Within the case of 7320, the digit within the tens put is 3, which is less than 5. Hence, we circular down the units digit to 0, and the number gets to be 7300.
Within the handle of adjusting to one noteworthy figure, we ought to see the digit within the tens put (the moment digit from the cleared out) and decide whether to circular up or down. On the off chance that the digit within the tens put is 5 or more prominent, we circular up the units digit. In the event that it is less than 5, we circulate down the units digit.
This streamlines the number and keeps as it were the foremost noteworthy digit, which is 7. Adjusting to one noteworthy figure could be a valuable way to quickly estimate the greatness of a number without requiring to know the correct esteem.
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In ΔDEF, d = 5.2 inches, e = 6.8 inches and ∠F=166°. Find the length of f, to the nearest 10th of an inch.
The length of side f is 8.38 in the triangle DEF.
In a triangle, the sum of the angles is always 180 degrees.
∠D + ∠E + ∠F = 180 degrees
∠D + ∠E + 166 degrees = 180 degrees
∠D + ∠E = 14 degrees
Now, we can use the Law of Cosines to find the length of side f:
f² = d² + e² - 2de cos(∠F)
f² = (5.2 inches)² + (6.8 inches)² - 2(5.2 inches)(6.8 inches) cos(166 degrees)
f² = 70.29 inches²
Taking the square root of both sides, we get:
f = 8.38 inches
Therefore, the length of side f is 8.38 in the triangle DEF.
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Giving the mid-point as( -4,7 ) and end point 3,8 calculate the other end point justify your answer
The other end point include the following: (-11, 6).
How to determine the coordinates of the other endpoint?In order to determine the midpoint of a line segment with two (2) end points, we would add each end point together and then divide by two (2):
Midpoint = [(x₁ + x₂)/2, (y₁ + y₂)/2]
Next, we would determine the coordinate of MP with midpoint M at (3, 8) as follows;
-4 = (3 + x₂)/2
-8 = 3 + x₂
x₂ = -8 - 3
x₂ = -11.
For the other coordinate of P on line segment MP, we have:
7 = (8 + y₂)/2
14 = 8 + y₂
y₂ = 14 - 8
y₂= 6.
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At a particular restaurant, 52% of all customers order an appetizer and 32% of all customers order dessert. If 27% of all customers order both an appetizer and dessert, what is the probability a randomly selected customer orders an appetizer or dessert or both?
Write your answer as a decimal (not as a percentage).
The probability of randomly selected customers ordering both an appetizer and dessert is 57%.
We have,
The probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.
Given data as:
P(E₁) = 52%
P(E₂) = 32%
P(E₁ or E₂) = 27%.
Using the formula:
⇒ P(E₁ or E₂) = P(E₁) + P(E₂) - P(E₁ & E₂)
Substitute the values and solve for P(E₁ & E₂)
⇒ P(E₁ & E₂) = 52% + 32% - 27%
⇒ P(E₁ & E₂) = 57%
Therefore, the probability of randomly selected customers ordering both an appetizer and dessert is 57%.
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Beth prepared 24 kilograms of dough after working 3 hours. How much dough did Beth prepare if she worked for 6 hours? Solve using unit rates.
Beth would have made 48 kg of dough if she worked for 6 hours.
First, let's find the amount of dough Beth prepares in one hour:
Dough prepared in 3 hours = 24 kg
Dough prepared in 1 hour = 24 kg ÷ 3 = 8 kg/hour
So, Beth can prepare 8 kilograms of dough in one hour.
Now, we can use this unit rate to find the amount of dough Beth prepares in 6 hours:
Dough prepared in 1 hour = 8 kg
Dough prepared in 6 hours = 8 kg/hour × 6 hours = 48 kg
Therefore, if Beth worked for 6 hours, she would have prepared 48 kilograms of dough.
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How many solutions does this system of equations have? 3x+2y=6 -4x+5y=15
3. A sample of 100 households in a town reports that the average number of pets per household is 2.8 with a margin of error of ±0.9. If there are 2500 households in the town, what is the estimated number of pets in the town?
between __ and __
The estimated number of pets in the town is given as follows:
Between 4750 and 9250.
How to obtain the estimated number of pets?The estimated number of pets is obtained applying the proportions in the context of the problem.
The average number of pets per household is 2.8 with a margin of error of ±0.9, hence the bounds of the interval are given as follows:
2.8 - 0.9 = 1.9.2.8 + 0.9 = 3.7.Considering that there are 2500 households, the bounds of the total amounts are given as follows:
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Use the theoretical method to determine the probability of the following outcome and event. State any assumptions made. Tossing two coins and getting either one head or two heads Choose the correct answer below. A. Assuming that each coin is fair and is equally likely to land heads or tails, the probability is 2 x 2. B. Assuming that each coin is fair and is equally likely to land heads or tails, the probability is 4/3
C. Assuming that each coin is fair and is equally likely to land heads or tails, the probability is 1/2
D. Assuming that each coin is fair and is equally likely to land heads or tails, the probability is 3/4
C. Assuming that each coin is fair and is equally likely to land heads or tails, the probability is 1/2.
When tossing two coins, there are four possible outcomes: HH (two heads), HT (one head and one tail), TH (one tail and one head), and TT (two tails).
Since we are interested in the probability of getting either one head or two heads, we need to add the probabilities of the first three outcomes: HH, HT, and TH.
Assuming that each coin is fair and is equally likely to land heads or tails, the probability of getting a head on one coin is 1/2 and the probability of getting a tail is also 1/2. Therefore, the probability of getting either one head or two heads is:
P(one head or two heads) = P(HH) + P(HT) + P(TH)
P(one head or two heads) = (1/2)*(1/2) + (1/2)*(1/2) + (1/2)*(1/2)
P(one head or two heads) = 1/2
Therefore, the answer is C. The probability of getting either one head or two heads when tossing two coins and assuming that each coin is fair and is equally likely to land heads or tails is 1/2.
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Triangles H J K and L M N are congruent. Triangle H J K is rotated about point H to form triangle L N M. Triangle L M N is higher than triangle H J K.
How can a translation and a rotation be used to map ΔHJK to ΔLMN?
Translate H to L and rotate about H until HK lies on the line containing LM.
Translate K to M and rotate about K until HK lies on the line containing LM.
Translate K to N and rotate about K until HK lies on the line containing LN.
Translate H to N and rotate about H until HK lies on the line containing LN.
For a translation and a rotation map of ΔHJK to ΔLMN is given by translating K to N and rotating about K until HK lies on the line containing LN. Option C is correct.
When a form travels around a fixed point or over the mirror line without altering, it is said to be translating.
When a form rotates around a fixed point, it is said to be rotating.
In conclusion, The translation and rotation of the map ΔHJK to ΔLMN Translate K to N and rotate about K until HK lies on the line containing LN.
Hence, Translate K to N and rotate about K until HK lies on the line containing LN is correct.
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Assume that adults have 10 scores that are normally distributed with a mean of 102.7 and a standard deviation of 23.5. Find the probability that a randomly selected adult has an IQ greater than 144.4
There is approximately a 3.84% chance that a randomly selected adult has an IQ greater than 144.4.
To find the probability that a randomly selected adult has an IQ greater than 144.4, assuming their scores are normally distributed with a mean of 102.7 and a standard deviation of 23.5, we will use the z-score formula.
First, calculate the z-score:
z = (X - μ) / σ
where X is the IQ score (144.4), μ is the mean (102.7), and σ is the standard deviation (23.5).
z = (144.4 - 102.7) / 23.5
z ≈ 1.77
Now, use a z-table to find the probability corresponding to this z-score. The z-table value for a z-score of 1.77 is approximately 0.9616. Since we want the probability of an IQ greater than 144.4, we will find the area to the right of this z-score.
Probability = 1 - 0.9616 = 0.0384
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california college students who drink according to the centers for disease control and prevention, 60% of all american adults ages 18 to 24 currently drink alcohol. is the proportion of california college students who currently drink alcohol different from the proportion nationwide? a survey of 450 california college students indicates that 66% currently drink alcohol. the null hypothesis is [ select ] . the alternative hypothesis is [ select ] . p in the hypotheses represents [ select ] the standard error is the z-score is [ select ] the p-value is [ select ] . the conclusion is [ select ] flag question: question 2 question 24 pts for the previous example, which statements are accurate conclusions? group of answer choices the proportion of drinkers in the population of ca college students is not 0.60. there is a statistically significant difference between the proportion of drinkers in the american adult population (0.60) and the proportion of drinkers in the population of ca college students. a larger proportion of ca college students drink alcohol compared to the adults nationwide. when we compare the american adult population to the population of ca college students, there is a 0.06 difference in the proportion of drinkers.
California college students who drink according to the centers for disease control and prevention, 60% of all american adults ages 18 to 24 currently drink alcohol. The proportion of drinkers in the population of CA college students is not 0.60.
We can infer the following from the provided information:
The proportion of college students in California who presently drink alcohol is the same as the proportion nationwide (p = 0.60), rejecting the null hypothesis (H0).
Alternative hypothesis (Ha): California college students are more likely to use alcohol than college students nationwide (p 0.60).
The population proportion is represented by the letter "p" in the hypotheses.
We need the sample size and the sample proportion to calculate the standard error and the z-score. According to the poll of 450 college students in California, 66% of them currently consume alcohol, yielding a sample proportion of 0.66.
SE = √(0.66*(1-0.66)/450) ≈ 0.023
z = (0.66 - 0.60) / 0.023 ≈ 2.61
By comparing the p-value to a preset significance level (such as 0.05), the conclusion is arrived at. We reject the null hypothesis if the p-value is less than the significance level. If not, we are unable to rule out the null hypothesis.
The appropriate inferences from the information are:
The percentage of drinkers among college students in California is not 0.60.
The percentage of drinkers in the adult American population (0.60) and the percentage of drinkers among college students in California differ statistically significantly.
Thus, this can be concluded regarding the given scenario.
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1) Construct an equilateral triangle showing the correct steps, marks, and use the compass.
2) Construct an equilateral triangle inscribed in a circle and show your marks and steps
using the compass.
3)Construct a square inscribed in a circle and show your marks and steps using the
compass.
This prompt is about constructing geometric shapes using a Mathematical Set such as rulers and compass.
How do you construct the shapes required above?1) First, note that an equilateral triangle is one whose sides are all equal. So, start by drawing a line segment with a ruler. Call it Side AB.
Then you take your compass, place the ponted end on point A, then extend it until it is at point B exactly. Make sure this does not change.
Now swing the compass such that it creates an arc some where above the line AB towads the middle of the line where you visualize the third Pont to be.
Without changing the extension of the compass, place the ponted end on point B and repeat. Now you have two arcs intersecting above the line AB.
Now tak eyour ruler and connect the point of intersection above with Points A and B below. Now you have an Equilateral Triangle
2) Equilateral Triangle inscribed in a Circle
Using your compass, draw a circle. Note you must keep the angle measurement the compass constant.Locate a point along the circumference of a circle.Next, place the pointed tip of the compass on the point on the circumference and make an arc on the circle. Do this until you have 6 arcs on the circle. By the time you get to the last arc, it should coincide with the first pont you marked.The points where the arcs cut the circle is called the points of intersection.Now you have six points but to make the equilateral triangle you need only threestarting from any of the points, mark one point and skip the next.then connect the three ponts usign a ruler. How you have an equilateral Triangle inscribed in a Circle
3) Square in a circle
Start with a circle with a center M.
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Find the sales tax. Then find the total cost for each item.
1. A suit costs $200. The sales tax is 7%
2. A bike costs $150. The sales tax is 5%
3. A television sells for $179. The sales tax is 6%
4. A CD player costs $113.40 The sales tax is 5%
5. A notebook sells for $5.99 The sales tax isn7%
Critical Thinking
Jan bought a game for $50. The sales tax was 5%. Bob bought a game for $48. The sales tax was 8%. Who paid the greater total cost? How much more?
Find the discount. Then find the sale price for each item.
1. A shirt cost $32. It is on sale at 30% off.
2. A pair of jeans sells for $32. The jeans are on sale at 20% off.
3. A VCR costs $104. It is on sale at 15% off.
4. A CD costs $14.95. It is on sale at 12% off.
5. Videos are priced at $19.95. They are on sale at 10% off.
Critical Thinking
Solve each problem show your work.
1. A watch cost $100. It is on sale at 20% off. After still going unsold, it goes on sale again at 10% off the sale price. What is the final sale price?
2. A watch costs $100. It is on sale at 30% off. What is the sale price? Is the sale price the same as the final sale price in question 1? Why or why not?
The sales tax for the suit is $14.00
The total cost for the suit is $214.00
How to solveThe suit will incur an additional charge of $14.00 due to a tax rate of 7% on the original price of $200, making its total expense amount to $214.00.
As for the bike, a sales tax rate of 5% on $150 would cost around $7.50 and sum up to $157.50 for its ultimate fee.
For the television set, a markup of 6% over its initial cost of $179 produces a total increase in value of $10.74 giving it a final asking amount of $189.74.
The CD player's extra cost comes out at approximately $5.67 charged from a 5% sales tax of its base worth: $113.40, leading to complete pricing attached to it totaling $119.07.
In comparison with the other products aforementioned, the notebook is relatively cheaper.
With a modest basic cost of $5.99, a tax addition of only $0.42 (at a sales tax rate also of 7%) is tacked onto that. The final product pricing amounts to just $6.41.
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The graphs of f(x) = −10x − 1 and g(x) =2^x
are shown. Create a new function h(x) by reflecting f(x) over the x-axis. How many times do the graphs of h(x) and g(x) intersect?
Answer:
2
Step-by-step explanation:
i just took the test and that was the correct answer
hii plsssss answer questionnnnnnn :)
Answer:
75π
Step-by-step explanation:
Length of an arc formula:
Arc Length = 2πr(θ/360)Where:
r = radiusθ = central angleHere we are given the following:
Radius(r) = 90mCentral Angle(θ) = 150°By plugging these values into the formula we acquire(Note that the answer must be in terms of π, meaning that we do not simplify it and leave it in the final answer):
Arc Length = 2π(90)(150/360)Arc Length = 2π(90)(5/12)Arc Length = 2π(37.5)Arc Length = 75πThe length of the arc is 75πm
if 5 students chosebasketball, 2 students chose tennis, 3 students chose baseball, 7 students chose soccer, and 8 students chose football, what percentage of the students selected football over tennis or baseball.
Answer: 12%
Step-by-step explanation:
2/25 is .08
3/24 is .12
Together that’s .20 so 20%
8/25 is 32
So 32-20=12%
you pick 4 cards from a deck replacing the card each time before picking the next card. what is the probability that all 4 cards are jacks?
Total number of cards is always 52 which has 4 jacks. In the given question we need to use the concept of probability.
The following steps are need to be followed:
1. First, let's identify some key information:
- A standard deck has 52 cards, with 4 jacks (one of each suit).
- You're drawing a card and then replacing it, which means each draw is independent and the probability remains constant.
2. Now, let's calculate the probability of drawing a jack on each draw:
- P(Jack) = 4 jacks / 52 total cards = 1/13
3. Since you want to find the probability of drawing a jack 4 times in a row, we'll multiply the probability of drawing a jack on each draw:
- P(All Jacks) = P(Jack) × P(Jack) × P(Jack) × P(Jack) = (1/13) × (1/13) × (1/13) × (1/13)
4. Simplify the probability:
- P(All Jacks) = 1/28561
So the probability of drawing all 4 jacks when you pick 4 cards from a deck, replacing the card each time before picking the next card, is 1/28,561.
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Find Z. Can someone help me find the answer to the third question aka question c?
The resulting value for the variable z from the figure is 25.
The secant secant theorem of a circleAccording to the secant segment theorem, if two secant segments cross outside of a circle, the product of one secant segment and its exterior portion is equal to the product of the other secant segment and its external portion.
Mathematically for the given figure:
3 * z = 5(10+5)
3z = 5(15)
3z = 75
Divide both side of the expression by 3
3z/3 = 75/3
z = 25
Hence the value of z from the given diagram is 25.
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A computer company wants to determine the proportion of defective computer chips from a day’s production. A quality control specialist takes a random sample of 100 chips from the day’s production and determines that there are 12 defective chips. Assuming all conditions are met, he constructs a 95% confidence interval for the true proportion of defective chips from a day’s production. What are the calculations for this interval?
12 plus-or-minus 1.65 StartRoot StartFraction 12 (1 minus 12) Over 100 EndFraction EndRoot
12 plus-or-minus 1.96 StartRoot StartFraction 12 (1 minus 12) Over 100 EndFraction EndRoot
0.12 plus-or-minus 1.65 StartRoot StartFraction 0.12 (1 minus 0.12) Over 100 EndFraction EndRoot
0.12 plus-or-minus 1.96 StartRoot StartFraction 0.12 (1 minus 0.12) Over 100 EndFraction EndRoot
answer d
Maya buys candy that costs $6 per pound. She will spend less than $42 on candy. What are the possible numbers of pounds she will buy?
Use p for the number of pounds Maya will buy.
Write your answer as an inequality solved for p.
The possible numbers of pounds she will buy is p < 7
Inequality can be defined as the relation which makes a non-equal comparison between two given functions.
We are given that Maya buys candy that costs $6 per pound. She will spend less than $42 on candy.
We need to find the possible amounts she will spend on candy
We will Use c for the amount (in dollars) Maya will spend on candy.
Therefore, the inequality solved for p becomes as
6p < $42
p < $42/6
p < 7
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The sum of all the positive integers from 5–√ to 62−−√ is
The sum of all the positive integers from √5 to √62 in an arithmetic series is 35.
To find the sum of all the positive integers from √5 to √62, we first need to determine the two integers closest to each square root and then find the sum of the arithmetic series between them.
The integer closest to √5 is 2, since 2² = 4 < 5 and 3² = 9 > 5. Similarly, the integer closest to √62 is 8, since 8² = 64 > 62 and 7² = 49 < 62.
So, we need to find the sum of the integers from 2 to 8. To do this, we can use the formula for the sum of an arithmetic series:
sum = (n/2)(first term + last term)
Here, n is the number of terms in the series, which is 8 - 2 + 1 = 7. The first term is 2, and the last term is 8.
So, the sum of all the positive integers from √5 to √62 is:
sum = (7/2)(2 + 8) = 35
Therefore, the sum of all the positive integers from √5 to √62 is 35.
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The question is -
The sum of all the positive integers from √5 to √62 is?
The slope of the line below is 0.8. Write the equation of the line in point-slope
form, using the coordinates of the labeled point. Do not use parenthesis on
the y side.
-5
5
(-2,-3)
-5
5
X
An equation of the line in point-slope form, using the coordinates of the labeled point is y + 3 = 0.8(x + 2).
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.At data point (-2, -3) and a slope of 0.8, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - (-3) = 0.8(x - (-2))
y + 3 = 0.8(x + 2)
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line graphs use bars of varying height or length to compare several pieces of information. group of answer choices true false
Line graphs do not use bars to represent data. Instead, they use lines to show the trend or pattern of the data over time or some other continuous variable so the given sentence is false.
The statement is false. Line graphs use points connected by lines to display changes in data over time or other continuous independent variable. The line represents the trend or pattern of the data and the points indicate specific data points. The height or length of bars is typically used in bar graphs or column charts to compare data values among different categories or groups.
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The triangle shown below is a right triangle with the right angle marked.
Which equation correctly expresses the Pythagorean Theorem for this triangle?
A)p²+q²=r²
B)r²+q²=p²
C)(p+q)²=r²
D)p²+r²=q²
Answer:
The Correct answer is A
Step-by-step explanation:
b) because r²=q²+p²,p²=r²-q² not
r²+q²
c) (p+q)²=r²
is not correct because
(p+q)²=(p+q)(p+q)
d) p²+r²=q² wrong
because
q²=r²-p²
You have a square pyramid sitting on top of a cube. The slant height of the pyramid is 5 and the sides of the cube are 3. What is the volume of both of the shapes?
The total volume of figure which has cube and pyramid is 33 cubic units.
The volume of a square pyramid is given by the formula V = (1/3)Bh, where B is the area of the base and h is the height of the pyramid.
Let's call the side length of the square base of the pyramid s.
(1/2)s² + h² = 5²
s² + 4h² = 25
Since the sides of the cube are 3, the side length of the square base of the pyramid is also 3.
9 + 4h² = 25
h = 2
So the height of the pyramid is 2.
Volume of pyramid = (1/3)(3^2)(2) = 6
The volume of a cube is given by the formula V = s³, where s is the length of a side.
Since the sides of the cube are 3, the volume of the cube is:
Volume of the cube = 3³ = 27
Therefore, the total volume of the pyramid and the cube is:
Total = 6 + 27
= 33
Hence, the total volume of figure which has cube and pyramid is 33 cubic units.
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Some storage boxes are stacked on a platform. The height of the stack, measured from the ground, is given by the expression 12.3b + 4.7 in inches,
where b is the number of
boxes?
a. Find the height of a stack of 5 boxes.
b. A stack made of all the boxes in the set is 103.1 inches tall, including the platform
How many boxes are in the set?
C.Kiran Looks at the expression and says, “4.7 much be the height of a single box” Do you agree with Kiran? Explaining your reasoning.
The shortest height at which the two stacks will be the same is 80 inches. There will be 5 boxes of 16 inches each and 4 boxes of 20 inches required.
Here, we have,
We have boxes that are 16 inches tall, are being stacked next to boxes that are 20 in inches tall.
We have to determine -
What is the shortest height at which the two stacks will be the same.
How many boxes will be in each stack.
You have 10 boxes of 2 inch each and a space of 16 inches to store them. Investigate whether or not the boxes will fit in this much space.
The total space needed for 10 such boxes will be = 2 x 10 = 20 inches. Hence, 16 inches of space is not enough to store them.
According to the question, we have -
Height of Box 1 = 16 inches.
Height of Box 2 = 20 inches.
Assume that it would take x Boxes of 16 inches and y boxes of 20 inches to reach the same height 'h'. Since, the height of both stacks is same, therefore -
16x = 20y
16x - 20y = 0
4x - 5y = 0
Plot this line on the graph [Refer to image attached].
Now, the boxes can only be used as a complete one box. This means that you cannot use half, quarter box to reach the same stack height. The nearest solution to this is the coordinate point P(5, 4).
Now -
h = 16x = 16 x 5 = 80 inches.
Hence, the shortest height at which the two stacks will be the same is 80 inches. There will be 5 boxes of 16 inches each and 4 boxes of 20 inches required.
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What fraction in this list is more than 3/5? 20/100, 6/10, 1/2, 2/12 or 2/3?
Answer: 2/3
Step-by-step explanation:
We will turn all of these fractions into decimals by dividing to compare them easier.
3/5 ➜ 0.6
20/100 ➜ 0.2
6/10 ➜ 0.6
1/2 ➜ 0.5
2/12 ➜ 0.16666
2/3 ➜ 0.6666
0.6666 > 0.6, so 2/3 > 3/5
This means our answer is 2/3
1400-615test the claim that the proportion of people who own cats is smaller than 90% at the 0.005 significance level. the alternative hypothesis would be:
The alternative hypothesis would be: The proportion of people who own cats is smaller than 90%.
The null hypothesis for this test would be: The proportion of people who own cats is equal to or greater than 90%.
To conduct the hypothesis test, we would need to collect a random sample of 1400 individuals and determine how many of them own cats. Based on this information, we could calculate the sample proportion of cat owners and use this to test the claim that the population proportion is smaller than 90%.
We would use a one-tailed hypothesis test with a significance level of 0.005. If the p-value for our test is less than 0.005, we would reject the null hypothesis and conclude that there is sufficient evidence to support the alternative hypothesis that the proportion of people who own cats is smaller than 90%.
Hi! I'd be happy to help you with this question. You want to test the claim that the proportion of people who own cats is smaller than 90% at the 0.005 significance level.
To do this, we will set up our null and alternative hypotheses as follows:
Null Hypothesis (H0): The proportion of people who own cats is equal to 90% (p = 0.90)
Alternative Hypothesis (H1): The proportion of people who own cats is smaller than 90% (p < 0.90)
Here's a step-by-step explanation of how to test this claim:
1. Determine the sample size (n) and the number of cat owners in the sample (x): In this case, n = 1400, and x = 615.
2. Calculate the sample proportion (p-hat): p-hat = x/n = 615/1400 ≈ 0.439.
3. Determine the significance level (alpha): In this case, alpha = 0.005.
4. Calculate the standard error (SE) of the sample proportion: SE = sqrt[p*(1-p)/n] = sqrt[0.9*(1-0.9)/1400] ≈ 0.008.
5. Calculate the z-score: z = (p-hat - p)/SE = (0.439 - 0.9)/0.008 ≈ -57.63.
6. Find the critical z-value for a one-tailed test at the 0.005 significance level: z-critical = -2.576 (from a standard normal distribution table).
7. Compare the calculated z-score with the critical z-value: Since the calculated z-score (-57.63) is less than the critical z-value (-2.576), we reject the null hypothesis.
In conclusion, based on this analysis, we have enough evidence to support the alternative hypothesis that the proportion of people who own cats is smaller than 90% at the 0.005 significance level.
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T/F : If the equation Ax=0 has a nontrivial solution, then A has fewer than n pivot points
True.
If the equation Ax=0 has a nontrivial solution, then the columns of A are linearly dependent.
If the equation Ax=0 has a nontrivial solution, then the columns of A are linearly dependent. This means that there exist constants c1, c2, ..., cn, not all zero, such that the vector
v = c1*a1 + c2*a2 + ... + cn*an
is the zero vector, where a1, a2, ..., an are the columns of A.
This implies that A has a non-pivot column, since we can write the vector v as a linear combination of the other columns. Therefore, A has fewer than n pivot columns, or equivalently, fewer than n pivot points.
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A botanist wishes to estimate the typical number of seeds for a certain fruit. She samples 70 specimens and counts the number of seeds in each. Use her sample results (mean = 18.7, standard deviation = 6.2) to find the 90% confidence interval for the number of seeds for the species. Enter your answer as an open-interval (i.e., parentheses) accurate to 3 decimal places. 90% C.I. = )
The 90% confidence interval for the number of seeds in the fruit is (17.480, 19.920). To find the 90% confidence interval for the number of seeds in the fruit, we will follow these steps:
1. Identify the sample size (n), sample mean (x), and sample standard deviation (s): n = 70, x= 18.7, s = 6.2.
2. Since we want a 90% confidence interval, we will use a z-score of 1.645 (from a standard normal distribution table or calculator).
3. Calculate the standard error (SE) using the formula: SE = s/√n = 6.2/√70 = 0.741.
4. Calculate the margin of error (ME) using the formula: ME = z * SE = 1.645 * 0.741 =1.220.
5. Determine the confidence interval by adding and subtracting the margin of error from the sample mean: (x - ME, x+ ME) = (18.7 - 1.220, 18.7 + 1.220) = (17.480, 19.920).
Therefore, the 90% confidence interval for the number of seeds in the fruit is (17.480, 19.920).
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Help please!!! Anything helps
Answer:
Step-by-step explanation: