9514 1404 393
Answer:
time to max height: 2.5 seconds
max height: 104 ft
range of function: [4, 104]
Step-by-step explanation:
The equation for ballistic motion is ...
h(t) = -16t^2 +v0·t +h0 . . . . where v0 is the initial upward speed and h0 is the initial height
For the given parameters, the height function is ...
h(t) = -16t^2 +80t +4
The time for maximum height is ...
-b/(2a) = -80/(2(-16)) = 2.5 . . . seconds
The maximum height is ...
h(2.5) = (-16·2.5 +80)(2.5) +4 = 104 . . . feet
The range of the function is from the minimum height (at launch) to the maximum height:
4 ft ≤ h(t) ≤ 104 ft.
At a plant that manufactures bars of steel, a machine is used to cut the bars to specific lengths. The machine has a dial that sets the length of the bars to be cut. However, the dial is currently out of alignment and the plant manager is collecting data to assess the situation. The following table shows 8 trials at different dial settings along with the actual output length of the bars that were cut. All measurements are in millimeters.
(a) Use the following grid to construct a scatterplot in which dial setting is the explanatory variable and output length is the response variable. Based on your graph, does a linear model seem appropriate? Justify your answer.
(b) Use the data to construct a least-squares regression line to predict output length from dial setting.
(c) Assume that all conditions for inference are met. Indicate the hypotheses appropriate to test whether there is a linear relationship between output length and dial setting
(d) The test statistic for the appropriate test is t=9.018. Do the data provide convincing statistical evidence that there is a linear relationship between output length and dial setting?
Check Attached Photos. Sorry, it didn't let me submit it through text because of "inappropriate language," despite me not having any in my answer.
For the plant which manufactures bars of steel, the conclusions are as follows;
A. The scatter graph is shown.
B. The equation is y = 2.204 + 1.007x
C. Null hypotheses (H₀); β = 0
Alternative hypotheses (Hₐ); β ≠ 0
D. P-value (0.0001) is less than the significance level (α = 0.05).
What are null hypotheses and alternative hypotheses?In null hypotheses, there is no relationship between the two phenomenons under the assumption or it is not associated with the group. And in alternative hypotheses, there is a relationship between the two chosen unknowns.
At a plant that manufactures bars of steel, a machine is used to cut the bars to specific lengths.
The machine has a dial that sets the length of the bars to be cut.
The dial is currently out of alignment and the plant manager is collecting data to assess the situation.
The following table shows 8 trials at different dial settings along with the actual output length of the bars that were cut.
All measurements are in millimeters.
Dail setting Output length
75 78
77 79
79 82
80 83
81 85
82 83
83 86
85 88
A. The scatter plot is shown below.
Based on the scatter plot, a linear model seems appropriate to the model relationships between the dial setting of the machine and the output length of the steel bar.
The scatter plot shows the strong (r = 0.965), positive, linear association. There do not appear to be any outliners.
B. From the data to construct a least-squares regression line to predict output length from dial setting. Then
y = (a + bx)
Let x be the dial setting machine and y be the output length of steel bars (in mm).
y = 2.204 + 1.007 x
C. All conditions for inference are met. Indicate the hypotheses appropriate to test whether there is a linear relationship between output length and dial setting.
Let β be the true slope of the population regression line relating the dial setting of the machine (x) and the output length of the steel bars (y) at the manufacturing plant.
Null hypotheses (H₀) ; β = 0
Alternative hypotheses (Hₐ) ; β ≠ 0
Appropriate test = slope of regression line t-test.
D. The test statistic for the appropriate test is t = 9.018 with 6 degrees of freedom (7 - 1)
The normal curve is shown;
Using calculator command t-CDF, with the alternative hypotheses as β≠0, then P-value = 0.0001.
In probability notation;
P(b≥0.017) = P(t≥9.018) = 0.00005
P-value = (2) × (0.00005) = 0.0001
P-value = 0.0001
Assume α = 0.05
Since our P-value (0.0001) is less than the significance level (α = 0.05), we do not convince statistical evidence that there is a linear relationship between output length and dial setting.
As the dial setting (x) increases, the output length of the steel bar (y) increases as well.
More about the null hypotheses and alternative hypotheses link is given below.
https://brainly.com/question/9504281
there is given the numbers equals to 8 and DC equals to 3.2 and BE quals to 9 and find BC
Given:
Consider [tex]AB\parallel DE[/tex] in triangle ABC and [tex]AD=8,DC=3.2,BE=9[/tex].
To find:
The length of BC.
Solution:
Basic proportionality theorem (BPT): If a line intersect the two sides of triangle and parallel to the third side, then that line intersects the other two sides proportionally.
Using Basic proportionality theorem, we get
[tex]\dfrac{AD}{DC}=\dfrac{BE}{EC}[/tex]
[tex]\dfrac{8}{3.2}=\dfrac{9}{EC}[/tex]
On cross multiplication, we get
[tex]8\times EC=9\times 3.2[/tex]
[tex]EC=\dfrac{28.8}{8}[/tex]
[tex]EC=3.6[/tex]
Now,
[tex]BC=BE+EC[/tex]
[tex]BC=9+3.6[/tex]
[tex]BC=12.6[/tex]
Therefore, the length of side BC is 12.6 units.
can someone please explain, i really need help
Answer:
x = 42.5
Step-by-step explanation:
A triangle formed inside of a circle using the diameter as one of its side lengths is a right triangle
The right angle would be the angle opposite of the diameter (∠C)
A right angle has a measure of 90°
That being said we use this equation to solve for x
90 = 2x + 5
step 1 subtract 5 from each side
90 - 5 = 85
5 - 5 cancels out
now we have 85 = 2x
step 2 divide each side by 2
85/2=42.5
2x/2=x
we're left with x = 42.5
In ΔMNO, the measure of ∠O=90°, OM = 1.7 feet, and NO = 6.7 feet. Find the measure of ∠N to the nearest degree.
Answer:
14
Step-by-step explanation:
Tan = opposite / adjacent = 1.7 / 6.7
tan N= 1.7 / 6.7
N = 14.237 = 14
Answer:
14
Step-by-step explanation:
the guy above knos why
lorena's backpack has a mass of 17,000 grams. what is the mass of lorena's backpack in kilograms
Answer:
17
Step-by-step explanation:
17
What is the circumference of a circle with a radius of 6 inches?
Answer:
37.7in
Step-by-step explanation:
C=2πr=2·π·6≈37.69911in
Answer:
37.6 (simplified)
Step-by-step explanation:
The formula for circumference is 2[tex]\pi[/tex]*r. Simply replace r with 6 and multiply from there. Normally you would simplify pi down to 3.14 as well.
a new TV cost R6900 cash it is available on hire purchase with a deposit of 15% followed by 12 instalments of R558,50 and find the total hire purchase price and extra amount that you will pay (on top of the cash price) using hire purchase.
no links!
The Ridgeport school district collected data about class
size in the district. The table shows the class sizes for five
randomly selected kindergarten and seventh-grade
classes.
Number of students in randomly
selected class
Mean Mean absolute
deviation
19
1.2
Kindergarten 17, 18, 19, 21, 20
Seventh 25, 30. 27, 29, 34
grade
29
2.4
Based on these data, which statement is true?
I think its option B) The average size of a seventh-grade class is larger and varies more than that of a Kindergarten-class.
it c. i think
Step-by-step explanation:
Only #6. I Would Appreciate Help On This One
Answer:
25π
Step-by-step explanation:
well the area is 78.53981633974 but in terms of pi, it's 25π
We’re doing similarity and I’m really confused
Answer:
Hello its ok Love!
I believe x = 2 hope this helps good luck!
Answer: 2 ft
Step-by-step explanation:
18 / 4.5 = 4
8 / 4 = 2
Each day Theo versus dog 15 minutes in the morning and 25 minutes in the afternoon evaluate the expression 7 x (15 + 25) to find how many minutes to theo dog each week
Answer: 280 minutes
Step-by-step explanation:
Given
Expression is [tex]7\times (15+25)[/tex]
Apply distributive law i.e.
[tex]a(b+c)=a\cdot b+a\cdot c[/tex]
[tex]\Rightarrow 7(15+25)=7\cdot 15+7\cdot 25\\\Rightarrow 7(15+25)=105+175=280[/tex]
Thus, theo dog took 280 minutes each week
HELP PLEASE 20 POINTS
Which scenario would result in 12 possible outcomes?
You roll a number cube twice.
You flip a coin twice.
You roll a number cube, and then you flip a coin. You roll a number cube once.
Answer:
You roll a number cube, and then you flip a coin.
Step-by-step explanation:
i don't even know how math is confusing. (this is the right answer on the quiz)
help please will give brainliest
Select the correct answer.
What are the solutions to this quadratic equation?
5x2 76 - 18 = 0
A.
T =
OB.
13
–7 + V409
10
7 + V409
5
-7 + 7409
5
7 I 409
10
O C.
OD.
Which equation represents a line that has a slope of – 2/3 and a y-intercept of 4?
A)
2x + 3y = 12
B)
2x - 3y = 12
C)
3x - 2y = 12
D)
3x + 2y = 12
Answer:
A
Step-by-step explanation:
Slope-intercept form: y=mx+b
2x+3y = 12
3y = 12-2x
y = (12-2x)/3
y = 4-2/3x
Here we can see that the slope is -2/3 and y-intercept 4. We already got the answer so we dont need to try the other options.
The line of which equation passes through points (0,6) and (4,-1)
Answer:
y=-7/4x+6
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(-1-6)/(4-0)
m=-7/4
y-y1=m(x-x1)
y-6=-7/4(x-0)
y-6=-7/4(x)
y-6=-7/4x
y=-7/4x+6
What is the vertex of the parabola f(x) = x^2 – 2x – 8 that has an axis of symmetry at 2 = 12
A (2,-8)
B (1,-9)
C (3,-5)
D (4,0)
Answer: i am pretty sure it is c
OR A
NOT SURE THOUGH trust ur gut
Step-by-step explanation:
solve the quadratic equation
8x^2+16x+8=0
Answer:
8x²+16x+8=0
x²+2x+1=0
D=4-4=0
x0=-2/2=-1
Answer:
x = -1Step-by-step explanation:
[tex]8x^2+16x+8=0[/tex] {divide both sides by 8}
[tex]x^2+2x+1=0\\\\a=1\,,\quad b=2\,,\quad c=1\\\\x=\dfrac{-2\pm\sqrt{2^2-4\cdot1\cdot1}}{2\cdot1}=\dfrac{-2\pm\sqrt{4-4}}2=\dfrac{-2\pm0}2=-1[/tex]
A researcher is trying to identify whether household substances are basic. Which approach would BEST help the researcher investigate
whether substances are basic?
A. Observe each substance and record its color.
o B. Measure the temperature of each substance.
C. Test each substance with red litmus paper.
OD. Mix each substance with a weak base and record the results.
Answer:
C. Test each substance with red litmus paper.
Step-by-step explanation:
C is the correct answer because when you apply a base with a red litmus paper the outcome color should result in blue.
The best approach best investigate whether substances are basic is to test each substance with red litmus paper.
What is basic compound?In general, bases are substances that can neutralise a small amount of acid. Ammonia and sodium carbonate are both bases even though neither of them includes OH groups.
When in contact with basic chemicals, red litmus paper turns blue instead of red. Thus we should use red litmus paper to test the basicity of home items.
Acids are the only substances that bases react with, hence using weak bases will not produce the intended results since weak bases only partially dissociate.Color does not indicate basicity or acidity.The acidity of a substance can be determined by placing red litmus paper in contact with acid, which causes the paper to turn blue.Hence, the test each substance with red litmus paper.
Learn more about Basic Compound here:
https://brainly.com/question/23047866
#SPJ2
Find the sale price if a customer buys a $40 shirt
that is 20% off.
Answer:
$8
Step-by-step explanation:
To find 10% of a number, move the decimal point over by one. Since the number is a whole the decimal point looks like this
$40.00
Move it once to get 10% which is 4. Then multiply it by 2 to get 20%.
Someone help me out please
Answer:
Coordinates are
(1,-5)
(-6,1)
45 POINTS!!
1. A quadratic function is represented by the graph.
(a) What is the equation of the axis of symmetry of the function?
(b) What are the coordinates of the vertex of the function?
(c) What are the coordinates of the x¬-intercepts of the function?
(d) What are the coordinates of the y-intercept of the function?
Also put a answer that makes sense, not just to get the points.
Answer:
c
Step-by-step explanation:
Angela rented a car for $29.99 a day plus a one-time insurance cost of $5.00. Her bill was $124.96. For how many days did she rent the car? Write an equation and then solve
Answer:
94 days
Step-by-step explanation:
That's a cheap rent-a-car place :)
Btw I took the test.
A 26-ft ladder leans against a building so that the angle between the ground and the ladder is 81 degrees. How high does the ladder reach on the building? the answer is in ft
Answer:
25.7 feets
Step-by-step explanation:
From the diagram attached, we could use trigonometry to obtain the height,h :
Using the trigonometric relation :
Sin θ = opposite / hypotenus
Opposite = h
Hypotenus = 26 feets
Sin 81° = h / 26
Height, h = 26 * sin 81°
h = 26 * 0.9876883
h = 25.679
Height, h = 25.7 feets
1. The range of guest on New Year's Eve was 15>
2. About 50% of Thanksgiving dinners had 17 or more people.
3. Everyone had at least one guest over for dinner at Thanksgiving.
4. The IQR of Thanksgiving dinner was 20.
5. The median number of people at New Years' Eve dinner was 15.
6. Three-fourths of New Years' Eve dinners had five or more people.
Answer:
1.False
2. True
3.) True
4. False
5.) False
6.) True
Step-by-step explanation:
1.)
Range = maximum - minimum
New year's eve :
Maximum = 22 ; minimum = 3
Range = 22 - 3 = 19
2.)
Median for Thanksgiving = 17
50% up to 17 ;hence the remaining 50% is also 17 and above
4.)
IQR for Thanksgiving
Q3 - Q1
23 - 12 = 11
5.)
The median number of people at new year's eve for dinner was 7 (line in between the box)
6.)
3/4th of new year eve's dinner = Q3 = 15
1/4 = Q1 ; have up to 5 people
Therefore ; the remaining (1 - 1/4) = 3/4 have 5 and above
Answer:
1.False
2. True
3.) True
4. False
5.) False
6.) True
Step-by-step explanation:
Luke has a board 5
6
of a yard long. He needs to cut the board into 5 equal sections.
Use the expression
to find the length of each section.
Each section is
yard long.
Answer:
1/6 of a yard
Step-by-step explanation:
Length of the board = 5/6 yard
He needs to cut the board into 5 equal sections.
Length of each section = length of the board ÷ number of sections
= 5/6 ÷ 5
= 5/6 × 1/5
= (5*1)/(6*5)
= 5/30
= 1/6
Length of each section = 1/6 of a yard
Select all the expressions that equal 6-10 Write out each solution.
A. 65 6²
5
B.
C. (6)
63
D.
67
E.
Answer:
i think c and e and d (im sorry if its wrong)
QuestionDuring their team meeting, both managers shared their findings. Complete the statement describing their combined results. Select the correct answer from each drop-down menu.The initial number of video views was the initial number of site visits, and the number of video views grew by the number of site visits.The difference between the total number of site visits and the video views after 5 weeks is .
Answer:
The initial number of video views was more than the initial number of site visits, and the number of video views grew by a smaller factor than the number of site visits. The difference between the total number of site visits and the video views after 5 weeks is 20,825
Step-by-step explanation:
the initial video view was 5120 and the initial number of site visits were 4800, so the initial video view was more than.
The video views grew by 5/4 and the number of site visits grew by 3/2, and since 3/2 is > 5/4, the video views grew by a smaller factor than the number of site visits.
the result for the video views after 5 weeks is 15,625 and the site visits after 5 weeks is 36450, so 36450-15,625=20,825
Answer:
Step-by-step explanation:
Here's proof of the answer correcto
happy earth day 2 years hehe
I really need to know the answer of this question
Answer:
Amir 20 Rita 45
Step-by-step explanation:
20/4=5
5*9=45
so this satisfices the ration 4:9
Answer:
Amir : 20 sweets and Rita : 45 sweets
Step-by-step explanation:
Rita has 25 more in all answers. to get the answer, this is to see which one : 4:9 ; 20:45.
we multiply 4 and 45 and 9 and 20. if we multiply them, both answers are 180. this means it is equal and that is the answer.
Determine the horizontal and vertical axis intercepts: r = 36 + 70sin θ.
Please show your work need help!
Answer:
See below for answers and explanations (along with a graph)
Step-by-step explanation:
Refer to the equations for a limaçon:
y=a+bcos∅ (horizontal line of symmetry) and y=a+bsin∅ (vertical line of symmetry) where a/b determines the type of limaçon.
This is an inner loop limaçon because 36/70<1, so its horizontal axis intercepts are 36 and -36 (marked in red) and its vertical axis intercepts are 0, 36+70=106 and 70-36=34 (marked in green)