The proportion of people who preferred foreign cars than domestic cars is 0.24 and the confidence interval for the population proportion of new cars over domestic cars of 98% confidence interval is (641.955,642.045).
Given sample size of 2676 and number of people preferred foreign cars than domestic cars is 642.
We have to calculate the proportion of people who preferred foreign cars than domestic cars and the confidence interval which shows the confidence interval of 98%.
Number of people prefer foreign cars than domestic cars=642
Sample size=2676
Proportion=642/2676
=0.2399
=0.24 (After rounding off)
Now we will find confidence interval.
X=642
n=2676
z value for the confidence interval 98% is 2.33
Confidence interval =X± z*s/[tex]\sqrt{n}[/tex]
Upper =642+2.33*1/[tex]\sqrt{2676}[/tex] (we have taken s=1)
=642+0.045
=642.045
Lower=642-2.33*1/[tex]\sqrt{2676}[/tex]
642-0.045 (putting values in formula given above)
=641.955
Hence the proportion of people preferred foreign cars than domestic cars is 0.24 and the confidence interval is (641.955,642.045).
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Writing an Informative Essay about an Event in History? HURRY
When writing an informative essay about an event in history, you should:
Pick an engaging topic with several sources of information. Clearly state your thesis in your introduction. Use every paragraph to expand on a separate point. Avoid using long sentences. Reference sources accurately. How can you write an informative essay on historical events?To avoid finding it difficult to find information on your topics, pick a topic that has been well researched and has several sources of information on it. European history is well researched.
In the introduction, talk about why you think this topic is significant and include a thesis statement that would be the main logic you are producing details about.
Then divide this thesis into several points and talk about each point in a different paragraph. Use sentences that are not too long so that people don't lose interest.
Use primary and secondary information sources but make sure you reference these sources in the required format.
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In circle S, m/TSU = 72º and the length of TU = 67. Find the length of ST.
Using the arc length formula, the length of ST in the circle is: 15 units.
What is the Arc length Formula?Arc length of a circle = ∅/360 × 2πr.
In the image given, we have:
∅ = m∠TSU = 72º
Arc length TU = 6π
r = ST
Plug in the values
6π = 72/360 × 2π(ST)
6π = 0.2 × 2π(ST)
6π/2π = 0.2 × ST
3 = 0.2(ST)
3/0.2 = ST
ST = 15 units.
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Find the tangent of each acute angle in the triangle below. Select all that apply.
OPTIONS:
17/15
8/15
15/8
8/9
8/17
Answer: 8/15, 15/8
Step-by-step explanation:
By the Pythagorean theorem, the length of the unknown side is
[tex]\sqrt{17^{2}-8^{2}}=15[/tex]
So, the tangents of the acute angles are [tex]\boxed{\frac{8}{15}, \frac{15}{8}}[/tex]
A deck has side lengths 16 feet, 18 feet, 16 feet, 8 feet, and 12 feet.
The dimensions of a proposed deck are written on the floor plan. What is the area of the proposed deck? Round to the nearest square foot.
317 square feet
413 square feet
437 square feet
513 square feet
The area of the deck is 413 square feet
How to determine the area of the proposed deck?Start by calculating the area of the outer rectangle using:
Area = Length * Width
This gives
Area1 = (18 + 12) * (16 + 8)
Area1 = 720
Next, calculate the area of the inner rectangle using:
Area = Length * Width
This gives
Area2 = 16 * (18 + 8)
Area2 = 416
Subtract these areas
A1 = Area1 - Area2
A1 = 720 - 416
A1 = 304
Next, calculate the area of the outer semicircle using:
Area = 0.5πR²
This gives
Area1 = 0.5 * 3 * (12-1)²
Area1 = 181.5
Next, calculate the area of the inner semicircle using:
Area = 0.5πr²
This gives
Area2 = 0.5 * 3 * (7)²
Area2 = 73.5
Subtract these areas
A2 = Area1 - Area2
A2 = 181.5 - 73.5
A2 = 108
Add A1 and A2
A = 304 + 108
Evaluate the sum
A = 412
Hence, the area of the deck is 413 square feet
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[tex]\boxed{\bf{Help\;Please}}[/tex]
______________________
[tex]\boxed{\bf{Answer\;Requirements-:}}[/tex]
No spam
No absurd answers
[tex]\bf{Only}[/tex]
People who are good at Trigonometry
[tex]\bf{should\;answer}[/tex]
Answer:
There you go:[tex]y = 4 \cos(4\pi \: t + \frac{\pi}{4} ) [/tex]
[tex]y = a\cos(w\: t + \alpha ) [/tex]
[tex]w = 4\pi[/tex]
[tex]2\pi \: f = 4\pi[/tex]
[tex]f = 2[/tex]
Answer:
[tex]\displaystyle 2[/tex]
Step-by-step explanation:
[tex]\displaystyle y = Acos(Bx - C) + D[/tex]
When working with a trigonometric equation like this, always remember the information below:
[tex]\displaystyle Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A|[/tex]
So, the first procedure is to find the period of this graph, and when calculated, you should arrive at this:
[tex]\displaystyle \boxed{\frac{1}{2}} = \frac{2}{4\pi}\pi[/tex]
You will then plug this into the frequency formula, [tex]\displaystyle T^{-1} = F.[/tex] Look below:
[tex]\displaystyle \frac{1}{2}^{-1} = F \\ \\ \boxed{2 = F}[/tex]
Therefore, the frequency of motion is two hertz.
I am delighted to assist you at any time.
There are exactly 1,944 of the 12-, or 0.5-, cubes inside a rectangular prism.
What is the volume of the rectangular prism in cubic centimeters?
Enter your answer as a number, like this: 42
The volume of the rectangular prism is 3359232 cubic centimeters
How to determine the volume?The length of the cube is given as:
Length, l = 12 cm
The volume of a cube is:
[tex]V = l^3[/tex]
So, we have:
[tex]V = 12^3[/tex]
Evaluate
V = 1728
The volume of 1944 cubes is then calculated as:
Volume = 1728 * 1944
Evaluate
Volume = 3359232
Hence, the volume of the rectangular prism is 3359232 cubic centimeters
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Complete questionThere are exactly 1,944 of the 12 cm, or 0.5 foot cubes inside a rectangular prism. What is the volume of the rectangular prism in cubic centimeters?
Which is equivalent to (negative 2 m 5 n) squared, and what type of special product is it?
The difference of squares is 4m^2 - 20mn + 25n^2
Its a perfect square trinomial.
What is perfect square trinomial?A perfect square trinomial is the square of a binomial. It follows a pattern when it is factored, so that the first and last terms are perfect squares of monomials and the middle term is twice their product. If the pattern does not fit for a particular trinomial, it is not a perfect square trinomial.
How to solve this equation?(-2m + 5n)^2
(-2m + 5n)(-2m + 5n)
4m^2-10mn-10mn+25n^2
4m^2 - 20mn + 25n^2
Thus, the difference of squares is 4m^2 - 20mn + 25n^2
Its a perfect square trinomial.
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Triangle A B C is shown. Side A C has a length of 27. Side C B has a length of 54.
Based on the diagram, which expresses all possible lengths of segment AB?
AB = 25
27 < AB < 81
AB = 85
AB< 27 or AB > 81
All possible lengths of segment AB wil be 27 < AB < 81.Option b is correct
What is the triangle?A triangle is a three-sided polygon. It is one of the most fundamental geometric forms.
Any two triangle sides' lengths added together are longer than the third side's length.
The triangular inequality theorem is applied in three ways;
1.
AC+BC > AB
27+54 > AB
81 > AB
2.
27+AB > 54
AB> 54-27
AB > -27
3.
54+AB > 27
AB > 27-54
AB > -27
All possible lengths of segment AB wil be 27 < AB < 81.
Hence option b is correct
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Answer:
27 < AB < 81
Step-by-step explanation:
The answer above is correct.
Eva bought 3 rainbow trout for dinner. They weighed 3 Ib 5 oz, 2 Ib 12 oz, and 3 Ib 8 oz. She cut off the heads and the tails and was left with 8 Ib 2 oz. What was the amount of waste
The amount of waste is 22 oz
How to determine the waste amount?The weights of the 3 rainbow trouts are:
3 Ib 5 oz, 2 Ib 12 oz, and 3 Ib 8 oz.
The total weight is:
Total = 3 Ib 5 oz + 2 Ib 12 oz + 3 Ib 8 oz
Evaluate the sum
Total = 8 Ib 25 oz
The amount she was left with is 8 Ib 2 oz
Subtract this amount from the total
Waste = 8 Ib 25 oz - 8 Ib 2 oz
Evaluate
Waste = 22 oz
Hence, the amount of waste is 22 oz
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Find the value of x and uh yeah
Answer:
2nd option
Step-by-step explanation:
the quadrilateral has 1 pair of parallel sides and is therefore a trapezoid.
• each lower base angle is supplementary to the upper base angle on the same side, that is
∠ 1 + ∠ 2 = 180° , so
x + x + 50 = 180
2x + 50 = 180 ( subtract 50 from both sides )
2x = 130 ( divide both sides by 2 )
x = 65
then
∠ 1 = x = 65°
∠ 2 = x + 50 = 65 + 50 = 115°
CAN SOMEONE HELP ME PLEASE???
Answer:
16
Step-by-step explanation:
Referring to the diagram, we can use Pythagoras' Theorem to find ZY. (which is the distance from Point Y to WX)
By Pythagoras' Theorem,
[tex]c^{2} =a^{2} +b^{2} \\WY^{2} =WZ^{2} +ZY^{2} \\(16\sqrt{2}) ^{2} =16^{2} +ZY^{2} \\ZY^{2} = (16\sqrt{2}) ^{2} -16^{2} \\ZY^{2} =512-256\\ZY^{2} =256\\ZY=\sqrt{256} \\ZY=16[/tex]
6 in.
If you'd like,
you can use a
10 in.
SA 2πr² + 2πrh
Use 3.14 for T.
Find the surface area of
a cylinder with a height
of 10 inches and base
diameter of 6 inches.
Do NOT round your answer.
SA [?] square inches
=
The surface area of the cylinder is 244. 92 inches²
How to find surface area of a cylinder?surface area of a cylinder = 2πr(r + h)
where
r = radiush = heightTherefore,
r = 6 / 2 = 3 inches
h = 10 inches
surface area of a cylinder = 2 × 3.14 × 3(3 + 10)
surface area of a cylinder = 18.84(13)
surface area of a cylinder = 244.92
surface area of a cylinder = 244. 92 inches²
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alguien me puede ayudar por favor se los agradeceria mucho
El cuadrado completo es:
[tex]\left[\begin{array}{ccc}0.048&0.056&0.016\\0.008&0.04&0.072\\0.064&0.024&0.032\end{array}\right][/tex]
¿Como completar el cuadrado magico?Tenemos el cuadrado:
[tex]\left[\begin{array}{ccc}0.048&a&0.016\\b&c&0.072\\0.064&e&f\end{array}\right][/tex]
Y queremos encontrar los valores de las letras, tal que cada suma de columna, fila y de cada diagonal de 0.12,
Entonces tenemos:
0.048 + b + 0.064 = 0.12
b = 0.12 - 0.048 - 0.064 = 0.008
0.016 + 0.072 + f = 0.12
f = 0.12 - 0.016 - 0.072 = 0.032
Tambien las diagonales deben dar 0.12, entonces:
0.064 + c + 0.016 = 0.12
c = 0.12 - 0.016 - 0.064 = 0.04
Reemplazando esos valores obtenemos:
[tex]\left[\begin{array}{ccc}0.048&a&0.016\\0.008&0.04&0.072\\0.064&e&0.032\end{array}\right][/tex]
Ahora las filas tambien deben dar 0.12:
0.048 + a + 0.016 = 0.12
a = 0.12 - 0.048 - 0.016 = 0.056
0.064 + e + 0.032 = 0.12
e = 0.12 - 0.064 - 0.032 = 0.024
El cuadrado completo es:
[tex]\left[\begin{array}{ccc}0.048&0.056&0.016\\0.008&0.04&0.072\\0.064&0.024&0.032\end{array}\right][/tex]
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Suppose that there are 9 faculty members in the math department and 11 in the computer science department. How many ways are there to select a committee to develop a discrete math course if the committee is to consist of three faculty from the math department and four from the computer science department
There are 9240 ways to select a committee to develop a discrete math course if the committee is to consist of three faculty from the math department and four from the computer science department.
It is given that there are 9 faculty members in the math department and 11 in the computer science department.
[tex]C^{9} _{3} * C^{11} _{4}[/tex]
[tex]= \frac{9!}{(9-3)!3!} * \frac{11!}{(11-4)!4!}\\= 28 * 330\\= 9240[/tex]
Therefore, there are 9240 ways to select the committee.
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Benoît has a home business selling antique watches. If he sells x watches, in thousands, his profit, P, in thousands of dollars, is given by
P=−50x^2 + 550x − 900
Determine Benoît’s break-even points
Determine his maximum profit and how many antique watches he must sell to achieve this profit.
The number of watches that just be sold is 90 and the profit is -356400.
How to calculate the profit?From the information given, the equation is given as:
P = −50x² + 550x − 900
P = -5x² + 55x - 90
= -5x² + 45x + 10x - 90
= -5x(x - 9) + 10(x - 9)
= (-5x + 10)(x - 9)
x - 9 = 0
x = 0 + 9 = 9
The watches that must be sold will be (9 × 10) = 90
The profit will be:
P = −50x² + 550x − 900
P = -50(90)² + 550(90) - 900
P = -405000 + 49500 - 900
P = -356400
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there are 3 students in a class who are left-handed. given that the percentage of left handed students in the class is 7.5%, find the total number of students in this class
Answer:
40 total students
Explanation:
Total students: 100%
Let the number of total students be x.
Solving stepwise:
7.5% : 100% --> 3 : x
[tex]\rightarrow \sf \dfrac{7.5}{100} = \dfrac{3}{x}[/tex]
[tex]\rightarrow \sf 7.5x = 3(100)[/tex]
[tex]\rightarrow \sf 7.5x = 300[/tex]
[tex]\rightarrow \sf x =40[/tex]
Which expression is equivalent to the difference shown?
5x+1/5x - 4x+1/4x
Answer:
1 9/20x or 29/20x
Step-by-step explanation:
Reorder so it can be seen better
5x-4x+1/5x+1/4x
Combine like terms
x+1/5x+1/4x
Common multiple
x+4/20x+5/20x
Combine like terms
9/20x+x
Finalize
29/20x
Simplified
1 9/20x
Answer: -1/20x
Step-by-step explanation:
got all 5 correct this one was one of my five
what are the domain and range of the function represented by the set of ordered pairs {(-6,5),(-3,2),(-1,0),(5,-4)}
Answer:
Greetings !domain ={-6,-3,-1,5}to find domain just take the first values of each ordered pairs
range ={5,2,0,-4}to find the range just take the second values of each ordered pairs.
Please help if you want, would really appreciate it
Answer: 140°
Step-by-step explanation:
- all straight lines are 180°
- since ACD and DCB help to create the straight line they must equal 180° when combined
- so 180 - 40 = 140
- therefore, ACD is 40° and DCB is 140°
hope this helps :)
Solve this system of linear equations. Separate
the x- and y-values with a comma.
-7x + 6y = -5
2x + 4y = -10
Enter the correct answer.
Answer: x=-1 and y=-2
Which equation represents the transformed function below?
parent function; y=√x
= transformed function
If we know the concepts of transformations and horizontal translation and that f(x) = √x and k = - 2, then the transformed function is g(x) = √(x + 2).
How to determine the transformed function in terms of its parent function
The transformation of functions are operations which modify the relationship between input and outputs in a function. The parent function represents a canonical square root function and the transformed function is the consequence of applying a horizontal translation.
This kind of transformation is defined by the following expression:
g(x) = f(x - k) (1)
Where k represents a rightward translation for k > 0.
If we know that f(x) = √x and k = - 2, then the transformed function is g(x) = √(x + 2).
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]Triangle R Q S is cut by line segment T V. Line segment T V goes from side Q R to side R S. The length of R V is x + 10, the length of V S is x, the length of R T is x + 4, and the length of T Q is x minus 3.
Which value of x would make Line segment T V is parallel to Line segment Q S?
3
8
10
11
The value of 'x' that would make Line segment T V is parallel to Line segment Q S is 10. Option C
How to determine the valueIt is important to note that for line TV to be parallel to line QS, the sides of the triangle must be divided equally.
Thus, we have
RT/TQ = RV/VS
RT = x + 10
TQ = x - 3
RV = x + 10
VS = x
Substitute the value
[tex]\frac{x + 4}{x-3} = \frac{x + 10}{x}[/tex]
Cross multiply
(x+ 4) × x = (x + 10) × (x-3)
x² + 4x = x² -3x + 10x -30
Divide through by x²
4x = -3x + 10x - 30
Collect like terms
4x + 3x - 10x = - 30
-3x = -30
x = -30/ -3
x = 10
Thus, the value of 'x' that would make Line segment T V is parallel to Line segment Q S is 10 Option C
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Kim scored 15 points, which was 30% of the team's t
How many points did the team score in all?
Answer:
50 points
Step-by-step explanation:
Let the total points scored by the team = x
30% of x = 15 points
[tex]\sf \dfrac{30}{100}*x = 15\\\\[/tex]
[tex]\sf x = 15* \dfrac{100}{30}\\\\ x = 50[/tex]
The team scored 50 points.
Which of the following expressions are equivalent to -3 x -6/10
A. 3/6 x 1/10
B. -3/10 x -6
C. None of the above
Solve to find x and y in the diagram.
The figure shows two parallel lines and a transversal. The intersection of the first line and the transversal forms four angles, the top right angle is labeled as a right angle, the bottom right angle measures 6 times x plus 5 times y degrees. The intersection of the second line and the transversal forms four angles, the bottom right angle measures 10 times y degrees.
The values of x and y by the descriptions in the task content are; 7.5 and 9 respectively.
What are the values of x and y?It follows from the task content that the description in the task content registers the bottom right angle measure of the second intersection as equal to 10y.
Hence, it follows that; 10y = 90 and; y = 9.
From the first intersection; 6x + 5y = 90;
6x + 5(9) = 90
6x + 45 = 90
6x = 45
x = 45/6 = 7.5
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Simplify and state any restrictions on the variable. Remember the order of operations. Show all your work for full
marks!
Step-by-step explanation:
6+8-90+90008-70000000
PLS HELP THIS IS URGENT!
GIVING BRAINLIEST
Answer: 36
Step-by-step explanation:
[tex]\overline{AB} \cong \overline{BC}[/tex] (Triangle ABC is isosceles)
[tex]m\angle CAB=m\angle CBA=30^{\circ}[/tex] (base angles of an isosceles triangle are congruent)
[tex]\angle MCB=90^{\circ}[/tex] (In triangle CMB, angles in a triangle add to 180 degrees)
[tex]\angle ACM=30^{\circ}[/tex] (triangle sum theorem)
[tex]MB=24[/tex] (30-60-90 triangle CMB)
[tex]AB=12[/tex] (sides opposite congruent angles in a triangle are congruent)
[tex]AB=36[/tex] (segment addition postulate)
The value of AB = 36
What is an isosceles triangle?An isosceles triangle is a triangle with base angles equal with any two sides equal.
Analysis:
∠ACB = 120
ABC is isosceles, so ∠CAB = ∠CBA = x
x + x + 120 = 180 ( sum of angles in Δ ABC)
2x = 60
x = 30
∠AMC = 180 - ∠BMC( angles on a straight line)
= 180 - 60 = 120
∠ACM = 180 - (30 + 120) = 180 - 150 = 30°
∠MCB = 90°
using sine rule,
12/sin 30 = AM/ sin 30
AM = 12
MB/sin 90 = 12/sin30
MB sin 30 = 12 sin 90
MB = 12/sin 30 = 12/0.5 = 24
AB = MB + AM = 24 + 12 = 36
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Triangle QRS is to be dilated using the rule D Subscript P, three-fourths.
Point P is the center of dilation. Triangle Q R S is shown. The length of P S is 8.
What will be the distance from the center of dilation, P, to the image S'?
2 units
4 units
6 units
8 units
The distance from the center of dilation, P, to.the image vertice S' is; 6 units.
What is the distance from the center of dilation, P, to the image S'?It follows from the task content that the center of dilation of the triangle QRS is point P and the length of segment PS in the pre-image is; 8 units.
Ultimately, since the dilation factor is; three-fourths, it therefore follows that the distance of point P to S' in the image is; (3/4) × 8 = 6 units.
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Answer: OPTION C
Step-by-step explanation:
Name the set(s) of numbers to which -10 belong
-10 belongs to the set of negative integers and rational numbers and also belongs to the set of real numbers.
For the following exercises, graph the given functions by hand.
48. f(x) = | 2x − 4 | − 3
A horizontal translation of the function by 4 units and a vertical translation down by 3 units
Graph of modulus functionThe parent function of the given function is g(x) = |x|. The resulting function (x) = | 2x − 4 | − 3 shows the following translations
A vertical stretch of the graph by 2 units
A horizontal translation of the function by 4 units and a vertical translation down by 3 units
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