f(x) = x^2-4x find f(2)
Answer: -4
Step-by-step explanation:
Given the value of x, you must plug it into the equation ( f(x) is basically y )
(2)^2 - 4(2)
4 - 8 = -4
A survey of 300 students is selected randomly on a large university campus. They are asked if they use a laptop in class to take notes. Suppose that based on the survey, 105 of the 300 students responded "yes."
a. What is the value of the sample proportion?
b. What is the standard error of the sample proportion?
c. Construct an approximate 95% confidence interval for the true proportion.
In a survey of 300 randomly selected students on a university campus, 105 of them responded "yes" when asked if they use a laptop in class to take notes. The sample proportion of students using laptops is 0.35. The standard error of the sample proportion is approximately 0.0289. By constructing an approximate 95% confidence interval, we find that the true proportion of students using laptops in class falls between 0.293 and 0.407.
To calculate the sample proportion, the standard error of the sample proportion, and construct an approximate 95% confidence interval for the true proportion.
a. The sample proportion is the ratio of the number of students who responded "yes" to the total number of students surveyed. In this case, the sample proportion is 105/300 = 0.35.
b. The standard error of the sample proportion measures the variability of the sample proportion. It can be calculated using the formula:
SE(p) = sqrt((p * (1 - p)) / n),
where p is the sample proportion and n is the sample size. Plugging in the values, we get:
SE(p) = sqrt((0.35 * (1 - 0.35)) / 300) ≈ 0.0289.
c. To construct an approximate 95% confidence interval for the true proportion, we can use the formula:
CI = p ± z * SE(p),
where CI represents the confidence interval, p is the sample proportion, z is the critical value corresponding to the desired level of confidence (in this case, for 95% confidence, z ≈ 1.96), and SE(p) is the standard error of the sample proportion.
Plugging in the values, we have:
CI = 0.35 ± 1.96 * 0.0289,
which gives us the confidence interval (approximately) as 0.293 to 0.407.
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The piston moves from the Top dead center as a result of a change * crank angle ratio of crank radius to connected length connected length crank radius the distance from TDC to the crank center equal to * a=crank radius b= connected length a*b a+b. the piston travel changed with * connected rod length crank angle R/L crank radius 2 points 2 points 2 points
The piston travel in an engine is influenced by the crank angle, crank radius, and connected rod length. The relationship between these variables is described by the formula a + b, where a represents the crank radius and b represents the connected rod length. The piston travel is directly related to the change in crank angle and is affected by the ratio of crank radius to connected rod length.
In an engine, the motion of the piston is driven by the crankshaft, which converts the rotational motion of the crank into linear motion of the piston. The distance traveled by the piston from the Top Dead Center (TDC) is influenced by various factors, including the crank angle, crank radius, and connected rod length.
The crank angle represents the angle through which the crankshaft rotates. As the crankshaft rotates, the piston moves up and down in the cylinder. The change in crank angle directly affects the piston travel.
The crank radius (a) is the distance from the center of the crankshaft to the point where the connecting rod is attached. The connected rod length (b) is the distance from the attachment point on the crank to the attachment point on the piston. The sum of the crank radius and the connected rod length, represented by a + b, determines the piston travel.
The ratio of crank radius to connected rod length also plays a role in the piston travel. This ratio affects the motion of the piston and determines the relationship between the crank angle and the linear displacement of the piston.
In summary, the piston travel in an engine is determined by the change in crank angle and is influenced by the ratio of crank radius to connected rod length. The formula a + b, where a represents the crank radius and b represents the connected rod length, describes the relationship between these variables. By understanding these factors, engineers can optimize the design and performance of internal combustion engines.
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© a In Fig. 6.28, show that APAX is similar to
AYAQ.
b Hence show that
Pal X JAQI = YAI X laxl.
c IfXal = 14 cm, Pal = 6 cm and
IYA) = 3 cm, calculate (AQI.
X
Р
А
Q
Y
The missing figure is attached down
Answer:
ΔPAX ≈ ΔYAQ ⇒ proved down
PA × AQ = YA × AX ⇒ proved down
AQ = 7 cm
Step-by-step explanation:
In two triangles: if their corresponding angles have the same measures, then they are similar
In triangles ABC and XYZ, if m∠ABC = m∠XYZ, m∠BCA = m∠YZX, m∠CAB = m∠ZXYThen, ΔABC ≈ ΔXYZIf two triangles are similar, then their corresponding sides are proportion
If ΔABC ≈ Δ XYZ, then[tex]\frac{AB}{XY}=\frac{BC}{YZ}=\frac{AC}{XZ}[/tex] ⇒⇒⇒ Their sides are proportionIn our question:
From the attached figure
∵ YQ // PX
∴ m∠AYQ = m∠APX ⇒ corresponding angles
∴ m∠AQY = m∠AXP ⇒ corresponding angles
∵ ∠A is a common angle
∴ ΔPAX ≈ ΔYAQ ⇒ proved
∵ ΔPAX ≈ ΔYAQ
∴ Their corresponding sides are proportion
→ side PA is corresponding to side YA
→ side AX is corresponding to side AQ
→ side PX is corresponding to side YG
∴ [tex]\frac{PA}{YA}=\frac{AX}{AQ}=\frac{PX}{YQ}[/tex]
∵ [tex]\frac{PA}{YA}=\frac{AX}{AQ}[/tex]
→ By using cross multiplication
∴ PA × AQ = YA × AX ⇒ proved
∵ AX = 14 cm
∵ PA = 6 cm
∵ YA = 3 cm
→ Substitute these values in the relation above
∴ 6 × AQ = 3 × 14
∴ 6 AQ = 42
→ Divide both sides by 6
∴ AQ = 7 cm
PLEASE HELP ITS DUE IN 13 MIN Rewrite y=x2+10x+33 in vertex form by completing the square. Then identify the vertex.
Answer:
Vertex form: y = (x+4)^2 - 9
Minimum y-value of function: [-9, ∞)
Step-by-step explanation:
Vertex form: y = a(x-h)^2 + k
To convert standard form into vertex form, you will need to complete the square. To find the minimum y-value, you will need to find the vertex and see the y-value (as it is a parabola and nothing goes above/below it).
Step 1: Move 7 over to the other side (or subtract 7)
y - 7 = x^2 + 8x
Step 2: Complete the Square
y - 7 + 16 = x^2 + 8x + 16
Step 3: Factor and combine like terms
y + 9 = (x + 4)^2
Step 4: Move 9 back to the right (or subtract 9)
y = (x + 4)^2 - 9
Final Answer: y = (x + 4)^2 - 9
Your vertex is located at (h, k), so at (-4, 9). Since the highest degree coefficient is positive, the parabola is facing up. Nothing will go below the y-value of 9.
Jessica bakes 112 muffins in 7 batches.How many muffins does each Bach contain
What is 1,000,000x4,573,500?
Answer:
1,000,000x4,573,500 = 4.5735e+12
Answer:
Hello!!! Princess Sakura here ^^
Step-by-step explanation:
Set up an equation like this...
[tex]1,000,000*4,573,500=?[/tex]
And now when you multiply them together you should get...
4.5735e12
I have dyslexia and it’s really hard 4 me but I’ve been doing better but I’m stuck on this⬇️
The temperature increased 612°F in the afternoon before decreasing 8.7°F in the evening.
What was the evening temperature? Enter your answer in the box in decimal form.
I will give the person who solves this 20 points. With a coupon, you can get a pair of shoes that normally costs $84 for only $72. What percentage was the discount? If necessary, round to the nearest tenth of a percent. Please Round
Answer:
The percentage of the discount is:
14.29% or 14.28%
How did it become 14.29%?
Its because the original answer is 14.2857143% that if you will simplify the answer will be 14.29%
Step-by-step explanation:
Answer:
19 percent off.
If a = 1/x − 1/y , what is the value of 1/a ?
Answer:
1/a = xy/(y-x)
Step-by-step explanation:
Simplify the reciprocal:
1/a = 1/(1/x -1/y) = 1/((y-x)/(xy))
1/a = xy/(y-x)
Please please help me!!
Answer:
B
Step-by-step explanation:
What’s 6 3/4 feet times 3 feet
Answer:
=6×3/4×3
Now, 3cut3
=6×4
=24
-26+13x+2>2-13x
could somone help me plz??
Answer:
x > 1
Step-by-step explanation:
-26 + 13x + 2 > 2 - 13x
combine like terms
-24 + 13x > 2 - 13x
add 24 to both sides to cancel out the -24
-24 is canceled out by +24
13x > 2 + 24 - 13x
combine like terms
13x > 26 - 13x
add 13x to both sides to cancel out -13x
13x + 13x > 26
combine like terms
26x > 26
divide both sides by 26
x > 1
Help pls I need help
Answer: hold ctrl alt and hit up
Step-by-step explanation:
In ∆ABC,|AB|=10cm and|AC|=18cm.M is the midpoint of BC and the bisector of angle A meets side BC at N.If |MN|=2cm , calculate |BC|
Step-by-step explanation:
i hope i have been useful buddy.
good luck ♥️♥️♥️♥️♥️.
A runner has run 2.281 kilometers of a 10 kilometer race. How much farther does he need to run to finish the race? Show your work.
Answer:
7.719km
Step-by-step explanation:
10 - 2.281 is 7.719
Which of these is a prime number? 156, 149, 133, 152
The weights of adult women are approximately normally distributed about a mean of 142 lbs. with a standard
deviation of 14 lbs. If Renee is at the 96 percentile in weight for adult women, then her weight, in lbs. is closest
to
Answer:
166. 5
Step-by-step explanation:
Given the following :
Mean weight (m) = 142 lbs
Standard deviation (sd) = 14 lbs
Renne = 96 percentile, what is Renne's weight
Using the equation :
Zscore = (score - mean) / standard deviation
96 percentile = 0.96 is equivalent to a Zscore of
1.75
Hence,
1.75 = (score - 142) / 14
14 * 1.75 = score - 142
24.5 = score - 142
24.5 + 142 = score
Score = 166.5
Please help if you answer this i’ll give brainlest
Answer:
you just need to get 93 and times it my the number next to it and you will get your answer which is 257
Find the slope of the line that passes through each pair of points. C(3, 5), D(2, 6)
17. Verizon charges a one time fee of $10.50, plus $0.15 per text.
AT&T charges a one time fee of $7.00, plus $0.25 per text. How many text messages
until the two plans cost the same?
Answer:
$10.50+(x*0.15)=$7.00+(y*0.25)
this will tell you your answer
Step-by-step explanation:
Find the distance between each pair of points.
1. 1-4.6) and (3.-7)
2. (-6,-5) and (2.0)
M=(-12,-1)
M=
4. (0.-8) and (3.2)
3. (-1, 4) and (1-1)
The distances between each pair of points are as follows:
1. (1, -4.6) and (3, -7): 3.12 (rounded to two decimal places)
2. (-6, -5) and (2, 0): √89 (exact value)
M = (-12, -1) and M = (4, 0): √257 (exact value)
4. (0, -8) and (3, 2): √109 (exact value)
3. (-1, 4) and (1, -1): √29 (exact value)
We may use the distance formula to calculate the separation between each pair of points:
d = √((x₂ - x₁)² + (y₂ - y₁)²),
where the two points' coordinates are represented by (x1, y1) and (x2, y2), respectively.
Let's determine the separation between each pair of points:
1. (1, -4.6) and (3, -7):
d = √((3 - 1)² + (-7 - (-4.6))²)
= √(2² + (-2.4)²)
= √(4 + 5.76)
= √9.76
= 3.12 (rounded to two decimal places)
2. (-6, -5) and (2, 0):
d = √((2 - (-6))² + (0 - (-5))²)
= √(8² + 5²)
= √(64 + 25)
= √89 (exact value)
M = (-12, -1) and M = (4, 0):
d = √((4 - (-12))² + (0 - (-1))²)
= √(16² + 1²)
= √(256 + 1)
= √257 (exact value)
4. (0, -8) and (3, 2):
d = √((3 - 0)² + (2 - (-8))²)
= √(3² + 10²)
= √(9 + 100)
= √109 (exact value)
3. (-1, 4) and (1, -1):
d = √((1 - (-1))² + (-1 - 4)²)
= √(2² + (-5)²)
= √(4 + 25)
= √29 (exact value)
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The graph of a line in the xy-plane has a slope of 1 and contains the point
1
(3, 0). The graph of a second line has a slope of - and contains the
point (-7,0). If the two lines intersect at the point (a, b), what is the
value of a + b ?
4
Choose 1 answer:
-8
-5
-2
-1
The value of a + b is given as follows:
B. 3.
How to define a linear function?The slope-intercept equation for a linear function is presented as follows:
y = mx + b
In which:
m is the slope, representing the rate of change.b is the intercept.Line 1 has a slope of 2, hence:
y = 2x + b
It contains the point (1,8), hence the intercept b is given as follows:
8 = 2 + b
b = 6.
Hence the line 1 is:
y = 2x + 6.
For the second line, we have that when x increases by 1, y decreases by 1, hence the slope m is given as follows:
m = -1.
Hence:
y = -x + b.
When x = 1, y = 2, hence the intercept b is given as follows:
2 = -1 + b
b = 3.
Hence the line 2 is:
y = -x + 3.
The x-coordinate of the intersection point, representing the value of a, is given as follows:
2x + 6 = -x + 3
3x = -3
x = -1 (a = -1).
The y-coordinate of the intersection point, representing the value of b, is given as follows:
y = -(-1) + 3
y = 4 (b = 4).
Hence the sum is given as follows:
-1 + 4 = 3.
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8x + 3 = 8x + 27
Please help
Answer: No solution
Steps: 8x + 3 = 8x + 27
Subtract 8x from both sides: 8x + 3 - 8x = 8x + 27 - 8x
Simplify: 3 ≠ 27
The sides are not equal so therefore there is no solution.
Plz mark brainliest:)
Answer:
No Solutions
Step-by-step explanation:
Step 1:
8x + 3 = 8x + 27 Equation
Step 2:
3 = 27 Subtract 8x on both sides
Step 3:
3 ≠ 27 No Solutions
Answer:
No Solutions
Hope This Helps :)
Graph the linear equation y=-7/3x+5
Answer:
Slope=− 2.000 /4.667 =−2.333
x−intercept=
7 /15 =2.14286
y−intercept=
3 /15 =5
Step-by-step explanation:
[20 points] -x + 4 = 9
Answer: x = -5
Step-by-step explanation:
-x + 4 = 9
-4 -4
-x = 5
divide by -1 on both sides
x = -5
Answer:
Step-by-step explanation:
Let's solve your equation step-by-step.
−x+4=9
Step 1: Subtract 4 from both sides.
−x+4−4=9−4
−x=5
Step 2: Divide both sides by -1.
−x /−1 = 5 /-1
x=−5
Answer:
x=−5
Pls help idk
which pattern it is
sas its sas oof hope this helps
PLEASE HELP ILL GIVE YOU LOTS OF POINTS!!!
Plot the preimage on grid number 1:
A (0 , 4) B (1 , 2)C (-1 , 3)
Reflect the preimage over the X-Axis; Give new coordinates:
A’ ( , )B’ ( , )C’ ( , )
Rotate Triangle A’B’C’ 90° counterclockwise; Give the new coordinates:
A’’ ( , )B’’ ( , )C’’ ( , )
Translate Triangle A”’B’’C’’ left 1 unit and up 3 units; Give the new coordinates:
A’’’ ( , )B’’’ ( , )C’’’ ( , )
Dilate Triangle A’’’B’’’C’’’ by a scale factor of 3; Give the new coordinates:
A’’’’ ( , )B’’’’ ( , )C’’’’ ( , )
Answer:
Is there a picture for that where i can try to help you??
Step-by-step explanation:
How many teaspoons of red paint would you need if you use 35 teaspoons of blue paint?
Answer:
35 teaspoons of red paint to make it even.
Step-by-step explanation:
There is 18 inches of snow on the ground. Snow is falling at a rate of 4 inches per hour. Write a function to represent the total amount of snow.
Answer:
[tex]f(x) = 4x + 18[/tex]
Step-by-step explanation:
Since there are 18 inches of snow already, 18 is our constant term in the function. Then, we describe x to be the number of hours that it snows for. We multiply this by 4 to find how many inches of snow fell during those hours. We add this term to the constant term to get the solution to y or [tex]f(x)[/tex]
