The 95% confidence interval for the true proportion of first-year students who intend on majoring in liberal arts is option B. 0.62 plus-or-minus 1.96 start root start fraction 0.62 (1 minus 0.62) over 100 end fraction end root .
What is Confidence Interval?Confidence interval in statistics is defined as the certain range of values that you estimate for the unknown parameter lies within.
Confidence interval for the population proportion can be calculated as,
p ± z × [tex]\sqrt{\frac{p(1-p)}{n} }[/tex]
Here, p is the sample proportion and n is the sample size.
z value for 95% confidence interval is 1.96.
Here, n = 100,
p = [tex]\frac{62}{100}[/tex] = 0.62
Substituting the values, confidence interval of true proportion is,
0.62 ± 1.96 × [tex]\sqrt{\frac{0.62(1-0.62)}{100} }[/tex]
Hence the 95% confidence interval for the true proportion of first-year students who intend on majoring in liberal arts is 0.62 ± 1.96 × [tex]\sqrt{\frac{0.62(1-0.62)}{100} }[/tex].
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To which quadrants is tan^-1 x restricted?
A. Quadrants I and IV
B. Quadrants III and IV
C. Quadrants II and III
The quadrants is tan⁻¹x restricted is A. Quadrants I and IV
To answer the question, we need to know what tan⁻¹x is.
What is tan⁻¹x?tan⁻¹x is the inverse trigonometric function of tanx, which is the value of the angle for tanx.
Quadrant in which tan⁻¹x is restrictedTo find the quadrants in which tan⁻¹x is restricted, we know that tanx lies in the range
-∞ ≤ tanx ≤ +∞ for -90° ≤ x ≤ 90°.
Since the inverse function of tanx is x.tan⁻¹x lies between -90° and 90°. That is -90° ≤ tan⁻¹x ≤ 90°.Since 90° lies in first quadrant and -90° lies in the fourth quadranttan⁻¹x lies between quadrant I and IV
So, the quadrants is tan⁻¹x restricted is A. Quadrants I and IV
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Diberi 1 ½s = ⅗t² + ⅓u², hitung (ii) nilai t apabila u = -6 dan s = 28
Answer:
√2' = t
Step-by-step explanation:
1 1/2s = 3/5t^2 + 1/3u^2; substitute known values
1 1/2 • 28 = 3/5 • t^2 + 1/3 • -6^2; simplify
42 = 3 • t^2 ÷ 5 + 1/3 • 36
42 = 3 • t^2 ÷ 5 + 12; apply property of subtraction of equality
42 – 12 = 3t^2 ÷ 5 + 12 – 12; simplify
30 = 3t^2 ÷ 5; apply property of multiplication of equality
30 • 5 = 3t^2 ÷ 5 • 5; simplify
6 = 3t^2; apply property of division of equality
6 ÷ 3 = 3t^2 ÷ 3; simplify
2 = t^2
√2' = t
anything that applies. sec0 is undefined for 0 =
If the sec θ is not defined, then the value of angle θ will be (2n + 1)π/2.
What is trigonometry?The connection between the lengths and angles of a triangular shape is the subject of trigonometry.
The trigonometric expression is given below.
⇒ sec θ
If the sec θ is not defined, then the value of angle θ will be (2n + 1)π/2.
Where n is the any integer.
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Consider the functions below.
f(x) = x² - 6x - 27
g(x) = x - 9
If 2a/4=b/4 and b≠0, what does 5b equal in terms of a?
A) 2a/15
B) 5a/6
C) 15/2a
D) 40a/3
Step-by-step explanation:
you must have made a typo here.
none of the answer options are correct for the given problem.
let me just show you what you told me, and how I can solve at least this :
2a/4 = b/4
this simply means (multiply both sides by 4) :
2a = b
so, 5b is then (multiplying both sides by 5) :
5×2a = 5b
10a = 5b
but again, "10a" is not among the offered answers.
so, I don't know if you made a mistake with the basic problem or with the answer options.
The area of a given hexagon is equal to the area of an equilateral triangle whose perimeter is 36 inches. Find the length
of a side of the regular hexagon.
A triangle is a three-edged polygon with three vertices. The length of a side of the regular hexagon is √24 inches.
What is a triangle?A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angle of a triangle is always equal to 180°.
Given the perimeter of the equilateral triangle is 36 inches, therefore, the length of the side of the equilateral triangle is 12 inches. Now, the area of the equilateral triangle is,
Area of the equilateral triangle = (√3)/4 a²
= (√3)/4 × (12)²
= (36√3) inches²
Since the area of the equilateral triangle is equal to the area of the hexagon , therefore we can write,
Area of equilateral triangle = Area of Hexagon
(36√3) = (3√3)/2× a²
a² = 24
a = √24 inches
Hence, the length of a side of the regular hexagon is √24 inches.
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Find the perimeter. Area=5.612x10^14
9.2x10^7
Answer:
1.962×10^8 cm
Step-by-step explanation:
The area and perimeter formulas can be use to find the perimeter of this rectangle, given its area and the length of one side.
A = LW
P = 2(L +W)
__
Solving the area formula for width, we have ...
W = A/L
Using that in the perimeter formula, we find the perimeter to be ...
P = 2(L +W) = 2(L +A/L)
Using the given values for area and length, we find the perimeter is ...
P = 2(9.2×10^7 +5.612×10^14/(9.2×10^7)) = 1.962×10^8 . . . cm
The perimeter of the rectangle is 1.962×10^8 cm, or 1962 km.
_____
Additional comment
The width is 6.1×10^6 cm, or 0.61×10^7 cm. Then the sum of length and width is (9.2 +0.61)×10^7 = 9.81×10^7 cm. The perimeter is twice that, or 19.62×10^7 cm = 1.962×10^8 cm. 1 km = 10^5 cm, so this is 1.962×10^3 km, or 1962 km.
Your scientific calculator or spreadsheet can use and present numbers in scientific notation directly. The "E" notation is used in place of "×10^". (This notation is an artifact of the earliest computer languages.)
what is this expression in simplified form?
Answer:
33.17 (A)
Step-by-step explanation:
the square root of 22 times (5x the square root of 2)
is 33.17 rounded to the nearest 10th
and 10 x the square root of 11 is 33.17
(they match)
ray and line segment difference
Answer:
A line segment is part of a line that has two endpoints and is finite in length. A ray is a line segment that extends indefinitely in one direction.
Step-by-step explanation:
hope it helps you and give me a brainliest
Answer:
A ray goes in one direction for forever, and also has an arrow.
A line segment is a segment, meaning that it has two end points and doesn't go on forever, it ends.
Step-by-step explanation:
Which equation shows an example of the associative property of addition?
Answer:
(2+3)+4 = 2+(3+4) this is an example of associative property
wright the follwing in decimlal form:3/4
Answer:
3/4 in decimal form is 0.75.
Step-by-step explanation:
I hope this helps! :)
Answer:
0.75
Step-by-step explanation:
3/4 is expressed as 0.75 in the decimal form.
to make a fraction into a decimal you just divide the numerator by the
denominator.
and the numerator is the part of a fraction that is above the line
denominator is at the bottom
so 3 / 4 = 0.75
3/4 in decimal form is 0.75
Hope This Helped
Which equation is showed in the graph above
Answer: A
It has a negative gradient.
Hope this helps :))
P.s. Can you mark me as the brainliest? <3
Answer:
Step-by-step explanation:
Remark
You can read the y intercept right off the graph. Follow the y axis upwards until the line intercepts the y axis. I think you will find it is at 0,5
So far what you know is
y = mx + 5
Finding m is a little harder. I would use 6,0 and 0,5 as the two points that will define m.
Givens
x1 = 6
x2 = 0
y1 = 0
y2 = 5
Equation
m = (y2 - y1) / (x2 - x1) Put the givens into this equation.
Solution
m = (5 - 0) / (0 - 6)
m = 5/-6
m = - 5/6
Answer
The line is
y = -5/6 x + 5
which statements are true regarding undefinable terms in geometry?
Using the expansion of (1-(x/2))^8 and a suitable value of x, evaluate 0.996^8 to 5 d p
Answer:
4j8rd⁸8xud4 ex fiiu8rftsuf
1. In the figure given below, < ABC and < BDC are right angles; If AB-5cm, AD = 3cm and BD = 4cm (3 points) find BC and DC ?
In the given figure, the length of BC is 6.66 cm and the length of DC is 5.33 cm
TrigonometryFrom the question, we are to determine the length of BC and DC
Considering the diagram,
First, we will determine the measure of angle A
Using SOH CAH TOA
We can write that
[tex]sin A = \frac{4}{5}[/tex]
sin A = 0.8
∴ A = sin⁻¹(0.8)
A = 53.13°
Now, we will determine the measure of angle C
∠A + ∠ABC + ∠C = 180° (Sum of angles in a triangle)
53.13° + 90° + ∠C = 180°
∠C = 180° - 90° - 53.13°
∠C = 36.87°
Also,
Using SOH CAH TOA
[tex]tan C = \frac{BD}{DC}[/tex]
[tex]tan36.87 ^\circ=\frac{4}{DC}[/tex]
[tex]0.7500 = \frac{4}{DC}[/tex]
[tex]DC = \frac{4}{0.75}[/tex]
DC = 5.33 cm
By the Pythagorean theorem,
/BC/² = /BD/² + /DC/²
/BC/² = 4² + 5.33²
/BC/² = 16 + 28.4089
/BC/² = 44.4089
/BC/ = √44.4089
/BC/ = 6.66 cm
Hence, the length of BC is 6.66 cm and the length of DC is 5.33 cm
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Please help on the area for 7 8 9 please all i need help is
The area of the equilateral, isosceles and right angled triangle are 12.6mm², 9.61in² and 16.81yds² respectively.
What is the area of the equilateral, isosceles and right angle triangle?Note that:
The area of an Equilateral triangle is expressed as A = ((√3)/4)a²
Where a is the dimension of the side.
The area of an Isosceles triangle is expressed as A = (ah)/2
Where a is the dimension of the base and h is the height.
The area of a Right angled triangle is expressed as A = (ab)/2
Where a and b is the dimension of the two sides other than the hypotenuse.
For the Equilateral triangle.
Given that;
a = 5.4mmArea A = ?A = ((√3)/4)(5.4mm)²
A = ((√3)/4)( 29.16mm² )
A = 12.6mm²
Area of the Equilateral triangle is 12.6mm²
For the Isosceles triangle.
Given that;
Base a = 3.4inSlant height b = 5.9inheight h = ?Area A = ?The height h is the imaginary line drawn upward from the center of a.
First, we calculate the height using Pythagorean theorem
x² = y² + z²
Where x = b = 5.9in, y = a/2 = 3.4in/2 = 1.7in, and z = h
(5.9in)² = (1.7in)² + h²
34.81in² = 2.89in² + h²
h² = 34.81in² - 2.89in²
h² = 31.92in²
h = √31.92in²
h = 5.65in
Now, the area will be;
A = (ah)/2
A = (3.4in × 5.65in )/2
A = 19.21in²/2
A = 9.61in²
Area of the Isosceles triangle is 9.61in².
For the Right angled triangle
Given that;
a = 8.2ydsb = 4.1ydsc = 9.17ydsArea A = ?A = (ab)/2
A = ( 8.2yds × 4.1yds)/2
A = ( 33.62yds²)/2
A = 16.81yds²
Area of the Right angled triangle is 16.81yds²
Therefore, the area of the equilateral, isosceles and right angled triangle are 12.6mm², 9.61in² and 16.81yds² respectively.
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Hi please help!!
Given the following function:
f(x)=2x^2
fill the table with coordinates that work for this function.
x y
(5 empty columns going down)
The table of values of the function y = 2x^2 is:
x 0 1 2 3 4
y 0 2 8 18 32
How to complete the table?The equation of the function is given as:
y = 2x^2
When x= 0, we have
y = 2 * 0^2 = 0
When x= 1, we have
y = 2 * 1^2 = 2
When x= 2, we have
y = 2 * 2^2 = 8
When x= 3, we have
y = 2 * 3^2 = 18
When x= 4, we have
y = 2 * 4^2 = 32
So, the table of values is:
x 0 1 2 3 4
y 0 2 8 18 32
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someone help please
Answer:
I think 40.
Step-by-step explanation:
what is true about this linear inequality
y>3/4-2
Inequalities help us to compare two unequal expressions. The statements that are correct are B, D, and E.
What are inequalities?Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed.
It is mostly denoted by the symbol <, >, ≤, and ≥.
The complete question is:
Which statements are true about the linear inequality y >3/4 x – 2? Check all that apply.
-The slope of the line is –2.
-The graph of y >3/4 x – 2 is a dashed line.
-The area below the line is shaded.
-One solution to the inequality is (0, 0).
-The graph intercepts the y-axis at (0, –2)
-The slope of the line is 3/4. Thus, the first statement is false.
-The graph of y >3/4 x – 2 is a dashed line. The given statement is true.
-The area below the line is shaded. The statement is false.
-One solution to the inequality is (0, 0). The given statement is true.
-The graph intercepts the y-axis at (0, –2) The statement is true.
Hence, the statements that are correct are B, D, and E.
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Determine the scale of a map if the distance between 2 towns is 20km and the map distance is 5cm
The required ratio or scale will be 5cm o the map represent 20km on land
Ratio and scalingScaling is a way of enlarging or reducing the figure on an xy-plane. Given the conversion rate;
Given the following
distance between 2 towns is 20km
The distance on map is 5cm. The required ratio or scale will be 5cm o the map represent 20km on land
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A jar contains five blue marbles, six red marbles, and four green marbles. What are the odds you will draw a blue marble from this jar?
Answer:
Probability=number of specific outcomes/total of all possible outcomes
There are 5 blue marbles and a total of 15 marbles.
So the probability of drawing a blue marble from the jar is:
5/15
1/3
Step-by-step explanation:
Hope this helps
Which one is the right answer
Answer:
The answer is C. Quadrant 3.
Step-by-step explanation:
Looking up a Unit Circle. We can see that 5pi/4 is in quadrant 3.
5pi/4 is also if in degree angle as 225°
■ Write an equivalent expression.
1 (12x+
(12x + 6x − 21) =
?
x
3
?
Answer:
6x - 7
Step-by-step explanation:
[tex]\frac{1}{3}[/tex] (12x + 6x - 21 ) ← multiply each term in the parenthesis by [tex]\frac{1}{3}[/tex]
= 4x + 2x - 7 ← collect like terms
= 6x - 7
Hey there!
ORIGINAL EQUATION:
1/3(12x + 6x - 21)
COMBINE the LIKE TERMS
= 1/3(18x - 21)
DISTRIBUTE 1/3 WITHIN the PARENTHESES:
= 1/3(18x) + 1/3(-21)
SIMPLIFY:
= 6x - 7
Therefore, the answer should be:
6x - 7
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
1. In a sample of 800 students in BNHS, 160, or
20%, are Grade 7 students Based on the above
information, the school's paper reported that "20% of
all the students at BNHS are grade 7." This report is
an example ofIn a sample of 800 students in BNHS, 160, or
20%, are Grade 7 students Based on the above
information, the school's paper reported that "20% of
all the students at BNHS are grade 7." This report is
an example of
a. a sample
b. a population
c. statistical inference
d. descriptive statistics
19.. A statistics professor asked students in a class
their ages. On the basis of this information, the
professor states that the average age of all the
students in the university is 21 years. This is an
example of
a. a census
b. descriptive statistics
c. an experiment
d. statistical inference
20. A tabular summary of a set of data showing the
fraction of the total number of items in several classes
is a
a. frequency distribution
b. relative frequency distribution
c. frequency
d. cumulative frequency distribution
Answer:
1. c. statistical inference
19. d. statistical inference
20. b. relative frequency distribution
If 2^2^x = 2^3 what is the value of x
Answer:
[tex]\dfrac 32[/tex]
Step-by-step explanation:
[tex]~~~~~~~2^{2x} = 2^3\\\\\implies \ln\left(2^{2x} \right) = \ln (2^3)\\\\\implies 2x \ln(2) = 3 \ln(2) \\\\\implies 2x = 3\\\\\implies x = \dfrac 32[/tex]
Answer:
B
Step-by-step explanation:
Sketch a graph of each of the four angles in the same coordinate plane. Label the ordered pairs that intersect the circle. The angles given are 30°, 150°, 210°, 330°
When two straight lines or rays intersect at a shared endpoint, an angle is generated.
What is an angle?When two straight lines or rays intersect at a shared endpoint, an angle is generated. An angle's vertex is the common point of contact. Angle is derived from the Latin word angulus, which means "corner."
The angle can be drawn as shown below. The angle 30°, 150°, 210°, and 330° will lie in 1st, 2nd, 3rd, and 4th quadrants respectively.
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answer fast pls .....
Considering the results from part a, it follows that the volume of a cylinder can be found in the same way as the volume of a rectangular prism. use your results and what you know about volume to explain how to find the volume of a cylinder with a base radius of r units and a height of h units.
To find the volume of a cylinder we must perform a mathematical operation that is expressed in the following formula V = Π h r².
How to find the volume of a cylinder?To find the volume of a cylinder we must solve the following mathematical formula:
V = Πhr²let's do an exampleOur example cylinder is 10 centimeters high and 6 centimeters in diameter. What is its volume?
To find the volume we substitute the values as follows:
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Do you know the answer to this
Answer:
[tex] 4x^2y\sqrt[4]{3y} [/tex]
Step-by-step explanation:
[tex] \sqrt[4]{768x^8y^5} = [/tex]
[tex] = \sqrt[4]{256 \times 3(x^2)^4y^4y} [/tex]
[tex] = \sqrt[4]{4^4 \times 3(x^2)^4y^4y} [/tex]
[tex] = 4x^2y\sqrt[4]{3y} [/tex]
The bouncy kat toys are manufactured using a layering process. the plastic is
added to the ball one layer at a time, with the radius of each ball increasing at a
rate of 0. 1 inch per second. we have been unable to correctly manage the volume
of plastic flowing into the machine. assuming the machine produces 100 toys at a
time, what is the appropriate flow rate of the plastic (in cubic inches per second)
when the radius of each toy is 0. 5 inch? what should the average flow rate of the
plastic be over each 10-second production cycle?
The flow rate to produce the balls is 12.5in/s and 1.25in/s
a. The rate flow to produce the ballsThe number of toys = 100
The increase in radius = 1inch/sec
5 toys are going to increase by 0.5 radius
The rate flow to produce the balls
5x100 = 500
Rate flow = 500 x 0.5³ / 5
= 12.5inch/s
b. New productionTime = 10 seconds x 5 = 50 seconds
radius = 0.5 inches
Flow rate = 50 * 0.5³/5*10
= 1.25 inches/s
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