The sample of the speeds of 20 cars and at a 0.05 confidence level, we
have;
(a) There is not enough convincing evidence to suggest that the true mean speed of all cars travelling on Elm Street is more than 25 mph
(b) Type II error
What are the process to test the hypothesis?(a) Based on the given data, using MS Excel, we have;
The sample size, n = 20
The mean, [tex]\overline x[/tex] = 25.86
The standard deviation of the sample, s = 2.284
The null hypothesis, H₀; [tex]\overline x[/tex] = 25 mph
Alternative hypothesis, Hₐ; [tex]\overline x[/tex] > 25 mph
Given that the sample size is less than 30, the t-test is used, and the t-score is found as follows;
[tex]t= \mathbf{\dfrac{\bar{x}-\mu }{\dfrac{s}{\sqrt{n}}}}[/tex]
Which gives;
[tex]t=\dfrac{25.86-25 }{\dfrac{2.284}{\sqrt{20}}} \approx \mathbf{1.684}[/tex]
Using a graphing calculator, we have;
The probability ≈ 0.054
The critical-t ≈ 1.729
Given that the probability is larger than the significance level, we fail to
reject the null hypothesis.
There is not enough convincing statistical evidence to conclude that the
true mean of all cars travelling on Elm Street is more than 25 mph.
(b) The type of error is Type II error, given that there is a possibility that
the null hypothesis is failed to be rejected when it is actually false.
Given that the sample size is less than 30, it may be insufficient for the
Central Limit Theorem to be in effect.
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6. select all the values for d that make the equation 9 = 18 / d true
Answer: 2
Step-by-step explanation:
The Thompson family was moving and hired Town Movers to move them for a fee of $30 plus $15 per hour. City Movers called and offered a fee of $72 plus $8 an hour, which they thought might be a better deal. The family made a graph of the two offers. When would City Movers be the better deal?
If the Thompsons need the movers for more than 6 hours, City movers would be the better deal. Therefore, option D is the correct answer.
What is the graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them. The length of the lines and position of the points do not matter.
Given that, the Thompson family was moving and hired Town Movers to move them for a fee of $30 plus $15 per hour.
Let the number of hours be x.
Now, 30+15x
Movers called and offered a fee of $72 plus $8 an hour, which they thought might be a better deal
72+8x
From the graph, both the movers have same charge at 6th hour and City movers charge is decreasing then compare to Town Movers.
Therefore, option D is the correct answer.
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What is 1 3/8 equals to
Answer:
1.375 in decimal form
Step-by-step explanation:
When I see an equation with parentheses, I need to use the Distributive Property.
O True
O False
Maki paid a $14 basic fee plus $25 a day to rent a car. Evaluate the expression 14 + 5 X 25 to find out how much it cost her to rent the car for 5 days
Answer:
25(5)+14=139
$139
Step-by-step explanation:
Ava's math certificate is 18 centimeters tall and 26 centimeters wide. Ava wants to put the certificate in a fancy frame that costs $1.53 per centimeter. How much will it cost to frame Ava's math certificate?
Janelle plans to paint her bedroom, which is the shape of a
rectangular prism. Its length is 10 feet, its width is 12 feet, and the
ceilings are 9 feet tall. She does not need to paint the floor or ceiling. How many square feet of wall space will she be covering?
Answer:
19 feet tall
Step-by-step explanation:
Kaitlyn solved the equation for x using the following calculations. Negative 5. 4 x = 12. 2. Minus 5. 4. X = 6. 8. What error, if any, did she make? She should have added 5. 4 to each side. She should have added the inverse of 5. 4 to each side. She made a computational error when she subtracted 5. 4 from 12. 2. She should have added 12. 2 to each side.
The value of x is 17.6. She should have added 5.4 on both sides to get the correct value of x. Then the correct option is A.
What is the linear system?A Linear system is a system in which the degree of the variable in the equation is one. It may contain one, two, or more than two variables.
Kaitlyn solved the equation for x using the following calculations.
[tex]\rm -5.4 + x =12.2[/tex]
and she did the calculation will be
[tex]\rm -5.4x = 6.8[/tex]
The mistake she did in this equation is the plus sign is removed between the -5.4 and x. And she subtracted 5.4 from 12.2.
The correct solution of the equation is to add both sides 5.4. Then we have
[tex]\begin{aligned} \rm -5.4 + x+5.4 &=12.2+5.4\\\\\rm x &= 17.6\end{aligned}[/tex]
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Each problem below gives the endpoints of a segment. Find the coordinates of the midpoint of the segment.
a. (-3,11) and (5,6)
b. (-4,-1) and (8,9)
Answer: A
Step-by-step explanation:
The ratio of the number of pears to the number of oranges in a basket
is 5:3. The rest of the fruits are apples. There are 54 more pears than
oranges and 3 more apples than oranges.
(a) How many pears are there in the basket?
(b) What percentage of the fruits are apples?
Answer:
(a) 135
(b) 28%
Step-by-step explanation:
We can write equations relating pears to oranges, solve them, and then find the number of apples. Let p, o, and 'a' represent the numbers of pears, apples, and oranges.
p/o = 5/3 . . . . . the ratio of pears to oranges is 5:3
p -o = 54 . . . . . there are 54 more pears than oranges
a -o = 3 . . . . . . there are 3 more apples than oranges
__
a)Multiply the first equation by 3/5o to get ...
3/5p = o
Substitute that into the second equation:
p -(3/5)p = 54
2/5p = 54 . . . . . . simplify
p = 54(5/2) = 135 . . . . multiply by 5/2 to get the number of pears
There are 135 pears in the basket.
__
b)a = 3 +o = 3 +3/5p = 3 +3/5(135) = 3 +81 . . . . solve for the number of apples
a = 84
The percentage of fruits that are apples is ...
apples/total = 84/(135 +81 +84) = 84/300 = 28/100 = 28%
28% of the fruits are apples
A convex pentagon has interior angles that measure 60, 80, 120, and 140. What is the measure of the fifth interior angle?
A convex pentagon has interior angles that measure 60, 80, 120, and 140. What is the measure of the fifth interior angle?
Explanation -:Given -
First interior angle = 60°Second interior angle = 80°Third interior angle = 120°Fourth interior angle = 140°To Find -
Fifth interior angleSolution -
Let us assume fifth interior angle as x
We know,
Sum of interior angles of a pentagon is 540°
60° + 80° + 120° + 140° + x° = 540°
→ 400° + x° = 540°
→ x° = 540° - 400°
→ x = 140°
Fifth interior angle of a pentagon = 140°
[tex] \rule{185pt}{7pt}[/tex]
What is the y-intercept in y= -2x + 5
Answer: 5
Step-by-step explanation:
the y intercept is the "b" value in the form y = mx + b
(9w^2+7w-2)+(8w^2-8w-7)-(-5w^2+5w+4)
Step-by-step explanation:
Our expression;
[tex](9w^2+7w-2)+(8w^2-8w-7)-(-5w^2+5w+4)[/tex]
Also represented as after using the distributive property;
[tex]9w^2+7w-2+8w^2-8w-7+5w^2-5w-4[/tex]
Simplify;
[tex]9w^2+7w-2+8w^2-8w-7+5w^2-5w-4[/tex]
[tex]22w^2+7w-2-8w-7-5w-4[/tex]
[tex]22w^2-6w-2-7-4[/tex]
[tex]22w^2-6w-13[/tex]
Answer:
22w² - 6w - 13
Step-by-step explanation:
Given expression: (9w² + 7w - 2) + (8w² - 8w - 7) - (-5w² + 5w + 4)
Step-1: Open the parenthesis
⇒ (9w² + 7w - 2) + (8w² - 8w - 7) - (-5w² + 5w + 4)⇒ 9w² + 7w - 2 + 8w² - 8w - 7 + 5w² - 5w - 4Step-2: Combine like terms
⇒ 9w² + 7w - 2 + 8w² - 8w - 7 + 5w² - 5w - 4⇒ w²(9 + 8 + 5) + w(7 - 8 - 5) + (-2 - 7 - 4)Step-3: Simplify the expression
⇒ w²(9 + 8 + 5) + w(7 - 8 - 5) + (-2 - 7 - 4)⇒ w²(22) + w(-6) + (-13)⇒ 22w² - 6w - 13Therefore, the simplified expression is 22w² - 6w - 13.
the squar of any rational number is non negative
[tex]\mathbb{FINAL\:ANSWER:}[/tex]
[tex]\huge\boxed{\sf{True}}[/tex]
[tex]\mathbb{SOLUTION\:WITH\:STEPS:}[/tex]
Hi! Hope you are having a nice day!
Yes, the square of a rational number is always positive.
We know that a negative times a negative equals a positive only.
Well, a negative squared also equals a positive.
For example, (-4)² is equal to 16.
Because
(-4)×(-4)=16
A negative times a negative is a positiveHope you could understand everything.
#CarryOnLearning
The table shows the approximate height of an object x seconds after the object was dropped. the function h(x) = –16x2 100 models the data in the table. a 2-column table with 5 rows. the first column is labeled time (seconds) with entries 0, 0.5, 1, 1.5, 2. the second column is labeled height (feet) with entries 100, 96, 84, 65, 37. for which value of x would this model make the least sense to use? –2.75 0.25 1.75 2.25
The value of x for which this model will make the least sense to use is at x=-2.75 seconds.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
The function that is given to us is h(x) = –16x²+100 where x is the time in seconds.
Now, use the function to know the height of the object, therefore, the height of the object can be written as,
Time, t₁=0
Now, the height can be written as,
[tex]h(x) = -16x^2+100\\\\h(0)=0+100\\\\h_1=100[/tex]
Thus, the height of the object when the time is 0 seconds is 100.
Time, t₂=0.5
Now, the height can be written as,
[tex]h(x) = -16x^2+100\\\\h(0.5)=-4+100\\\\h_2=96[/tex]
Thus, the height of the object when the time is 0.5 seconds is 96.
Time, t₃=1
Now, the height can be written as,
[tex]h(x) = -16x^2+100\\\\h(1)=-16+100\\\\h_1=84[/tex]
Thus, the height of the object when the time is 1 second is 84.
Time, t₄=1.5
Now, the height can be written as,
[tex]h(x) = -16x^2+100\\\\h(1.5)=-36+100\\\\h_4=64[/tex]
Thus, the height of the object when the time is 1.5 seconds is 64.
Time, t₅=2
Now, the height can be written as,
[tex]h(x) = -16x^2+100\\\\h(2)=0+100\\\\h_5=36[/tex]
Thus, the height of the object when the time is 2 seconds is 36.
Now as we can see that the error in the height of the object can be a maximum of 1, therefore, for different values of x, the change in height will be,
Time, t₆= -2.75
Now, the height can be written as,
[tex]h(x) = -16x^2+100\\\\h(-2.75)=-121+100\\\\h_6= -21[/tex]
Thus, the height of the object when the time is -2.75 seconds is -21.
Hence, the value of x for which this model will make the least sense to use is at x=-2.75 seconds.
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Answer:
-2.75
Step-by-step explanation:
A
11. What is the value of x in the figure shown? (15x) 15 °
Answer:
x = 11
Step-by-step explanation:
15x + 15x + 15 + 15 = 360 (sum of all sides equal to 360)
30x + 30 = 360
30x = 360 - 30
30x = 330
30x/30 = 330/30
x = 11
Why is math literacy important?
Answer:
Math literacy (also known as numeracy) means having the ability to problem-solve, reason, and analyze information.
Step-by-step explanation:
if a town with a population of 500 doubles in size ever 9 years, what will the population be 36 years from now?
The population of the town in 36 years would be 8000.
What would be the population of the town in 36 years?The formula that can be used to determine the town's population is:
FV = P (1 + r)^n
Where:
FV = Future value P = Present value R = rate of growth = 100%N = number of years = 36/9 = 4500 x 2^4 = 8000
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Write this in an equation: 5 less than a number is twice the sum of that number and 9
Answer:
n-5=2n+9
Step-by-step explanation:
Help help help help help help help help
Answer:
Roughly 10%
Step-by-step explanation:
We just need to reduce this fraction: 13/119
It is in the lowest terms already, so now we need to make this fraction a percent.
13/119 = 10.12
10.12 ≈ 10%
4. Akeego is making a ribbon shirt. She has 60 cm of ribbon that she will cut into 5 pieces with 2 different lengths: 2 pieces have the same length and the remaining 3 pieces also have equal lengths.
a) Generate some data for this relation showing the possible lengths of the pieces.
b) Graph the data.
c) Write an equation for the relation in general form.
d) i) Can each of 2 pieces be 18 cm long and each of 3 pieces be 3 cm long?
ii) Can each of 2 pieces be 3 cm long and each of 3 pieces be 18 cm long?
Use the graph and the equation to justify your answers.
Answer:
1m
Step-by-step explanation:
because there is some thing to tell I am a kid and my age is 13 and how should I answer your question.
Can you help please I really need it
Answer:
65cm
Step-by-step explanation:
100cm= 1 metre
?=2.5m
=2.5*100=250cm
250-(60+35+90)=65cm
remaining length=65cm
What is the ratio of the Patio?
Answer:
B
Step-by-step explanation:
the are of the square would be: 4*6=24
the are of one triangle would be: (6*2)/2=6 (12 in total because there are two triangles
to find the whole area, you add 24 and 12 which is B) 36 meters squared
Which rule can be used to describe the x-coordinates in the translation below?. on a coordinate plane, triangle a b c is shifted 6 units up. x 0 x 6 x – 6 x 2
The rule that can be used to describe the x-coordinates in the translation is (x+6).
What is a translation?A translation is a sort of transformation that moves each point in a figure in the same direction by the same amount of distance.
We know that the coordinate is moving up, therefore, the coordinate of x will be increasing by 6 units.
Hence, the rule that can be used to describe the x-coordinates in the translation is (x+6).
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Answer:
x + 6
Step-by-step explanation:
What type of graph would you use for a set of categorical data with 25 people surveyed?bar graphline graphpictographstem-and-leaf plot
The type of graph I would use for a set of categorical data with 25 people surveyed is bar graph.
Which types of graphs are good for categorical data?The type of graph or chart that is good for showing categorical data are:
Frequency tables Pie chartsBar chartsNote that bar graph is one of the the most appropriate graphical form of displays for any categorical variables.
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PLEASE HELP
I put a photo
Really Easy, Help pleaseee
1 minute = 0.25km
Step-by-step explanation:
divide both numbers that were given by 8. 8÷8 is 1 and 2÷8 is 0.25.
A server makes $200 a week working at a local restaurant. The server saves 35% of the $200 weekly earnings each week for 4 weeks.
If the server saves 78 of the 5th week’s $200 earnings, how much money will the server have saved in total after the 5 weeks?
please i need help and i taking a test
Answer:
He would of saved 455$
Step-by-step explanation:
Because for 4 weeks he saved 35% of 200$ which would be 70 and 70+70+70+70 is 280$ and then he saved 175 dollars on the 5th week because 7/8 of 200 is 175 so 280+175= 455
I hope this helps!
Find the perimeter of the triangle as a simplified polynomial if the sides are 3x + 2, 5x - 5, and 8x + 7
Answer: 16x+4
Step-by-step explanation:
perimeter = side + side + side
So in this case:
Perimeter= 3x+2+5x-5+8x+7= 3x+8x+5x+2+7-5 = 11x+5x+9-5 = 16x+4
(7xy-8yz+3x)-(4x-8yz)
Answer:
7xy-8yz+3x-4x+8yz
7xy-8yz+8yz+3x-4x
7xy-x
Step-by-step explanation: