current is 22.36 mph.
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Enter your response in the box below.
Find the height, x, of the triangle.
X
90
-100
Answer:
Step-by-step explanation:
height x is in the wrong spot of the triangle -90 x 100 then divide sum like that.. (:
(a^2b^4)(ab^-2) into positive
Therefore , the solution of the given problem of expressions comes out to be (a²b⁴)(ab⁻²) = a³b² with positive exponents.
What is an expression?It is preferable to use shifting integer numbers that can be increasing, reducing, or blocking rather than approximations generated at random. They were only able to assist one another by exchanging resources, knowledge, or answers to problems. A declaration of truth equation may include the justifications, components, and mathematical comments for strategies like extra disapproval, manufacture, and mixture.
Here,
The following exponent properties can be used to condense the equation (a 2 b 4) (ab -2) and express it using only positive exponents:
(a²b⁴)(ab⁻²) = a²⁺¹ b⁴⁻² = a³b²
a³b² is the simplified form of the equation (a²b⁴)(ab⁻²) with positive exponents.
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Which inequality is equivalent to 7-2(x+2)-4-3(1-x)
?
The simplified fοrm οf the inequality is -5x < -10.
What is inequality?The term "inequality" is used in mathematics tο describe a relatiοnship between twο expressiοns οr values that is nοt equal tο οne anοther. Inequality results frοm a lack οf balance. When twο quantities are equal, we use the symbοl '=', and when they are nοt equal, we use the symbοl. If twο values are nοt equal, the first value can be greater than (>) οr less than (), οr greater than equal tο () οr less than equal tο ().
Here the given inequality is,
=> 7-2( x + 2) <-4 - 3(1 – x)
Nοw simplifying the inequality then,
=> 7-2( x + 2) <-4 - 3(1 – x)
=> 7-2x-4 < -4-3+3x
=> 3-2x < 3x-7
=> -2x -3x < -7-3
=> -5x < -10
Hence the simplified fοrm οf the inequality is -5x < -10.
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First try was incorrect
Convert the following metric length into millimeters. You may enter an
exact answer or round to the nearest thousandth.
2.38 km
2.38 km is equivalent to 2,380,000 millimeters.
What is metric system?A method for measuring temperature, length, volume, weight, and distance is known as the metric system. It is founded on three fundamental units that allow us to measure almost anything in the universe.
M- meter, used to measure the length
Kg- kilogram, used to measure the mass
S- second, used to measure time
To convert 2.38 km into mm,
We know 1 km = 1000 m
And 1 m = 1000 mm
So, 2.38 km is equivalent to 2,380,000 millimeters. (rounded to the nearest thousandth)
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A coffee shop recorded the drinks that were recently sold.
mochas 1
macchiatos 3
Americanos 5
lattes 7
espressos 4
Considering this data, how many of the next 15 drinks sold would you expect to be espressos?
Based on the given data, it is expected that approximately 4 of the next 15 drinks sold will be espressos.
To find the expected number of espressos out of the next 15 drinks sold, we can use the proportion of espressos in the recorded drinks as an estimate.
The proportion of espressos in the recorded drinks is 4 out of a total of 20 drinks, or 4/20 = 0.2. This means that about 20% of the recorded drinks were espressos.
To estimate how many of the next 15 drinks sold would be espressos, we can use the proportion of espressos in the current data.
Out of a total of 20 drinks (1 mocha + 3 macchiatos + 5 Americanos + 7 lattes + 4 espressos), the proportion of espressos is 4/20 = 0.2.
Therefore, we can expect that approximately 0.2 * 15 = 3 of the next 15 drinks sold will be espressos.
So we can expect that three of the next 15 drinks sold will be espressos.
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a crane is 15 meters tall. its shadow is 8 meters long. close by, there is a bell tower that is 45 meters tall. how long is the bell tower's shadow?
Answer: 24 meters
Step-by-step explanation:
15/45 = 8/x
15x = 360
x = 24
The length of the bell tower's shadow is 24 meters. This can be answered by the concept of similar triangles.
To determine the length of the bell tower's shadow, we can use the concept of similar triangles. The height of the crane, the length of its shadow, and the height of the bell tower form one set of similar triangles. We can write the proportion:
height of crane / length of crane's shadow = height of bell tower / length of bell tower's shadow
Plugging in the given values, we get:
15 / 8 = 45 / x
Solving for x, we get x = 24.
Therefore, the length of the bell tower's shadow is 24 meters.
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ten mile run ~ a random sample of 50 runners from all the runners who finished the cherry blossom ten mile run in 2009 had a mean finishing time 94.5 minutes and a standard deviation of 18.5 minutes. what is the lower bound for a 95% confidence interval for the actual mean finishing time? give your answer to 4 decimal places.
The lower bound for a 95% confidence interval for the actual mean finishing time is approximately 89.251 minutes.
How lower bound for a 95% confidence interval approximately 89.251 minutes?The standard error of the mean (SEM) is calculated as the standard deviation of the sample divided by the square root of the sample size:SEM = s / sqrt(n) = 18.5 / sqrt(50) ≈ 2.613
where s is the sample standard deviation, n is the sample size, and sqrt represents the square root function.
The margin of error (ME) is calculated as the product of the critical value from the t-distribution and the SEM. For a 95% confidence interval with 49 degrees of freedom (50 - 1 = 49), the critical value is 2.009.ME = t * SEM = 2.009 * 2.613 ≈ 5.249
where t is the critical value from the t-distribution.
The confidence interval is calculated as the sample mean plus or minus the margin of error. The lower bound for a 95% confidence interval is:Lower bound = sample mean - ME = 94.5 - 5.249 ≈ 89.251
Therefore, the lower bound for a 95% confidence interval for the actual mean finishing time is approximately 89.251 minutes.
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A basketball player shoots the ball with a velocity of 17.0 ft/s at an angle of 34.1° with the horizontal. To the nearest tenth, find the magnitude of the horizontal component of the resultant vector.
We need to find the initial horizontal component of the vector that represents the velocity of the ball. Let us represent that initial horizontal component by, [tex]\bold{v_x}[/tex].
Now, since basketball player shoots the ball with an initial velocity, [tex]\bold{v}[/tex], of 17.0 ft./sec at an angle of 34.1 degrees with the horizontal, we can find the initial horizontal component by, [tex]\bold{v_x}[/tex] using the following formula:
[tex]\bold{v_x}=\bold{v}\text{cos}(\theta)=17.0\times\text{cos}(34.1^\circ)\thickapprox14.1[/tex] ft./sec
DANIEL WANTS TO PREDICT HOW FAR HE CAN HIKE BASED ON THE TIME HE SPENDS ON THE HIKE. HE COLLECTS SOME DATA ON THE TIME (IN HOURS) AND DISTANCE (IN KILOMETERS) OF SOME OF HIS PREVIOUS HIKES.
EQUATION: y=2x+1.5
BASED ON THIS EQUATION ESTIMATE THE DISTANCE DANIEL CAN HIKE IN 6 HOURS (IN KILOMETERS)‼️
If Daniel wants to predict how far he can hike. He can estimate that he can hike approximately 13.5 kilometers in 6 hours.
How to find the distance?Using the equation y = 2x + 1.5, where x is the time spent hiking in hours and y is the distance hiked in kilometers:
If Daniel spends 6 hours hiking, we can estimate the distance he can hike as:
y = 2x + 1.5
y = 2(6) + 1.5
y = 12 + 1.5
y = 13.5
Therefore, based on the equation, Daniel can estimate that he can hike 13.5 kilometers in 6 hours.
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What is the simplified form of this expression? (4x − 4) − 8x A. -4x − 4 B. -4x + 4 C. 12x − 4 D. -8x
The simplified form of the expression (4x - 4) - 8x is option A) -4x - 4.
What is linear equation?
A linear equation is a mathematical equation that describes a straight line in a two-dimensional plane. It is an equation of the form:
y = mx + b
where 'x' and 'y' are variables, 'm' is the slope of the line, and 'b' is the y-intercept (the point where the line intersects the y-axis).
Linear equations can also be expressed in the standard form
ax + by = c.
To simplify the expression, we can start by distributing the negative sign to the term (8x) inside the parentheses:
(4x - 4) - 8x = 4x - 4 - 8x
Next, we can combine the like terms 4x and -8x to get:
= -4x - 4
Therefore, the simplified form of the expression (4x - 4) - 8x is option A) -4x - 4.
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