Answer:
A. 804Step-by-step explanation:
Given the total number of students in the school to be 2229 students. If among a sample of 452 students from this school district, 163 have mathematics scores below grade level, then we can determine the number of students in this school district with mathematics scores below grade level based on the sample scores using ratio.
Let the number of students in this school district with mathematics scores below grade level be x. The ratio of the students with math score below grade level to total population will be x:2229
Also, the ratio of the sample students with math score below grade level to sample population will be 163:452
On equating both ratios, we will have;
x:2229 = 163:452
[tex]\dfrac{x}{2229} = \dfrac{163}{452}\\ \\cross\ multiplying;\\\\\\452*x = 2229*163\\\\x = \dfrac{2229*163}{452}\\ \\x = \frac{363,327}{452}\\ \\x = 803.8\\\\x \approx 804[/tex]
Hence the estimate of the number of students in this school district with mathematics scores below grade level based on the sample is 804
isted below are amounts (in millions of dollars) collected from parking meters by a security service company and other companies during similar time periods. Do the limited data listed here show evidence of stealing by the security service company's employees? Security Service Company: 1.5 1.7 1.6 1.4 1.7 1.5 1.8 1.4 1.4 1.5 Other Companies: 1.8 1.9 1.6 1.7 1.8 1.9 1.6 1.5 1.7 1.8 Find the coefficient of variation for each of the two samples, then compare the variation. The coefficient of variation for the amount collected by the security service company is nothing%. (Round to one decimal place as needed.)
Answer:
Means:
1.55
1.73
Standard Deviation:
0.1434
0.1338
Coefficient of variation:
9.2
7.7
the limited data listed here shows evidence of stealing by the security service company's employees.
Step-by-step explanation:
Given data:
security Service Company Other Companies
x₁ x₂
1.5 1.8
1.7 1.9
1.6 1.6
1.4 1.7
1.7 1.8
1.5 1.9
1.8 1.6
1.4 1.5
1.4 1.7
1.5 1.8
n₁ = 10 n₂ = 10
To find:
coefficient of variation for each of the two samples
Solution:
The formula for calculating coefficient of variation of sample is:
Coefficient of Variation (CV) = (Standard Deviation / Mean) * 100%
Calculate Mean for Security Service Company data:
Mean = (Σ x₁) / n₁
= (1.5 + 1.7 + 1.6 + 1.4 + 1.7 + 1.5 + 1.8 + 1.4 + 1.4 + 1.5) / 10
= 15.5 / 10
Mean = 1.55
Calculate Standard Deviation for Security Service Company data:
Standard Deviation = √∑(x₁ - Mean)²/n₁-1
= √∑(1.5-1.55)² + (1.7-1.55)² + (1.6-1.55)² + (1.4-1.55)² + (1.7-1.55)² + (1.5-1.55)² + (1.8-1.55)² + (1.4-1.55)² + (1.4-1.55)² + (1.5-1.55)² / 10-1
=√∑ (−0.05)² + (0.15)² + (0.05)² + (−0.15)² + (0.15)² + (−0.05)² + (0.25)² + (−0.15)² + (−0.15)² + (−0.05)² / 10 - 1
= √∑0.0025 + 0.0225 + 0.0025 + 0.0225 + 0.0225 + 0.0025 + 0.0625 + 0.0225 + 0.0225 + 0.0025 / 9
= √0.185 / 9
= √0.020555555555556
= 0.14337208778404
= 0.143374
Standard Deviation = 0.143374
Coefficient of Variation for Security Service Company:
CV = (Standard Deviation / Mean) * 100%
= (0.143374 / 1.55) * 100
= 0.09249935 * 100
= 9.249935
CV = 9.2
CV = 9.2%
Calculate Mean for Other Companies data:
Mean = (Σ x₂) / n₂
= (1.8 + 1.9 + 1.6 + 1.7 + 1.8 + 1.9 + 1.6 + 1.5 + 1.7 + 1.8) / 10
= 17.3 / 10
Mean = 1.73
Calculate Standard Deviation for Other Companies data:
Standard Deviation = √∑(x₂-Mean)²/n₂-1
= √∑[(1.8-1.73)² + (1.9-1.73)² + (1.6-1.73)² + (1.7-1.73)² + (1.8-1.73)² + (1.9-1.73)² + (1.6-1.73)² + (1.5-1.73)² + (1.7-1.73)² + (1.8-1.73)²] / 10 - 1
= √∑ [(0.07)² + (0.17)² + (-0.13)² + (-0.03)² + (0.07)² + (0.17)² + (-0.13)² + (-0.23)² + (-0.03)² + (0.07)²] / 9
= √∑ (0.0049 + 0.0289 + 0.0169 + 0.0009 + 0.0049 + 0.0289 + 0.0169 + 0.0529 + 0.0009 + 0.0049) / 9
= √(0.161 / 9)
= √0.017888888888889
= 0.13374935098493
= 0.13375
Standard Deviation = 0.13375
Coefficient of Variation for Other Companies:
CV = (Standard Deviation / Mean) * 100%
= (0.13375 / 1.73) * 100
= 0.077312 * 100
= 7.7312
CV = 7.7
CV = 7.7%
Yes, the limited data listed here shows evidence of stealing by the security service company's employees because there is a significant difference in the variation.
for the functions f(x) = 4x^4+4x^3-8x^2-13x-5 and g(x) = x+1, find (f/g)(x) and (f/g)(2)
Answer:
(f/g)(x) = 4x³ - 8x - 5(f/g)(2) = 11Step-by-step explanation:
f(x) = 4x⁴ + 4x³ - 8x² - 13x - 5
g(x) = x + 1
To find (f/g)(2) first find (f/g)(x)
To find (f/g)(x) factorize f(x) first
That's
f(x) = 4x⁴ + 4x³ - 8x² - 13x - 5
f(x) = ( x + 1)( 4x³ - 8x - 5)
So we have
[tex] (f/g)(x) = \frac{( x + 1)( 4x³ - 8x - 5)}{x + 1} [/tex]
Simplify
We have
(f/g)(x) = 4x³ - 8x - 5To find (f/g)(2) substitute 2 into (f/g)(x)
That's
(f/g)(2) = 4(2)³ - 8(2) - 5
= 4(8) - 16 - 5
= 32 - 16 - 5
= 11
(f/g)(2) = 11Hope this helps you
What is 4/5 to the 5th power
Find the missing side or angle.
Round to the nearest tenth.
Answer:
65.8
Step-by-step explanation:
Use the sin formula
100/sin (28) = x/ sin (18)
(sin (18) (100))/ sin (28) = x
x = 65.8223
x = 65.8
Answer:
65.8
Step-by-step explanation:
Accellus Correct
Given that −4i is a zero, factor the following polynomial function completely. Use the Conjugate Roots Theorem, if applicable. f(x)=x4−2x3+x2−32x−240
Answer:
[tex]\large \boxed{\sf \bf \ \ f(x)=(x-4i)(x+4i)(x+3)(x-5) \ \ }[/tex]
Step-by-step explanation:
Hello, the Conjugate Roots Theorem states that if a complex number is a zero of real polynomial its conjugate is a zero too. It means that (x-4i)(x+4i) are factors of f(x).
[tex]\text{Meaning that } (x-4i)(x+4i) =x^2-(4i)^2=x^2+16 \text{ is a factor of f(x).}[/tex]
The coefficient of the leading term is 1 and the constant term is -240 = 16 * (-15), so we a re looking for a real number such that.
[tex]f(x)=x^4-2x^3+x^2-32x-240\\\\ =(x^2+16)(x^2+ax-15)\\\\ =x^4+ax^3-15x^2+16x^2+16ax-240[/tex]
We identify the coefficients for the like terms, it comes
a = -2 and 16a = -32 (which is equivalent). So, we can write in [tex]\mathbb{R}[/tex].
[tex]\\f(x)=(x^2+16)(x^2-2x-15)[/tex]
The sum of the zeroes is 2=5-3 and their product is -15=-3*5, so we can factorise by (x-5)(x+3), which gives.
[tex]f(x)=(x^2+16)(x^2-2x-15)\\\\=(x^2+16)(x^2+3x-5x-15)\\\\=(x^2+16)(x(x+3)-5(x+3))\\\\=\boxed{(x^2+16)(x+3)(x-5)}[/tex]
And we can write in [tex]\mathbb{C}[/tex]
[tex]f(x)=\boxed{(x-4i)(x+4i)(x+3)(x-5)}[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
How many g of amino acids are in a 2,000mL total parenteral nutrition of 4.25% travesol (amino acids and 20%dextrose?
Answer:
The mass of amino acid present is 85 g
Step-by-step explanation:
From the question we are told that
The volume of the total parenteral nutrition is [tex]V = 2000 mL[/tex]
Generally the volume of the amino acid present is
[tex]V_a = 0.0425 * 2000[/tex]
[tex]V_a = 85 mL[/tex]
Generally
[tex]mass \ \ \alpha \ \ volume[/tex]
So the mass of amino acid present is 85g
A ladder 10 ft long leans against a vertical wall. If the lower end is being moved away from the wall at the rate of 6 ft/sec, how fast is the height of the top changing (this will be a negative rate) when the lower end is 6 feet from the wall?
Answer:
-4.5ft per sec
Step-by-step explanation:
Assume that vertical wall has a distance of y and the horizontal floor is x (6 ft).
This forms a triangle with the ladder as the hypothenus of length 10ft
We have dy/dt = 6ft per sec
According to Pythagoras law the relationship between x and y is
(x^2) + (y^2) = (hypothenus ^2) = 10^2
When we differentiate both sides of the equation
2x(dx/dt) + 2y(dy/dt) = 0
dy/dt = (x/y) * (dx/dt)
y= √(10^2) - (6^2) = 8ft
So dy/dt = (6/8)* (6/1)= -4.5 ft per sec
It is a negative rate
which of the following best describes the bases of a cylinder? A. Congruent B. Polygons C. Parallel D. Discs (Check All That Apply)
Answer:
A. Congruent and D. Discs
Step-by-step explanation:
You won't see a cylinder that doesn't have congruent bases
Look at the shape of the bases and look at a disc compare their shape
We can describe the bases of a cylinder as congruent.
What is the volume of cylinder?The volume of cylinder is given by -
V = πR²h
Given is to describe the bases of a cylinder.
The cylinders are uniform in cross - section. Therefore, the bases of the cylinder will have the same area. So, we can conclude that the given bases are congruent.
Therefore, we can describe the bases of a cylinder as congruent.
To solve more questions on cylinders, visit the link below-
https://brainly.com/question/16134180
#SPJ7
In a binomial distribution, n = 8 and π=0.36. Find the probabilities of the following events. (Round your answers to 4 decimal places.)
a. x=5
b. x <= 5
c. x>=6
Answer:
[tex]\mathbf{P(X=5) =0.0888}[/tex]
P(x ≤ 5 ) = 0.9707
P ( x ≥ 6) = 0.0293
Step-by-step explanation:
The probability of a binomial mass distribution can be expressed with the formula:
[tex]\mathtt{P(X=x) =(^{n}_{x} ) \ \pi^x \ (1-\pi)^{n-x}}[/tex]
[tex]\mathtt{P(X=x) =(\dfrac{n!}{x!(n-x)!} ) \ \pi^x \ (1-\pi)^{n-x}}[/tex]
where;
n = 8 and π = 0.36
For x = 5
The probability [tex]\mathtt{P(X=5) =(\dfrac{8!}{5!(8-5)!} ) \ 0.36^5 \ (1-0.36)^{8-5}}[/tex]
[tex]\mathtt{P(X=5) =(\dfrac{8!}{5!(3)!} ) \ 0.36^5 \ (0.64)^{3}}[/tex]
[tex]\mathtt{P(X=5) =(\dfrac{8 \times 7 \times 6 \times 5!}{5!(3)!} ) \times \ 0.0060466 \ \times 0.262144}[/tex]
[tex]\mathtt{P(X=5) =(\dfrac{8 \times 7 \times 6 }{3 \times 2 \times 1} ) \times \ 0.0060466 \ \times 0.262144}[/tex]
[tex]\mathtt{P(X=5) =({8 \times 7 } ) \times \ 0.0060466 \ \times 0.262144}[/tex]
[tex]\mathtt{P(X=5) =0.0887645}[/tex]
[tex]\mathbf{P(X=5) =0.0888}[/tex] to 4 decimal places
b. x ≤ 5
The probability of P ( x ≤ 5)[tex]\mathtt{P(x \leq 5) = P(x = 0)+ P(x = 1)+ P(x = 2)+ P(x = 3)+ P(x = 4)+ P(x = 5})[/tex]
[tex]{P(x \leq 5) = ( \dfrac{8!}{0!(8!)} \times (0.36)^0 \times (1-0.36)^8 \ ) + \dfrac{8!}{1!(7!)} \times (0.36)^1 \times (1-0.36)^7 \ +[/tex][tex]\dfrac{8!}{2!(6!)} \times (0.36)^2 \times (1-0.36)^6 \ + \dfrac{8!}{3!(5!)} \times (0.36)^3 \times (1-0.36)^5 + \dfrac{8!}{4!(4!)} \times (0.36)^4 \times (1-0.36)^4 \ + \dfrac{8!}{5!(3!)} \times (0.36)^5 \times (1-0.36)^3 \ )[/tex]
P(x ≤ 5 ) = 0.0281+0.1267+0.2494+0.2805+0.1972+0.0888
P(x ≤ 5 ) = 0.9707
c. x ≥ 6
The probability of P ( x ≥ 6) = 1 - P( x ≤ 5 )
P ( x ≥ 6) = 1 - 0.9707
P ( x ≥ 6) = 0.0293
"Julien is trying to determine his variable type in order to select the proper statistical tests. He is measuring the height of a part. What type of variable is this"
Answer:
Quantitative
Step-by-step explanation: Quantitative or numerical variable are statistical or measured variables which involves numbers. Numerical variables allows for mathematical operations such as addition, subtraction and so on to be performed in them. Quantitative variables include height, age, weight, population and other measured variable with have numerical attributes. They can be measured on either ordinal, ratio or interval scales. Hence, since Julien is trying to determine height, the variable is a quantitative or numeric variable.
what is the difference between growth and development
Answer:
growth is usually reffered to as physical growth happening in size while development happens more gradually and happens mentally.
Step-by-step explanation:
idk if u meant pyscologically or not but that is my understanding.
Explain how to solve the inequality (x + 1)(x – 2) ∙ (x – 3) > 0. Explain in your own words, each step necessary to solve the inequality, making sure to follow the proper order of operations. Is this inequality accurate? Explain why or why not.
Answer:
[tex]x > -1[/tex] or
[tex]x > 2[/tex] or
[tex]x > 3[/tex]
Step-by-step explanation:
Given
[tex](x + 1)(x - 2) (x - 3) > 0[/tex]
Required
Solve; with steps
[tex](x + 1)(x - 2) (x - 3) > 0[/tex]
Start by splitting the inequality as follows
[tex]x + 1 > 0[/tex] or [tex]x - 2 > 0[/tex] or [tex]x - 3 > 0[/tex]
Solve the inequalities one after the other
Solving: [tex]x + 1 > 0[/tex]
Subtract 1 from both sides
[tex]x + 1 - 1 > 0 - 1[/tex]
[tex]x > -1[/tex]
Solving: [tex]x - 2 > 0[/tex]
Add 2 to both sides
[tex]x - 2 +2 > 0 +2[/tex]
[tex]x > 2[/tex]
Solving: [tex]x - 3 > 0[/tex]
Add 3 to both sides
[tex]x - 3 +3> 0+3[/tex]
[tex]x > 3[/tex]
Hence, the solution to the inequality is
[tex]x > -1[/tex] or
[tex]x > 2[/tex] or
[tex]x > 3[/tex]
HCF of x minus 2 and X square + X - 6
Answer:
[tex] \boxed{ \sf{ \bold{ \huge{ \boxed{x - 2}}}}}[/tex]Step-by-step explanation:
[tex] \sf{x - 2} \: and \: { {x}^{2} + x - 6}[/tex]
To find the H.C.F of the algebraic expressions, they are to be factorised and a common factor or the product of common factors is obtained as their H.C.F
Let's solve
First expression = x - 2
Second expression = x + x - 6
Here, we have to find the two numbers which subtracts to 1 and multiplies to 6
= x + ( 3 - 2 ) x + 6
Distribute x through the parentheses
= x + 3x - 2x + 6
Factor out x from the expression
= x ( x + 3 ) - 2x + 6
Factor out -2 from the expression
= x ( x + 3 ) - 2 ( x + 3 )
Factor out x+3 from the expression
= ( x + 3 ) ( x - 2 )
Here, x - 2 is common in both expression.
Thus, H.C.F = x - 2
Hope I helped!
Best regards!!!
Answer:
x - 2
Step-by-step explanation:
by factorization method
1) x - 2
2) x^2 + x - 6
by splitting method
x^2 + 3x - 2x - 6
taking separate common from the first two terms and last two terms
x(x + 3) - 2(x + 3)
now writing x+3 once and the other term to get the right answer
(x + 3)(x - 2)
in both parts just see the similar term and write it as HCF
HCF= x - 2
and the second method by which you can get this answer is division method
BRAINLIEST IF CORRECT!!! and 15 points solve for z -cz + 6z = tz + 83
Answer:
z = 83/( -c+6-t)
Step-by-step explanation:
-cz + 6z = tz + 83
Subtract tz from each side
-cz + 6z -tz= tz-tz + 83
-cz + 6z - tz = 83
Factor out z
z( -c+6-t) = 83
Divide each side by ( -c+6-t)
z( -c+6-t)/( -c+6-t) = 83/( -c+6-t)
z = 83/( -c+6-t)
A certain vector in the xy plane has an x component of 4 m and a y component of 10 m. It is then rotated in the xy plane so its x component is doubled. Its new y component is about:
Answer:
New length of component y' = 7.2 m (Approx)
Step-by-step explanation:
Given:
Length of component x = 4 m
Length of component y = 10 m
New length of component x' = 8 m
Find:
New length of component y' = ?
Computation:
Length vector of rotation = √x² + y²
Length vector of rotation = √4² + 10²
Length vector of rotation = √16 + 100
Length vector of rotation = √116
Length vector of rotation = √x'² + y'²
√116 = √x'² + y'²
116 = x'² + y'²
116 = 8² + y'²
New length of component y' = 7.2 m (Approx)
Use the graph of f to estimate the local maximum and local minimum. Local maximum: (0,1); local minimum: three pi over two, negative 1 and negative pi, negative 1 Local maximum: (0,0) and approx (0,1); local minimum: negative three pi over two, negative 1 Local maximum: (0,0); local minimum: three pi over two, negative 1 Local maximum: (0,1); local minimum: approx. (0,0) and three pi over two, negative 1
Answer:
The answer is A.
Step-by-step explanation:
Local maximums are whenever the graph reaches it's highest y value.
Local minimums are whenever the graph reaches it's lowest y value.
From the graph, we can see that the maximum y-value the graph reaches is y=1. And this happens when x=0.
This only happens once (from the graph shown). Thus, the local maximum would be:
[tex](0,1)[/tex]
The minimum values we can see from the graph is at y=-1. This happens twice from the graph, once at -π and again at 3π/2.
Thus, the local minimums are:
[tex](-\pi,-1), (3\pi/2,-1)[/tex]
A triangle has vertices at (-4,-6),(3,3),(7,2). Rounded to two decimal places, which of the following is closest aporoximation of the perimeter of the triangle
Answer:
Perimeter= 29.12 unit
Step-by-step explanation:
Perimeter of the triangle is the length of the three sides if the triangle summef up together
Let's calculate the length of each side.
For (-4,-6),(3,3)
Length= √((3+4)²+(3+6)²)
Length= √((7)²+(9)²)
Length= √(49+81)
Length= √130
Length= 11.40
For (-4,-6),(7,2)
Length= √((7+4)²+(2+6)²)
Length= √((11)²+(8)²)
Length= √(121+64)
Length= √185
Length= 13.60
For (3,3),(7,2)
Length=√( (7-3)²+(2-3)²)
Length= √((4)²+(-1)²)
Length= √(16+1)
Length= √17
Length= 4.12
Perimeter= 4.12+13.60+11.40
Perimeter= 29.12 unit
1) Dada a função, em reais, definida por f(x)=3.x-5. calcule :
a) f(2)=
b) f(-1)=
Answer:
f(x)= 3x-5
f(2) = 3(2)-5 = 6-5= 1
f(-1)= 3(-1)-5= -3-5= -8
Hope this helps
if u have question let me know in comments ^°^
nd the measure of angle m
2. Find the length of sie
m
18.2m
61°
15:1m
х
105mm
Answer:
1). m° = 56.1°
2). X= 91.8 mm
Step-by-step explanation:
For angle m°
Using the sine rule
15.1/sin m= 18.2/sin 90
But Sin 90= 1
15.1/sin m= 18.2
15.1= 18.2*sin m
Sin m = 15.1/18.2
Sin m=0.8297
m= sin^-1(0.8297)
m= 56.06°
m° = 56.1°
For length of side x
Using sine rule
X/sin 61= 105/sin 90
But sin 90= 1
X/sin 61= 105
X = sin61 *105
X=0.8746*105
X= 91.833 mm
X= 91.8 mm
i will rate you brainliest
Answer:
(3x+11)/ (5x-9)
Step-by-step explanation:
The numerator is what is on the top of the bar in the middle
(3x+11)/ (5x-9)
Answer:
[tex]\large \boxed{\mathrm{Option \ B}}[/tex]
Step-by-step explanation:
The numerator of a fraction is the top section of the fraction.
These two triangles are congruent by the Hypotenuse-Leg Theorem.
Answer:
[tex] y = - 2 [/tex]
Step-by-step explanation:
Given that the 2 triangles are congruent based on the Hypotenuse-leg theorem, this implies that:
[tex] x - y = x + 2 [/tex] , and [tex] 2x - y = 4x + 2y [/tex]
Using the expression, [tex] x - y = x + 2 [/tex], solve for y:
[tex] x - y - x = x + 2 - x [/tex]
[tex] - y = 2 [/tex]
[tex] y = - 2 [/tex]
Kyle buys $30,000 of company XYZ's shares, at a share price of $50. A year later, XYZ's share price is $55, and Kyle sells all his shares. How many dollars did Kyle's investment gain
Answer:
$3,000
Step-by-step explanation:
Given that the shares are $50 per share and that Kyle buys $30,000 worth of shares,
Number of shares bought = total price of shares ÷ price per share
= $30,000 ÷ $50
= 600 shares
We are also give that a year later, the shares are worth $55
Total value of shares 1 year later = Price per share one year later x number of shares
= $55 x 600
= $33,000
Hence the investment gained $33,000 - $30,000 = $3,000
Answer:
10%
Step-by-step explanation:
x - amount of shares bought
x * 50[$] = 30000[$]
x = 30000/50 = 600
if he bought 600 shares then he sold earning in total:
600 * 55[$] = 33000[$]
that means investmant gain can be calculate as:
return on investment = (gain from investment – cost of investment) / cost of investment
return on investment = (33000 - 30000) / 30000 = 3000/30000 =0.1 = 10%
A ball is released at a height of 16 inches to roll inside a half-cylinder. It rolls
to a height of 8 inches on the other side of the cylinder on roll 1. Each time it
rolls up a side of the cylinder, the ball reaches a point that is as high as it
had reached on the other side.
-lo
This explicit formula models the height of the ball, in inches, the nth time it
rolls up a side of the cylinder.
How high does the ball roll on its 5th time up the cylinder's side?
Answer:
Step-by-step explanation:
Using the given formula, we put n = 5
[tex]h = 8* {(\frac{1}{2}) ^{n-1}[/tex]
h = 8 / 16
h = 1 / 2 inches
the terms in this sequence increase by the same amount each time. _19_ _ 34_ a) work out the missing terms.
Answer:
The sequence is 14, 19, 24, 29, 34, 39.
Step-by-step explanation:
Let's call the common difference (the difference between two consecutive terms) as d. We see that the second term is 19 and the 5th term is 34 and since 5 - 2 = 3, we add d 3 times to 19 to get 34 so therefore:
19 + 3d = 34
3d = 15
d = 5 so the first term is 19 - 5 = 14, the third would be 19 + 5 = 24, the fourth would be 24 + 5 = 29 and the sixth would be 34 + 5 = 39.
how many solutions are there to this non-linear systems/graph a. one solution,b.two solutions,c.no solutions
Identify which equations have one solution, infinitely many solutions, or no solution. No solution: One solution: Infinitely solution:
Answer:
Top left: no
Top middle: one
Top right: no
Bottom left: infinite
Bottom middle: one
Bottom right: one
Step-by-step explanation:
Top left: no
Top middle: one
Top right: no
Bottom left: infinite
Bottom middle: one
Bottom right: one
Find all solutions to the equation. 2sin theta - squareroot 3 = 0
Write your answer in radians in terms of pi, and use the "or" button as necessary.
Example: theta = pi/5 + 2 k pi, k element Z or theta = pi/7 + k pi, k element Z
Answer:
[tex]\theta[/tex] =2mπ + π/3 for m ∈ Z.
Step-by-step explanation:
Given the equation [tex]2sin\theta - \sqrt{3} = 0[/tex], we are to find all the values of [tex]\theta[/tex] that satisfies the equation.
[tex]2sin\theta - \sqrt{3} = 0\\\\2sin\theta = \sqrt{3} \\\\sin\theta = \sqrt{3}/2 \\\\\theta = sin{-1} \sqrt{3}/2 \\\\\theta = 60^0[/tex]
General solution for sin[tex]\theta[/tex] is [tex]\theta[/tex] = nπ + (-1)ⁿ ∝, where n ∈ Z.
If n is an even number say 2m, then [tex]\theta[/tex] = (2m)π + ∝ where ∝ = 60° = π/3
Hence, the general solution to the equation will be [tex]\theta[/tex] = 2mπ + π/3 for m ∈ Z.
Ethan has collected 417 football cards. He shares them equally between himself and his two friends. How many will each person get
Answer:
139 cards
Step-by-step explanation:
This is basically just a division statement - we have 417 cards and want to split it with 3 people (two friends + himself = 3 people).
We can divide these using a calculator or long division, but either way you will get:
[tex]417\div3=139[/tex]
Hope this helped!
Answer: 139
Step-by-step explanation:
417 divided by 3 gives you 139.
Is 1.45 times 10 to the -7 power a scientific notation
Answer:
Yes.
It is 1.45 x 10^-7 or 0.000000145
Hope it helps!
Answer:
It is 1.45 x 10^-7 or 0.000000145
Step-by-step explanation:
The head of a computer science department is interested in estimating the proportion of students entering the department who will choose the new computer engineering option. Suppose there is not information about the proportion of students who might choose the option. What size sample should the department head take if he wants to be 95% confident that the estimate is within 0.10 of the true proportion
Answer:
96
Step-by-step explanation:
From the given information:
At 95% Confidence interval level,Level of significance [tex]\alpha[/tex] 0.05, the value of Z from the standard normal tables = 1.96
Margin of Error = 0.10
Let assume that the estimated proportion = 0.5
therefore; the sample size n can be determined by using the formula: [tex]n =(\dfrac{Z}{E})^2 \times p\times (1-p)[/tex]
[tex]n =(\dfrac{1.96}{0.1})^2 \times 0.5\times (1-0.5)[/tex]
[tex]n =(19.6)^2 \times 0.5\times (0.5)[/tex]
n = 96.04
n [tex]\approx[/tex] 96
