Answer:
That would be written as $16,800.00, or as $19,811.90 if you convert it at the current rate of exchange.
Step-by-step explanation:
Periods are used in European numbers to split up each third placed number while commas are used in the U.S.
Answer:
= 19824 us dollars
Step-by-step explanation:
Today august 09 2020:
1€ = 1.18 us dollars
then:
16800€ = 16800*1.18 = 19824 us dollars
Find the work done by the force field F(x,y,z)=6xi+6yj+6k on a particle that moves along the helix r(t)=3 cos(t)i+3sin(t)j+2 tk,0≤t≤2π.
Answer:
the work done by the force field = 24 π
Step-by-step explanation:
From the information given:
r(t) = 3 cos (t)i + 3 sin (t) j + 2 tk
= xi + yj + zk
∴
x = 3 cos (t)
y = 3 sin (t)
z = 2t
dr = (-3 sin (t)i + 3 cos (t) j + 2 k ) dt
Also F(x,y,z) = 6xi + 6yj + 6k
∴ F(t) = 18 cos (t) i + 18 sin (t) j +6 k
Workdone = 0 to 2π ∫ F(t) dr
[tex]\mathbf{= \int \limits ^{2 \pi} _{0} (18 cos (t) i + 18 sin (t) j +6k)(-3 sin (t)i+3cos (t) j +2k)\ dt}[/tex]
[tex]\mathbf{= \int \limits ^{2 \pi} _{0} (-54 \ cos (t).sin(t) + 54 \ sin (t).cos (t) + 12 ) \ dt}[/tex]
[tex]\mathbf{= \int \limits ^{2 \pi} _{0} 12 \ dt}[/tex]
[tex]\mathbf{= 12 \times 2 \pi}[/tex]
= 24 π
If the sin of angle x is 4 over 5 and the triangle was dilated to be two times as big as the original, what would be the value of the sin of x for the dilated triangle? Hint—Use the slash symbol ( / ) to represent the fraction bar, and enter the fraction with no spaces. (4 points)
Answer:
Sin of x does not change
Step-by-step explanation:
Whenever a triangle is dilated, the angle remains the same as well as the ratio for sides of triangle. For smshapes with dimensions, when shapes are dilated the dimensions has increment with common factor.
From trigonometry,
Sin(x)=opposite/hypotenose
Where x=4/5
Sin(4/5)= opposite/hypotenose
But we were given the scale factor of 2 which means the dilation is to two times big.
Then we have
Sin(x)=(2×opposite)/(2×hypotenose)
Then,if we divide by 2 the numerator and denominator we still have
Sin(x)=opposite/hypotenose
Which means the two in numerator and denominator is cancelled out.
Then we still have the same sin of x. as sin(4/5)
Hence,Sin of x does not change
Answer:
Step-by-step explanation:
sin of angle x = [tex]\frac{4}{5}[/tex]
If the triangle is dilated 2 times - it becomes two time larger.
4 times 2 = 8 and 5 times 2 = 10
So the ratio would be [tex]\frac{8}{10}[/tex], which when reduced (divide numerator and denominator by 2) becomes [tex]\frac{4}{5}[/tex].
This is correct as dilation changes the size of an image - but not its angles or proportions, meaning ratios remain the same.
So the answer is 4/5.
cSuppose you are standing such that a 45-foot tree is directly between you and the sun. If you are standing 200 feet away from the tree and the tree casts a 225-foot shadow, how tall could you be and still be completely in the shadow of the tree? x 225 ft 200 ft 45 ft Your height is ft (If needed, round to 1 decimal place.)
Answer:
you could stand at 5.0 ft and still be completely in the shadow of the tree
Step-by-step explanation:
From the diagram attached below;
We consider;
[tex]\overline {BC}[/tex] to be the height of the tree and [tex]\overline {DE}[/tex] to be the height of how tall you could be and still be completely in the shadow of the tree.
∠D = ∠B = 90°
Also;
ΔEAD = ΔBAC (similar triangles)
Therefore, their sides will also be proportional
i.e
[tex]\dfrac{\overline {DE}}{ \overline {BC}}= \dfrac{\overline{AD}}{ \overline{AC}}[/tex]
[tex]\dfrac{x}{ 45}= \dfrac{225-220}{225}[/tex]
[tex]\dfrac{x}{ 45}= \dfrac{25}{225}[/tex]
By cross multiply
225x = 45 × 25
[tex]x = \dfrac{45 \times 25}{225}[/tex]
[tex]x = \dfrac{1125}{225}[/tex]
x = 5.0 ft
Therefore, you could stand at 5.0 ft and still be completely in the shadow of the tree
Listed below are numbers of Internet users per 100 people and numbers of scientific award winners per 10 million people for different countries. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the P-value of r. Determine whether there is sufficient evidence to support a claim of linear correlation between the two variables. Use a significance level of α= 0.01.
Internet Users 80.3 78.2 56.4 67.6 77.7 38.6
Award Winners 5.6 9.3 3.2 1.6 10.9 0.1
Required:
a. Construct a scatterplot.
b. Determine the null and alternative hypotheses.
c. The test statistic is:_________
d. The P-value is:_________
Answer:
There is not sufficient evidence to support a claim of linear correlation between the two variables.
Step-by-step explanation:
(a)
The scatter plot for the provided data is attached below.
(b)
The hypothesis to test significance of linear correlation between the two variables is:
H₀: There is no linear correlation between the two variables, i.e. ρ = 0.
Hₐ: There is a significant linear correlation between the two variables, i.e. ρ ≠ 0.
(c)
Use the Excel function: =CORREL(array1, array2) to compute the correlation coefficient, r.
The correlation coefficient between the number of internet users and the award winners is,
r = 0.786.
The test statistic value is:
[tex]t=r\sqrt{\frac{n-2}{1-r^{2}}}[/tex]
[tex]=0.786\times\sqrt{\frac{6-2}{1-(0.786)^{2}}}\\\\=2.5427\\\\\approx 2.54[/tex]
Thus, the test statistic is 2.54.
(d)
The degrees of freedom is,
df = n - 2
= 6 - 2
= 4
Compute the p-value as follows:
[tex]p-value=2\cdot P(t_{n-2}<2.54)=2\times 0.032=0.064[/tex]
*Use a t-table.
p-value = 0.064 > α = 0.05
The null hypothesis will not be rejected.
Thus, it can be concluded that there is not sufficient evidence to support a claim of linear correlation between the two variables.
An 8×8×8 cm cube was painted red, and then broken up into small cubes with side lengths of 1 cm. How many small cubes have none of their faces painted red?
Answer:
216
Step-by-step explanation:
If you just paint the surface of the cube, then the inside of the cube would not have any of their faces painted red.
Just looking at the cube from a side view, you would realize that there would be a smaller cube, 6 x 6 x 6 (not 7 since you have to account for both the top side and the bottom side), and so that is the answer, 6 ^ 3, which is 216.
Answer:
216
Step-by-step explanation:
8 * 8 * 8 = 512
8 * 8 = 64
Each face is 64 cubes, overlapping at the edges, with 6 faces total.
16 + 12 = 28 for each overlapping cube on each side
64 * 6 = 384
384 - 2(28) = 328
Top & Bottom dealt with, overlap from them is 56 units total, 14 units on top and bottom of each face..
64 - 14 = 50
50 * 2 = 100
Front & Back dealt with.
328 - 100 = 228
64 - 28 = 36
36 * 2 = 72
228 - 72 = 156
...
OR
6^3 = 216
Given the two functions, which statement is true?
fx = 3^4, g(x) = 3^x + 5
Answer:
third option
Step-by-step explanation:
Given f(x) then f(x) + c represents a vertical translation of f(x)
• If c > 0 then shift up by c units
• If c < 0 then shift down by c units
Given
g(x) = [tex]3^{x}[/tex] + 5 ← this represents a shift up of 5 units
Thus g(x) is the graph of f(x) translated up by 5 units
Answer:
[tex]\boxed{\sf{Option \: 3}}[/tex]
Step-by-step explanation:
g(x) is translated up 5 units compared to f(x). In a vertical translation, when the graph is moved 5 units up, 5 is added to the function. When the graph is moved 5 units down, 5 is subtracted from the function. The graphs are shifted in the direction of the y-axis.
convert 407 in base 8 to decimal
[tex]4\cdot8^2+0\cdot8^1+7\cdot8^0=256+7=263[/tex]
[tex]407_8=263_{10}[/tex]
A semicircular plate with radius 7 m is submerged vertically in water so that the top is 3 m above the surface. Express the hydrostatic force against one side of the plate as an integral and evaluate it. (Round your answer to the nearest whole number. Use 9.8 m/s2 for the acceleration due to gravity. Recall that the weight density of water is 1000 kg/m3.)
Answer:
F = 585844 N
Step-by-step explanation:
Given that:
A semicircular plate with radius 7 m is submerged vertically in water so that the top is 3 m above the surface.
The objective of this question is to express the hydrostatic force against one side of the plate as an integral and evaluate it.
To start with the equation of a circle: a² + b² = r²
The equation of circle with radius r = 7 can be expressed as:
a² + b² = 7²
a² + b² = 49
b² = 49 - a²
b = [tex]\sqrt{49 -a}[/tex]
NOW;
The integral of the hydrostatic force with a semicircular plate with radius 7 m and the top is 3 m above the surface can be calculated as follows:
[tex]\mathtt{F = 2 \rho g \int \limits^7_3 (a -3) \sqrt{49 -y^2} \ \ da}[/tex]
[tex]\mathtt{F = 2 \rho g \begin {pmatrix}\dfrac{\sqrt{49 -a^2} \ (2a^2-9a - 98)-(441 \times sin^{-1} (\dfrac{a}{3})) }{6} \end{pmatrix}}[/tex]
where;
density of water is 1000 kg/m3
and acceleration due to gravity is 9.8 m/s
Solving the integral; we have:
F = 2 × 1000 kg/m³ × 9.8 m/s × (29.89)
F = 585844 N
if the perimeter of Milo's rectangular backyard Is 16 feet. which of the following could be the dimensions of the yard? circle all that apply. explain your choice
Answer:
the answer is a and d
Step-by-step explanation:
6 + 6 + 2 +2 = 16
3 + 3 + 5 + 5 = 16
to find perimeter, double each factor and add :)
determine whether the series is absolutely convergent, conditionally convergent, or divergent sin(n)/3^n convergent
Answer:
absolutely convergent
Step-by-step explanation:
given data
sin(n)/3^n
solution
we have given term [tex]\frac{sin(n)}{3^n}[/tex]
when n = 1
and we know that
value of sin(n) ≤ 1
so that we can say that
[tex]\frac{sin(n)}{3^n}[/tex] ≤ [tex]\frac{1}{3^n}[/tex] or [tex](\frac{1}{3})^n[/tex]
here [tex]\frac{1}{3^n}[/tex] is converges this is because common ratio in geometric series
here r is [tex]\frac{1}{3}[/tex] and here it satisfy that -1 < r < 1
so it is converges
and
[tex]\frac{sin(n)}{3^n}[/tex] is also similar
so it is converges
and here no [tex](-1)^n[/tex] term is
so we can say series is absolutely convergent
The sum of two numbers is twenty-four. The second number is equal to twice the first number. Call the first number m and the second number n.
Answer:
Step-by-step explanation:
Hello, please consider the following.
m and n are the two numbers.
m + n = 24, right?
n = 2 m
We replace n in the first equation, it comes
m + 2m =24
3m = 24 = 3*8
So, m = 8 and n = 16
Thank you
The first number is 8 and second number is 16.
What is equation?Equation is the defined as mathematical statements that have a minimum of two terms containing variables or numbers is equal.
What are Arithmetic operations?Arithmetic operations can also be specified by the subtract, divide, and multiply built-in functions.
Given that the sum of two numbers is twenty-four
The second number is equal to twice the first number
Let x and y are the two numbers.
According to the question,
m + n = 24,
n = 2m
Substitute the value of n in the first equation,
m + 2m =24
3m = 24
m = 24/3
m = 8
Substitute the value of m in the n = 2m
So, n = 2(8)
n = 16
Hence, the first number is 8 and second number is 16.
Learn more about equation here:
brainly.com/question/10413253
#SPJ5
The perimeter of a rectangle is 80 inches, if the width is 18 inches what is the area of the rectangle? A.22 sq.in B.324 sq.in C.396 sq.in D.6,400 sq.in
Answer:
396 in^2
Step-by-step explanation:
The perimeter of a triangle is given by the formula:
● P = 2w+2L
L is the length and w is the width
■■■■■■■■■■■■■■■■■■■■■■■■■■
The width hereis 18 inches and the perimeter is 80 inches.
Replace w by 18 and P by 80 to find L.
● P= 2L+2w
● 80 = 2L + 2×18
● 80 = 2L + 36
Substrat 36 from both sides
● 80-36 = 2L+36-36
●44 = 2L
Divide both sides by 2
● 44/2 = 2L/2
● 22 = L
So the length is 22 inches
■■■■■■■■■■■■■■■■■■■■■■■■■■
The area of a rectangle is given by the formula:
● A= L×w
● A = 22×18
● A = 396 in^2
Solve the system by graphing y=-4x-2 -2x+y=-2 Plot both lines and point of intersection by moving the dots to the correct location
Answer:
The point of intersection is (0,-2).
Step-by-step explanation:
Equation 1: [tex]y=-4x-2[/tex]
Equation 2 : [tex]-2x+y=-2[/tex]
Plot the lines on the graph
Refer the attached figure
Equation 1: [tex]y=-4x-2 ---- Red[/tex]
Equation 2 : [tex]-2x+y=-2 ---- Blue[/tex]
Point of intersection : A point where both the lines intersect is called point of intersection.
So, Both lines intersect at point (0,-2)
So, Point of intersection is (0,-2)
Hence The point of intersection is (0,-2).
For any real number r, which of the following must be greater than r?
An expression is a set of numbers, variables, and mathematical operations. The correct option is C, r² + 1.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
Since real numbers contain positive integers, negative integers, positive decimals, negative decimals, and zero.
Therefore, For any real number r, the expression that will be always greater than r will be (r²+1). This is because,
√r :- If r=2, then √r will be 1.4142, therefore, √r will be lesser than r.2r :- If r is negative then 2r will also be negative and will be a smaller number than that.r² + 1 :- Irrespective of r is negative or positive, decimal or integer, the given expression will be always greater than r.r³ + 1 :- If the value of r is negative, then the expression will return a smaller negative number.Hence, the correct option is C, r² + 1.
Learn more about Expression here:
https://brainly.com/question/13947055
#SPJ5
Find the SURFACE AREA of the composite figure below
ASAP
Answer:
248.26 cm²
Step-by-step explanation:
Surface area of the composite figure = (surface area of cuboid + surface area of hemisphere) - 2(base area of hemisphere)
Surface area of cuboid = [tex] 2(lw + lh + hw) [/tex]
Where,
l = 10 cm
w = 5 cm
h = 4 cm
Plug in the values into the formula:
[tex] SA = 2(10*5 + 10*4 + 4*5) [/tex]
[tex] SA = 2(50 + 40 + 20) [/tex]
[tex] SA = 2(110) = 220 cm^2 [/tex]
Surface area of hemisphere = 3πr²
Where,
π = 3.14
r = 3 cm
SA of hemisphere = 3*3.14*3² = 3*3.14*9 = 84.78 cm²
Base area of hemisphere = πr²
BA = 3.14*3² = 3.14*9 = 28.26 cm²
Surface area of the composite shape = (220 + 84.78) - 2(28.26)
= 304.78 - 56.52
SA = 248.26 cm²
As part of a group exercise, four students each randomly selected 3 cards with angle measures written on them. The table shows the results. Which student selected angle measures that could form a triangle? A. Aella B. Aisha C. Ah Lam D.Andrew
Answer = A. Aella
Step-by-step explanation: Add 60, 25, and 95 degrees because that will equal 180 which is what the triangle equals.
Mr Gomez wants to put a ceramic Tile border along for all four sides of his kitchen wall mr. Gomez has measured and knows he needs enough tiles to make three rows with 63 tiles in each row on each of his for how many tiles is mr. Goma's need to make the border tiles are sold in boxes with 14 tiles in each box how many boxes of tile does mr. Gomez need to buy show all your mathematical thinking please explain step by step
Answer:
14 boxes
Step-by-step explanation:
We are given that he needs 3 rows with 63 tiles per row.
Hence total number of tiles needed:
= 3 rows x 63 tiles per row
= 189 tiles
we are also given that tiles come in boxes of 14 tiles.
Hence the number of boxes of tiles needed,
= 189 tiles ÷ 14 tiles per box
= 13.5 boxes
but because he cannot just buy 0.5 of a box (i.e he needs to buy whole boxes), we must round this number up to the next whole box
hence
13.5 boxes rounded up to next whole box = 14 boxes.
average person lives for about 78 years. Does the average person live for at least 1,000,000 hours? (Hint: There are 365 days in each year and 24 hours in each day.)
Answer:
683,280 hours is what I caculated. Is that right?
Step-by-step explanation:
Answer:
There are (365 x 24) hours for each year.
and 365 x 24 are 8760.
and 8760 x 78 are 683,280.
so, the average person does not live at least 1 Million hours, but they live more than 500 thousand hours, or 5 x 10^5 hours.
Hope it helps!
Bye!
P.S. Please give me Brainliest...
I desperately need one more Brainliest...
Given that f(x) = x + 4 and g(x) = x + 7, find (g - 4(x).
Answer: The value of [tex](g - f)(x)=4 .[/tex]
Step-by-step explanation:
Given functions : [tex]f(x) = x + 4[/tex] and [tex]g(x) = x + 7[/tex]
To find : [tex](g - f)(x)[/tex]
Difference between two functions: [tex](u-v)(x)=u(x)-v(x)[/tex]
Then, [tex](g-f)(x)=g(x)-f(x)[/tex]
[tex]=(x+7)-(x+4)=x+7-x-4\\\\=7-4=3[/tex]
Hence, the value of [tex](g - f)(x)=4 .[/tex]
Fertilizing bromeliads. Bromeliads are tropical flowering plants. Many are epiphytes that attach to trees and obtain moisture and nutrients from air and rain. Their leaf bases form cups that collect water and are home to the larvae of many insects. As a preliminary to a study of changes in the nutrient cycle, Jacqueline Ngai and Diane Srivastava examined the effects of adding nitrogen, phosphorus, or both to the cups. They randomly assigned 8 bromeliads growing in Costa Rica to each of 4 treatment groups, including an unfertilized control group. A monkey destroyed one of the plants in the control group, leaving 7 bromeliads in that group. Here are the numbers of new leaves on each plant over the seven months following fertilization:
Nitrogen Phosphorus Both Neither
15 15 14 14
14 17 18 19
18 13 14 11
16 13 15 16
14 14 15 13
11 17 14 15
13 12 15 15
(a) Give the degrees of freedom for the F statistic. numerator degrees of freedom denominator degrees of freedom
(b) Find the F-statistic. (Round your answer to two decimal places.)
(c) Find the associated P-value. (Round your answer to four decimal places.)
Answer:
Calculated value of F = 0.0535
The critical region is F >F ₀.₀₅ (6,21) = 2.575
Reject H0
Step-by-step explanation:
1. Null hypothesis
H0: µ Nitrogen = µ Phosphorus = µ Both = µ Neither
2. Alternative hypothesis
H1: Not all means are equal.
3. The degrees of freedom for the numerator of the F-ratio = k- 1= 7-1=6
4.The degrees of freedom for the denominator of the F-ratio = n-k= 28-7
= 21
5. The significance level is set at α-0.05
The critical region is F >F ₀.₀₅ (6,21) = 2.575
The test statistic to use is
F = sb²/ sw²
Which if H0 is true has an F distribution with v₁=k-1 and v₂= n-k degrees of freedom
Correction Factor = CF = Tj²/n = (410)²/28= 6003.57
Total SS ∑∑X²- C. F = 6108- 6003.57= 104.43
Between SS ∑T²j/r - C.F = 42036/ 7 - 6003.57 = 1.57286
Within SS = Total SS - Between SS= 104.43- 1.573= 102.86
The Analysis of Variance Table is
Source Of Sum of Mean Computed
Variation d.f Squares Squares F
Between
Samples 6 1.57286 0.2621 0.0535
Within
Samples 21 102.86 4.898
Calculated value of F = 0.0535
Pvalue = 2.575
Since it is smaller than 5 % reject H0.
renea is going to the lake to visit some freinds if the lake is 60 miles away and renae is driving at 40 miles per hour the entire time how long will it take her to get to the lake
Answer:
1.5 hours
Step-by-step explanation:
Set up a proportion:
[tex]\frac{40 miles}{1 hour}[/tex] = [tex]\frac{60 miles}{x}[/tex]
Cross multiply:
40x = 60
x = 1.5
= 1.5 hours
Heidi bought a machine that throws tennis balls for her dog to fetch. The height of each ball thrown by the machine, in feet, is modeled by the function f(x) = –x2 + x + 2, where x represents time in seconds. How many seconds after the machine throws the ball does it hit the ground?
Answer:
2 seconds
Step-by-step explanation:
Given the equation:
[tex]f(x) = -x^2 + x + 2[/tex]
Where f(x) represents the height of each ball thrown by machine.
and x represents the time in seconds.
To find:
The number of seconds after which the machine throws the balls hits the ground = ?
Solution:
In other words, we have to find the value of [tex]x[/tex] after which the [tex]f(x) = 0[/tex]
(Because when the ball hits the ground, the height becomes 0).
Let us put [tex]f(x) = 0[/tex] and solve for [tex]x[/tex]
[tex]f(x) = -x^2 + x + 2 =0\\\Rightarrow -x^2 + x + 2 =0\\\Rightarrow x^2 - x - 2 =0\\\Rightarrow x^2 - 2x+x - 2 =0\\\Rightarrow x(x - 2)+1(x - 2) =0\\\Rightarrow (x+1)(x - 2) =0\\\Rightarrow x =-1, 2[/tex]
[tex]x=-1[/tex] sec is not a valid answer because time can not be negative.
So, the answer is after 2 seconds, the ball hits the ground.
I NEED HELP ASAP PLEASE
Answer:
3 and 2
Step-by-step explanation:
I can't see your orginal equation. But it's probably 3 cos x . Which the amplitude is 3 then. Vertical translation would be how I move this graph up or down compared to the y axis. So if I were to add a +2 to the end of 3cos(x) I will move the graph up 2 spaces. So my final equation is 3cos (x)+2.
The lines shown below are parallel. If the green line has a slope of -1/2, what is the slope of the red line?
A.
2
B.
-
C.
-2
D.
Explanation: Parallel lines have the same slopes, but different y intercepts.
Answer:
the slope of the red line is also -1/2
Step-by-step explanation:
let p and p+2 be prime numbers (i.e they are twin primes) with p>3. Show that 6|(p+1)
from the well known theorem that, primes are multiple of 6 ±1 ( eg 5,7,11,13,17,19...)
and one of them has [tex]-1[/tex] and other has $+1$ from the multiple of 6
let , $p=6n-1$, so $p+2=6n+1$
$\implies p+1=6n$
$\therefore 6|(p+1)$
QED
Identify the decimals labeled with the letters A, B, and C on the scale below. Letter A represents the decimal Letter B represents the decimal Letter C represents the decimal
There are [tex]10[/tex] divisions between $3.2$ and $3.3$
so that means each division is $\frac{3.3-3.2}{10}=0.01$
A is the 3rd division after $3.2$, So A is $3.2+3\times0.01=3.23$
similarly, C is 3 division behind $3.2$ so it will be $3.17$
and B is $3.34$
A represents the decimal 3.23
B represents the decimal 3.34
C represents the decimal 3.17
Calculating the decimal values:We can see that there are 10 divisions between 3.2 and 3.3.
The difference between the two points for 10 divisions is 3.3 -3.2 = 0.1 unit.
Therefore, one division will be equal to 0.1/10 = 0.01 unit
So, point A is 3 divisions after 3.2, thus
A = 3.2 + 0.01×3
A = 3.23
Similarly,
B = 3.3 + 0.01×4
B = 3.34
And,
C = 3.2 - 0.01×3
C = 3.17
Learn more about decimals:
https://brainly.com/question/548650?referrer=searchResults
There are 8 books needing re-shelving in a library where 65% of the library's collection consists of reference books. Let X be the number of reference books a student helper re-shelves out of the 8 on her cart. a) What is the probability that all 8 of them are reference books
Answer:
0.0319
Step-by-step explanation:
To approximate this probability, we shall be using the Bernoulli approximation of the Binomial distribution.
Let p = probability of selecting a reference book = 65% = 0.65
Let q = probability of selecting other books= 1-p = 1-0.65 = 0.35
Now, we want to find the probability that all of these 8 books to be re-shelved are reference book.
We set up the probability as follows;
P(X = 8) = 8C8 •p^8•q^0
P(X = 8) = 1 * (0.65)^8 * (0.35)^0
P(X = 8) = 0.031864481289 which is 0.0319 to 4 decimal places
The function g(x) = x2 is transformed to obtain function h:
h(x) = g(x) – 5.
Which statement describes how the graph of his different from the graph of g?
A.
The graph of h is the graph of g horizontally shifted right 5 units.
B.
The graph of h is the graph of g vertically shifted up 5 units.
C.
The graph of h is the graph of g vertically shifted down 5 units.
OD.
The graph of h is the graph of ghorizontally shifted left 5 units.
Answer:
Option C
The graph of g is vertically shifted 5 units down
Y varies inversely with x. If Y=17 and k(The constant of variation) =76, what is x? Round to the nearest tenth if necessary.
Answer:
x ≈ 4.5
Step-by-step explanation:
Given y varies inversely with x then the equation relating them is
y = [tex]\frac{k}{x}[/tex] ← k is the constant of variation
Here k = 76 and y = 17 , thus
17 = [tex]\frac{76}{x}[/tex] ( multiply both sides by x )
17x = 76 ( divide both sides by 17 )
x ≈ 4.5 ( to the nearest tenth )
14. Find the distance between (7,217pi/180 ) and (5,-23pi/36 ) on the polar plane.
Answer: the distance is 3.49 units
Step-by-step explanation:
There are some ways to find the exact distance, i will calculate the distance in rectangular coordinates.
When we have a point (R, θ) in polar coordinates, we can transform it into rectangular coordinates as:
x = R*cos(θ)
y = R*sin(θ)
Then we have:
(7,217pi/180 )
R = 7
θ = (217/180)*pi
x = 7*cos( (217/180)*pi) = -5.59
y = 7*sin( (217/180)*pi) = -4.21
So this point is (-5.59, -4.21) in rectangular coordinates.
And the other point is (5,-23pi/36 )
R = 5
θ = -(23/36)*pi
x = 5*cos( -(23/36)*pi ) = -2.11
y = 5*sin( -(23/36)*pi ) = -4.53
So this point is (-2.11, - 4.53)
Then the point distance between those points is:
D = I (-2.11, -4.53) - (-5.59, -4.21) I
D = I (-2.11 + 5.59, -4.53 + 4.21) I
D = I (3.48, -0.32) I = √( (3.48)^2 + (-0.32)^2) = 3.49
