As a result, Mr. Rodriguez can produce 10 sacks, each containing two blueberries and three grapes.
So, 10 bags must be the solution.
Which meaning of "common factor" is the best?The largest number that can split evenly into two other numbers is known as the greatest common factor in mathematics. For instance, the number 6 is the most frequent factor between 12 and 30. The greatest common denominator is another name for the greatest common component.
We must find the GCF, or greatest common factor, between 20 and 30 to calculate how many bags Mr. Rodriguez can produce. This is necessary because each bag must contain the same quantity of blueberries and grapes, requiring that they both have a similar factor of 20 or 30.
1, 2, 4, 5, 10, and 20 are the elements that make up 20.
1, 2, 3, 5, 6, 10, 15, and 30 make up the number 30.
1, 2, 5, and 10 are the common variables between 20 and 30.
Since the quantity of blueberries and grapes in each bag must be the same, we can split both 20 and 30 by the GCF of 10, which is 10.
The correct number of bags needed is 10 .
This results in:
2 blueberries are in each container of 20/10.
3 grapes per container (30/10)
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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.
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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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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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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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
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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145.678 rounded to the nearest hundred
Answer:
145.68
Step-by-step explanation:
When rounding 145.678 to the nearest hundred, we look at the digit in the tens column, which is 4. Since 4 is less than 5, we round down to the nearest hundred. Therefore, 145.678 rounded to the nearest hundred is 100.
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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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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its just math but I'm just stoopid
also it says the price of each ticket underneath the picture
Answer: It would be 8 tickets to break even.
Step-by-step explanation: 8×6.75=54
Using the given information, the drama club must sell 50 tickets to break even.
Calculating how many tickets must be sold to break evenFrom the question we are to determine the number of tickets that must be sold to at least break even
From the given information,
The drama club has $1262.50 from fund raising
and
They estimated that the entire production will cost $1600.00
Thus,
They need to raise $1600.00 - $1262.50 to break even
$1600.00 - $1262.50 = $337.5
Also from the given information,
Each ticket cost $6.75
Therefore,
The must sell $337.5/$6.75 tickets to break even
$337.5/$6.75 = 50
Hence, the must sell 50 tickets
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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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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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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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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
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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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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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
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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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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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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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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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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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.. (:
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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(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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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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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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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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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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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.