Therefore, Mr. Tompkins lives 240 miles from the airport.
Define acceleration.Acceleration is the rate of change of velocity of an object. It is a vector quantity that has both magnitude and direction. Mathematically, it is the derivative of velocity with respect to time. In simpler terms, it is the change in speed or direction of an object over time.
What is velocity?Velocity is a vector quantity that describes the rate of change of an object's position. It has both magnitude and direction. The magnitude of velocity is the speed of an object, which is the distance covered per unit of time.
We can start solving the problem by using the formula: distance = speed x time.
Let x be the distance from Mr. Tompkins' home to the airport in miles.
Therefore, the distance from the airport to the other city is (670 - x) miles
we know that the total traveling time is 4 hours
so we can set up two equations:
x/30 + (670 - x)/250 = 4
x + (670 - x)/8 = 120
we can solve for x
x = 240 miles
Therefore, Mr. Tompkins lives 240 miles from the airport.
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A study of the career paths of hotel general managers sent questionnaires to an SRS of 230 hotels belonging to major U.S. hotel chains. There were 109 responses. The average time these 109 general managers had spent with their current company was 12.08 years. (Take it as known that the standard deviation of time with the company for all general managers is 2.7 years.) (a) Find the margin of error for an 80% confidence interval to estimate the mean time a general manager had spent with their current company: years (b) Find the margin of error for a 99% confidence interval to estimate the mean time a general manager had spent with their current company: years (c) In general, increasing the confidence level the margin of error (width) of the confidence interval. (Enter: ''DECREASES'', ''DOES NOT CHANGE'' or ''INCREASES'', without the quotes.)
Answer:
a)
The margin of error is of 0.33 years.
b)
The margin of error is of 0.67 years.
c)
INCREASES
Step-by-step explanation:
In this question, we have that:
Sample of 109 means that [tex]n = 109[/tex]
The standard deviation of time with the company for all general managers is 2.7 years, which means that [tex]\sigma = 2.7[/tex]
Question a:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.8}{2} = 0.1[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.1= 0.9[/tex], so Z = 1.28.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
So
[tex]M = 1.28\frac{2.7}{\sqrt{109}} = 0.33[/tex]
The margin of error is of 0.33 years.
Question b:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.99}{2} = 0.005[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.005= 0.995[/tex], so Z = 2.575. So
[tex]M = 2.575\frac{2.7}{\sqrt{109}} = 0.67[/tex]
The margin of error is of 0.67 years.
(c) In general, increasing the confidence level the margin of error (width) of the confidence interval.
We have that:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
That is, M and z are direct proportional, and since z increases when the confidence level increases, the marign of error will increase. So the answer is INCREASES.
Need help :(( you can answer one or both of the questions
24. What is the volume of a rectangular prism with f = 4 1/2 cm, w= 3 1/2 cm, and h= 6 cm
A 902 cubic centimeters
B 942 cubic centimeters
C 95 cubic centimeters
D 952 cubic centimeters
A new school is ordering math text books. They are 3/4 of an inch thick. How many these books will fit into a book shelf that is 2 feet long.
Answer:
Step-by-step explanation:
Answer:
32
Step-by-step explanation:
24 inches are 2 feet
3/4 x 32 = 24
24 inches = 2 feet
what is the answer to [(x²+4x)-2]²
Answer:
[tex]x^{4}[/tex] + 8x³ + 12x² - 16x + 4
Step-by-step explanation:
Given
[(x² + 4x) - 2 ]² ← simplify contents of bracket
= (x² + 4x - 2)² = (x² + 4x - 2)(x² + 4x - 2)
Each term in the second factor is multiplied by each term in the first factor, that is
x²(x² + 4x - 2) + 4x(x² + 4x - 2) - 2(x² + 4x - 2) ← distribute parenthesis
= [tex]x^{4}[/tex] + 4x³ - 2x² + 4x³ + 16x² - 8x - 2x² - 8x + 4 ← collect like terms
= [tex]x^{4}[/tex] + 8x³ + 12x² - 16x + 4
URGENT: please help!!!!!!!!!
Answer:
In the form of y=mx+b:
y = -5/6x-5
Step-by-step explanation:
I'm not that good at explaining, but I'll try:
Slope intercept is y=mx+b, M is the slope of the line which is rise over run, the rise is -5 (distance traveled along y-axis) and the run is 6 (distance traveled along x-axis) found from two points: (-6, 0) and (0, -5). Using this data -5/6 can be plugged in for M, and b is the y variable at (0, _) in this case the y variable is -5. The final answer after plugging everything in is y=-5/6x-5, I hope this wasn't too confusing.
What is the image of (-5,-6)(−5,−6) after a reflection over the line y=-xy=−x?
The graph shows a parabola and its focus. Write the equation of the parabola in vertex form.
Parabola (0, 2)
Focus (0, -1)
9514 1404 393
Answer:
y = -1/12x² +2
Step-by-step explanation:
For vertex (h, k) and vertex-to-focus distance p, the vertex form equation is ...
[tex]y=\dfrac{1}{4p}(x-h)^2+k[/tex]
Here, the vertex-to-focus distance is -1-2 = -3 units. The vertex is (h, k) = (0, 2). So, the equation of the parabola is ...
[tex]\boxed{y=-\dfrac{1}{12}x^2+2}[/tex]
The UR Nuts Company sells Deluxe and Premium nut mixes, both of which contain only cashews, brazil nuts, almonds, and peanuts. The Premium nuts are much more expensive than the Deluxe nuts. A consumer group suspects that the two nut mixes are really the same. To find out, the group took separate random samples of 20 pounds of each nut mix and recorded the weights of each type of nut in the sample. Here are the data:
Type of mix
Type of nut Premium Deluxe
Cashew 6lb 5lb
Brazil nut 3lb 4lb
Almond 5lb 6lb
Peanut 6lb 5lb
Required:
Explain why we can't use a chi-square test to determine whether these two distributions differ significantly.
Answer:
No the conditions for this test are not met, as 20% of the data has expected value less than 5. And 37.5% data is equal to 5.
Step-by-step explanation:
The conditions for the chi square test independence are
1) the sample is a random sample
2) the variable under study is categorical
3) all expected value of the number of sample observations are greater or equal to 5.
A)The observations must be independent
B) for 2 categories the expected values must be at least 5
C) for the 3 categories the expected values must be at least 1 and no more than 20% may be smaller than 5
The observations given have equal chances of occurrences or are dependent on each other.
The sample collected has 20 % of data having expected values less than 5.
And 37.5% data is equal to 5.
We cannot use a chi-square test to determine whether these two distributions differ significantly because the expected value for some cells is less than 5.
What are the requirements for chi square test of independence?The variables under study must be categoricalSample is random sampleThe expected frequency count for each cell of the contingency table is at least 5.For the considered case, the sample is not large enough.
Although the sample was taken randomly and values are categorical, expected values are sometimes less than 5 for some cells of the contingency table.
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The first, second and fourth terms of
a proportion are 16, 24 and 54
respectively. Then the third term is:
Answer: 36
Step-by-step explanation:
This is a geometric progression. The formula for a geometric progression is given as:
= ar^n-1
where
a = first term = 16
r = common ratio = 24/16 = 1.5
n = 3
Therefore, the 3rd term will be:
= ar^n-1
= 16 × 1.5^3-1
= 16 × 1.5²
= 36
Therefore, the third term of the progression is 36.
Lucas hosted a New Year's dinner for his employees.
The total bill was $1,011.50. He left the server a 20%
tip. How much money did Lucas tip the server?
Round your answer to the nearest hundredth.
Answer:
$202.30
Step-by-step explanation:
You want to know the value of a 20% tip on a bill of $1011.50.
TipThe tip amount can be found by multiplying the bill amount by the tip percentage:
20% · $1011.50 = $202.30
Lucas tipped the server $202.30.
__
Additional comment
You know that 10% of the amount can be found by moving the decimal point one place: $101.15.
20% of the amount will be double this value: $202.30. You can do this math mentally.
In triangle RST, find the value of X. Round to the nearest tenth.
Answer:
238.9
Step-by-step explanation:
check the above attachment to verify the answer.
help pls fractionsss tyy
The amount of syrup she needs is 3/4 cups of syrup. Option A
What is a fraction?A fraction can be described as the part of a whole variable, element or number.
The several types of fractions are;
Mixed fractionsProper fractionsImproper fractionsComplex fractionsSimple fractionsAlso, proportion can be defined as a mathematical comparison between two numbers
From the information given, we have that;
6 cups of soap = 1 /4 cup of syrup
Then 18 cups of soap = x cups of syrup
cross multiply, we get;
6x = 18(1/4)
multiply the values
6x = 18/ 4
Divide both sides by the coefficient of x , we get;
x = 18/ 4 × 1/6
x = 3/ 4 cup of syrup
Hence, the value is 3/4
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A cylindrical grain bin has a radius of 9 feet and a height of 30 feet. How many cubic feet of grain can the bin hold?
Answer:1696.46
Step-by-step explanation:
V = π r 2 h
Johnny combined 7/4 cups of pancake mix and 3/4 of a cup of water to
make pancake batter. If he uses 1/4 of a cup of batter to make each
pancake, how many pancakes can Johnny make from his batter?
CAN U PLS PUT STEP BY STEP PLS?
Answer:
10
Step-by-step explanation:
in total there are 10/4 mixture so if one pancake is 1/4 10 pancakes can be made
Suppose that the relation S is defined as follows. S={(-6,9), (7, 2), (-6, -1)} Give the domain and range of S.
Answer:
[see below]
Step-by-step explanation:
The domain are all the x-values of the relation or function, while the range are all the y-values of the relation.
The x-values of the relation are -6 and 7.
The y-values of the relation are -1, 2, and 9.
Therefore:
Domain: {-6, 7}
Range: {-1, 2, 9}
Hope this helps you.
what is the slope for the equation?
Answer:
Slope: -1/2
Step-by-step explanation:
You can find the slope from this equation by adding 1/2 to each side of the equation since the way you find the slope of a line is by using: y = mx + b. The "m" must ALWAYS be on the right for it to be a valid slope equation, therefore, we have to use inverse operations for -1/2x to bring it to the right side.
Now, after we added 1/2x to each side, we get this equation:
-y = 1/2x + 3/4
We are not yet done since the y is accompanied by a negative 1, so, to isolate the variable, you use inverse operations once again and you get this equation:
y = -1/2x - 3/4
Therefore, the slope for this equation is -1/2.
Hope this helped! :D
HELP ME PLEASEEEEEEE
Answer:
It would be in this order:
Types of Quads:
Rectangle
Square
Rhombus
Trapezoid
Type of Triangles:
Equaliteral
Isoceles
Scalene
Step-by-step explanation:
Hope it helps
please hurry need done asap
Answer:
the answer is the third equation
hope it helps
Answer:
Last option is the correct answer
[tex] (\sqrt[3]{2x - 6})^{3} = (- \sqrt[3]{2x + 6})^{3}[/tex]
Step-by-step explanation:
[tex] \sqrt[3]{2x - 6} + \sqrt[3]{2x + 6} = 0 \\ \sqrt[3]{2x - 6} = - \sqrt[3]{2x + 6}\\ cubing \: both \: sides\\ (\sqrt[3]{2x - 6})^{3} = (- \sqrt[3]{2x + 6})^{3}[/tex]
Solve -2y>10
A - y<-5
B - y>-5
C - y<5
D - y>5
Answer:
y < -5
Step-by-step explanation:
The catch for this problem is remembering that when you divide by a negative number, your > or < will switch, so in this case, our > sign will become a < sign, otherwise its not too complicated!
-2y > 10
y < -5
Megan made a 4 lb batch of spaghetti sauce she put them in jars that can each hold 2/3 pound of sauce how many jars was she be able to feel
If the original price is $18.00and the markup is %70 what is the total
Answer:
$30.60
Step-by-step explanation:
Please write that as 70%.
The total is the original price plus 70% of that price, or
100% plus 70%, or
170%
Change 170% to 1.70 and multiply the original price by that:
Total price including markup: 1.70($18) = $30.60
Which buying method involves ordering a set amount of inventory at regular times? A. Last in first out B. Fixed order C. Just in time D. Economic order quantity Please select the best answer from the choices provided A B C D
Answer:
fixed order
Step-by-step explanation:
Answer:
Step-by-step explanation:
It’d be C
** If you cannot see, please zoom in and my apologies.
Cassie used a random sample from class A and class B to create these box plots.
Which box plot has a greater variability?
A. Box plot A because it has a greater range.
B. Box plot B because it has a greater range.
C. Box plot A because it has a greater median.
D. Box plot B because it has a greater median.
PLEASE, don’t answer if you don’t know the answer to this question. Whoever answers correctly will get Brainliest! :)
Answer:
A
Step-by-step explanation:
The greater the range the greater the variability of the numbers
Answer: A
Box plot A because it has a greater median.
Step-by-step explanation:
Hope this help!
Need help with this help me out
What is an angle that is supplementary to AEB?
Answer:
There are two. <CEB and <AED. You could put either one.
Step-by-step explanation:
There are two. <CEB and <AED. You could put either one.
The weight of a bag of Brand A cookies is labeled as 4 ounces on the bag. However, the actual weights of the bags vary by a small amount. According to the package
specifications, the weights are approximately normally distributed with a mean of 4.10
ounces and a standard deviation of 0.10 ounce. During a quality control check on the bag weights, a bag was found that weighted 3.95 ounces. how many standard deviations below the mean was the bag weight?
Answer:
2
Step-by-step explanation:
Mark me the brainliest please
The weight of the bag is 1.5 standard deviations down the mean weight.
What is normal distribution?
'Normal distribution is a continuous probability distribution wherein values lie in a symmetrical fashion mostly situated around the mean.'
According to the given problem,
Mean weight (μ) = 4.10 ounces
Standard deviation (σ) = 0.10
Target weight (x) = 3.95
We know,
Z = ( x - μ ) / σ
= (3.95 - 4.10) / 0.10
= -1.5
Hence, we can conclude, the target weight is 1.5 standard deviations down.
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Subtract: [tex]\frac{6}{2x^2+8x} -\frac{x}{4x^2+12-16} =\frac{6}{2x(x+4)} -\frac{x}{4(x+4)(x-1)} =\frac{6*2(x-1)}{2x(x+4)*2(x-1)} -\frac{x*x}{4(x+4)(x-1)*x}[/tex]
A:[tex]\frac{-2x^2+12x-12}{2(x+4)(x-1)}[/tex]
B:[tex]\frac{-x^2+6x-6}{2(x+4)(x-1)}[/tex]
C:[tex]\frac{-2x^2+12x-12}{4(x+4)(x-1)}[/tex]
D:[tex]\frac{-x^2+12x-12}{4x(x+4)(x-1)}[/tex]
Step-by-step explanation:
I think D
Please help as fast as possible
Answer:
Hello There!!
Step-by-step explanation:
6n=6×n
6×7=42
hope this helps,have a great day!!
~Pinky~
two subtracted from the product of 9 and a number is greater than or equal to 19 .
translate the sentence into an inequality
Answer: 9x - 2 >= 19.
Step-by-step explanation:
The sentence can be translated into the inequality 9x - 2 >= 19.
Here is a step-by-step breakdown:
"Two subtracted from the product of 9 and a number" can be written as 9x - 2.
"Is greater than or equal to 19" can be written as >= 19.
Putting these two pieces together, we get the inequality: 9x - 2 >= 19.