Answer:
[tex](a)\ P(White) = \frac{1}{2}[/tex]
(b) 10 additional white balls
(c) 10 additional black balls
Step-by-step explanation:
Given
[tex]White = 5[/tex]
[tex]Black =3[/tex]
[tex]Red = 2[/tex]
Solving (a): P(White)
This is calculated as:
[tex]P(White) = \frac{White}{Total}[/tex]
[tex]P(White) = \frac{5}{5+3+2}[/tex]
[tex]P(White) = \frac{5}{10}[/tex]
[tex]P(White) = \frac{1}{2}[/tex]
Solving (b): Additional white balls, if [tex]P(White) = \frac{3}{4}[/tex]
Let the additional white balls be x
So:
[tex]P(White) = \frac{White+x}{Total+x}[/tex]
This gives:
[tex]\frac{3}{4} = \frac{5+x}{10+x}[/tex]
Cross multiply
[tex]30+3x = 20 + 4x[/tex]
Collect like terms
[tex]4x - 3x = 30 - 20[/tex]
[tex]x = 10[/tex]
Hence, 10 additional white balls must be added
Solving (c): Additional black balls, if [tex]P(White) = \frac{1}{4}[/tex]
Let the additional black balls be x
So:
[tex]P(White) = \frac{White}{Total+x}[/tex]
So, we have:
[tex]\frac{1}{4} = \frac{5}{10+x}[/tex]
Cross multiply
[tex]10+x = 5 * 4[/tex]
[tex]10+x = 20[/tex]
Collect like terms
[tex]x = 20 -10[/tex]
[tex]x = 10[/tex]
Hence, 10 additional black balls must be added
Identify the domain of the table of values shown
Answer:
{-6,0,2,4}
Step-by-step explanation:
If $3000 is invested at 3% interest, find the value of the investment at the end of 7 years if the interest is compounded as follows. (Round your answers to the nearest cent.)
(i) annually
(ii) semiannually
(iii) monthly
(iv) weekly
(v) daily
(vi) continuously
Answer:
annualy=$3689.62
semiannually=$3695.27
monthly=$3700.06
weekly=$3700.81
daily=$3701.00
Continuously=$3701.03
Step-by-step explanation:
Given:
P=3000
r=3%
t=7 years
Formula used:
Where,
A represents Accumulated amount
P represents (or) invested amount
r represents interest rate
t represents time in years
n represents accumulated or compounded number of times per year
Solution:
(i)annually
n=1 time per year
[tex]A=3000[1+\frac{0.03}{1} ]^1^(^7^)\\ =3000(1.03)^7\\ =3689.621596\\[/tex]
On approximating the values,
A=$3689.62
(ii)semiannually
n=2 times per year
[tex]A=3000[1+\frac{0.03}{2}^{2(4)} ]\\ =3000[1+0.815]^14\\ =3695.267192[/tex]
On approximating the values,
A=$3695.27
(iii)monthly
n=12 times per year
[tex]A=3000[1+\frac{0.03}{12}^{12(7)} \\ =3000[1+0.0025]^84\\ =3700.0644[/tex]
On approximating,
A=$3700.06
(iv) weekly
n=52 times per year
[tex]A=3000[1+\frac{0.03}{52}]^3^6 \\ =3000(1.23360336)\\ =3700.81003[/tex]
On approximating,
A=$3700.81
(v) daily
n=365 time per year
[tex]A=3000[1+\frac{0.03}{365}]^{365(7)} \\ =3000[1.000082192]^{2555}\\ =3701.002234[/tex]
On approximating the values,
A=$3701.00
(vi) Continuously
[tex]A=Pe^r^t\\ =3000e^{\frac{0.03}{1}(7) }\\ =3000e^{0.21} \\ =3000(1.23367806)\\ =3701.03418\\[/tex]
On approximating the value,
A=$3701.03
need help now!!! Please and thanks
Answer:
the answer of r is 8 i hope it will help
John's age 4 years ago, if he will be y years old in 5 years
9514 1404 393
Answer:
y -9
Step-by-step explanation:
From 4 years ago until 5 years from now, John will age 9 years. That is, his age 4 years ago is 9 years less than it will be in 5 years.
John's age 4 years ago is y-9 years.
find the length of side AB
Answer:
AB = 5.6 cm
Step-by-step explanation:
Reference angle (θ) = 62°
Hypotenuse = 12 cm
Adjacent = AB
Apply the trigonometric ratio formula, CAH, which is:
Cos θ = Adj/Hyp
Plug in the values
Cos 62° = AB/12
12*Cos 62° = AB
5.63365876 = AB
AB = 5.6 cm (1 decimal place)
SCALCET8 3.9.015. A street light is mounted at the top of a 15-ft-tall pole. A man 6 ft tall walks away from the pole with a speed of 4 ft/s along a straight path. How fast is the tip of his shadow moving when he is 35 ft from the pole
Answer:
[tex]X=6.67ft/s[/tex]
Step-by-step explanation:
From the question we are told that:
Height of pole [tex]H_p=15[/tex]
Height of man [tex]h_m=6ft[/tex]
Speed of Man [tex]\triangle a =4ft/s[/tex]
Distance from pole [tex]d=35ft[/tex]
Let
Distance from pole to man=a
Distance from man to shadow =b
Therefore
[tex]\frac{a+b}{15}=\frac{b}{6}[/tex]
[tex]6a+6b=15y[/tex]
[tex]2a=3b[/tex]
Generally the equation for change in velocity is mathematically given by
[tex]2(\triangle a)=3(\triangle b )[/tex]
[tex]2*4=3(\triangle b)[/tex]
[tex]\triangle a=\frac{8}{3}[/tex]
Since
The speed of the shadow is given as
[tex]X=\triangle b+\triangle a[/tex]
[tex]X=4+8/3[/tex]
[tex]X=6.67ft/s[/tex]
Need the answers from a - e
Answer:
10
Step-by-step explanation:
Sorry. I needed to answer this question to get access.
Question 2
A force F=5i+3j-2k is applied to move a block of cement from A(0,1,1) to B(4.-1,3).
Determine the work done by the force.
The work is simply the dot product of the force and displacement (which I assume are given in Newtons and meters, respectively):
W = F • d
W = (5i + 3j - 2k) N • ((4i - j + 3k) m - (j + k) m)
W = (5i + 3j - 2k) • (4i - 2j + 2k) Nm
W = (20 - 6 - 4) Nm
W = 10 J
Find the distance between the points (-5, -4) and (3, 1).
On a coordinate plane, points are at (3, 1), (negative 5, negative 4).
Step-by-step explanation:
it will help u
In order to win a prize, Heather randomly draws two balls from a basket of 40. There are 25 blue balls, and the rest are green balls. Of the blue balls, 12% are winning balls. Of the green balls, 20% are winning balls. Calculate the expected number of winning balls that Heather draws.
Answer:
The expected number of winning balls that Heather draws is 0.3.
Step-by-step explanation:
The balls are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
The probability of x successes is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of successes.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
Expected value of the hypergeometric distribution:
The expected value is given by:
[tex]E(X) = \frac{nk}{N}[/tex]
Expected number of blue and green balls:
40 balls, which means that [tex]N = 40[/tex]
2 are chosen, which means that [tex]n = 2[/tex]
25 are blue, which means that [tex]k = 25[/tex]
So
[tex]E(X) = \frac{nk}{N} = \frac{25(2)}{40} = 1.25[/tex]
1.25 balls are expected to be blue and 2 - 1.25 = 0.75 green.
Of the blue balls, 12% are winning.
Of the green balls, 20% are winning.
Calculate the expected number of winning balls that Heather draws.
[tex]E_w = 1.25*0.12 + 0.75*0.2 = 0.3[/tex]
The expected number of winning balls that Heather draws is 0.3.
Find the median: 16.12.7.9.10.16
Answer:
hey hi mate
hope you like it
plz mark it as brainliest
Which represents can be used to determine the slope of the linear function graphed below
The parametric equations for the paths of two projectiles are given. At what rate is the distance between the two objects changing at the given value of t? (Round your answer to two decimal places.) x1 = 10 cos(2t), y1 = 6 sin(2t) First object x2 = 4 cos(t), y2 = 4 sin(t) Second object t = π/2
Answer:
- [tex]\frac{4}{\sqrt{29} }[/tex]
Step-by-step explanation:
The equations for the 1st object :
x₁ = 10 cos(2t), and y₁ = 6 sin(2t)
2nd object :
x₂ = 4 cos(t), y₂ = 4 sin(t)
Determine rate at which distance between objects will continue to change
solution Attached below
Distance( D ) = [tex]\sqrt{(10cos2(t) - 4cos(t))^2 + (6sin2(t) -4sin(t))^2}[/tex]
hence; dD/dt = - [tex]\frac{4}{\sqrt{29} }[/tex]
ABCD is a square of side 12 cm. It is formed from two rectangles AEGD and
EBCG. H is a point on AD and F is a point on BC.
Find the area of EFGH.
Answer:72 [tex]cm^{2}[/tex]
Solution 1:
Step 1: Find EF use Pythagorean theorem
[tex]EF^{2} = EB^{2} + BF^{2}[/tex]
[tex]EF^{2} = 6^{2} + 6^{2}[/tex]
EF = [tex]\sqrt{6^{2} + 6^{2} }[/tex] = 6[tex]\sqrt{2}[/tex] cm
Step 2: The area of EFGH = [tex]EF^{2}[/tex]= [tex](6\sqrt{2} )^{2}[/tex] = 72
Solution 2: See that the area of EFGH is equal [tex]\frac{1}{2}[/tex] the area of ABCD
The area of ABCD = 12x12 = 144
Thus, the area of EFGH = 144: 2 = 72:)
Have a nice day!
10=−4x+3x^2 solve
please help!
Answer:
-1.28 AND 2.61
Step-by-step explanation:
[tex]10= -4x+3x^2\\ 3x^2 -4x - 10 = 0\\\\[/tex]
use quadratic formula
x = [tex]\frac{-b+\sqrt{b^{2} -4ac} }{2a}[/tex] x = [tex]\frac{-b-\sqrt{b^{2} -4ac} }{2a}[/tex]
Solution/X-Intercepts: -1.28 AND 2.61
Martina made$391for17hours of work. At the same rate, how many hours would she have to work to make$253? a 11 hours b 9 hours c 22 hours d 33 hours
Answer:
11 hours is right answer i hope it will help you
what is the value of -2x²y³ when ×=2 and y=4?
Answer:
1024
Step-by-step explanation:
Given :-
x = 2 y = 4Value of -2x²y³
2x³ y³2 * (2)³ * (4)³2 * 8 * 64 1024Answer:
254
Step-by-step explanation:
^ <- this is the square sign
-2x^y^3
x=2
y=4
put x values in to x place and y value in to y place.
-2(2)^2(4)^3
Find the squares and - it with 2
-2(4)(64)
2-256=254
:. the value of -2x^2y^3 =254
That the answer.
Hope this is what you asked.
The solution of this equation has an error. Which of the following steps has the error? 18 − (3x + 5) = 8
Step 1: 18 − 3x + 5 = 8
Step 2: -3x + 23 = 8
Step 3: -3x = -15
Step 4: x = 5
Step 1 Step 2 Step 3 Step 4. ?
Answer:
Step 1
Because the number in front of the bracket is 1 and it is also affected by the negative sign(-),5 is supposed to be negative not positive because (negative by positive is negative)
And since the first step has an error in it,the remaining steps would also be wrong.
19. The sum of a number m and a number n, multiplied by ninety-one 20. Forty-one times the difference when six is subtracted from a num- bera 21. A number r divided by the difference between eighty-three and ten 22. The total of a number p and twelve, divided by eighteen 23. The product of a number c and three more than the sum of nine and twelve 24. The sum of a number y and ten, divided by the difference when a number x is decreased by five. I need to convert all of them into expressions. PLEASE HELP.
Answer:
Step-by-step explanation:
19.
The numbers are m and n
Sum of m and n = m + n
Sum is multiplied by 91 = 91 x ( m + n )
20.
Let the number be = m
Six subtracted from the number = m - 6
41 times the difference = 41 x ( m - 6)
21.
Let the number be = r
Difference between 83 and 10 = 83 - 10 = 73
[tex]The \ number\ divided \ by\ the \ difference \ = \frac{r}{73}[/tex]
22.
Total of p and 23 = p + 12
[tex]Total \ divided \ by \ 18 = \frac{p + 12 }{18}[/tex]
23.
The product of c and 3 = 3c
Sum of 9 and 12 = 21
Product is more than Sum = 3c + 21
24.
Sum of y and 10 = y + 10
Number x decreased by 5 = x - 5
[tex]Sum \ divided \ by \ difference = \frac{ y + 10 }{x - 5}[/tex]
1. Find the Perimeter AND Area of the figure
below.
2 ft
5 ft
2 ft
5 ft
Answer:
A = 16 ft^2
P = 20 ft
Step-by-step explanation:
P = perimeter
A = area
STEP 1: divide the shape into rectangles
Rectangle 1: 2ft*3ft
Rectangle 2: 2ft*5ft
STEP 2: Find the area of each rectangle
Equation for area of a rectangle = bh
Rectangle 1: b = 2, h = 3
Rectangle 2: b = 2, h = 5
(2 * 3) + (2 * 5)
6 + 10
16 ft^2
Now, we have to find the perimeter
STEP 1: Find the unknown side lengths.
To find the lengths of the sides not labeled, you have to use the lengths of the sides we already know.
The length of one parallel side is 5, and the length of another parallel side is 2. The length of the unknown side starts at the same place as the top of the side length that is 5, and ends at the top of the side length that is 2. This means that we have to subtract 2 from 5 in order to find the unknown side length.
STEP 2: Add up all the side lengths
P = 2 + 5 + 5 + 2 + 3 + 3
P = 20 ft
Don't forget to label your answers!!
I hope this made sense, it's is a little hard to explain in simple terms without being able to draw, but I hope it helped.
There is a bag filled with 3 blue and 5 red marbles.
A marble is taken at random from the bag, the colour is noted and then it is not replaced.
Another marble is taken at random.
What is the probability of getting 2 of the same colour?
JUST NEED THE ANSWER IN A FRACTION PLEASE
[tex]\frac{13}{28}[/tex]
Step-by-step explanation:Given:
Blue marbles: 3
Reb marbles: 5
Total marbles: 8
Two marbles are selected at random, one after the other with replacement.
Getting the same colour of marbles from the selection means the two marbles are both red or both blue.
(a) Probability of getting 2 marbles being red in colour
i. Probability of picking a red at the first selection:
Number of red marbles ÷ Total number of marbles
=> 5 ÷ 8 = [tex]\frac{5}{8}[/tex]
ii. Probability of picking a red at the second selection:
Number of remaining red marbles ÷ Total number of remaining marbles
Since after the first pick, the marble is not replaced, the remaining red marbles is 4 while the total number of remaining marbles is 7
=> 4 ÷ 7 = [tex]\frac{4}{7}[/tex]
iii. The probability of getting both marbles being red is the product of i and ii above. i.e
[tex]\frac{5}{8}[/tex] x [tex]\frac{4}{7}[/tex] = [tex]\frac{5}{14}[/tex]
(b) Probability of getting 2 marbles being blue in colour
i. Probability of picking a blue at the first selection:
Number of blue marbles ÷ Total number of marbles
=> 3 ÷ 8 = [tex]\frac{3}{8}[/tex]
ii. Probability of picking a blue at the second selection:
Number of remaining blue marbles ÷ Total number of remaining marbles
Since after the first pick, the marble is not replaced, the remaining blue marbles is 2 while the total number of remaining marbles is 7
=> 2 ÷ 7 = [tex]\frac{2}{7}[/tex]
iii. The probability of getting both marbles being blue is the product of i and ii above. i.e
[tex]\frac{3}{8}[/tex] x [tex]\frac{2}{7}[/tex] = [tex]\frac{3}{28}[/tex]
(c) Probability of getting 2 marbles of the same colour.
The probability of getting 2 marbles of same colour is the sum of the probability of getting both marbles of red colour and the probability of getting both marbles as blue colour. i.e The sum of a(iii) and b(iii)
[tex]\frac{5}{14}[/tex] + [tex]\frac{3}{28}[/tex] = [tex]\frac{13}{28}[/tex]
The probability of getting 2 of the same colour is [tex]\frac{13}{28}[/tex]
A Professor at a Nigerian University sent his phone number in a disorderly manner to his students. The disordered phone number was 82002273285.To know his real phone number, he gave the student the following conditions:(1) Eight (8) must come between two zeros (0's). (2)The first number after the first condition is met must not be an odd number and it must be greater than 5. (3)The seventh number must be 1. (4) The fifth and sixth numbers must be two numbers whose difference is 1 and the bigger number must come first.(5)The fifth and sixth numbers are greater than 2.(6)The ninth and tenth numbers are the same.(7)The eighth number is greater than the last number (8) The phone number must be 11 digits. What is the Professor's real phone number?
Answer:
I think you have a type.. "the seventh number must be a 1"
there are no 1's in the original set of numbers
Step-by-step explanation:
If 128x is a perfect square number what is the least value of x
Please answer the question fast
Answer:
in a square all sides are equal so x has to equal
128
Hope This Helps!!!
PLSHELPASAPDFFFFFFFFFFFFFFFFFFFFFFFFFF
im struggling with the same one
If 4x³+kx²+px +2 is divisible by x²+ α prove that kp=8.
Answer:
Attached images
It was just easier for me this way.
Let me know in comments if you have questions.
Step-by-step explanation:
Which answers describe the shape below? Check all that apply.
A. Square
B. Quadrilateral
C. Rhombus
D. Trapezoid
E. Rectangle
F. Parallelogram
Answer:
b and f
Step-by-step explanation:
In your office desk drawer you have 10 different flavors of fruit leather. How many distinct flavor groupings can you make with your fruit leather stash?
Do you want to own your own candy store? Wow! With some interest in running your own business and a decent credit rating, you can probably get a bank loan on startup costs for franchises such as Candy Express, The Fudge Company, Karmel Corn, and Rocky Mountain Chocolate Factory. Startup costs (in thousands of dollars) for a random sample of candy stores are given below. Assume that the population of x values has an approximately normal distribution.
Answer:
[tex]\bar x = 107.11[/tex]
[tex]\sigma_x = 31.07[/tex]
Step-by-step explanation:
See comment for complete question
Given
[tex]x: 97\ 178\ 129\ 90\ 75\ 94\ 116\ 100\ 85[/tex]
Solving (a): The sample mean
This is calculated using:
[tex]\bar x = \frac{\sum x}{n}[/tex]
So, we have:
[tex]\bar x = \frac{97+ 178+ 129+ 90+ 75+ 94+ 116+ 100+ 85}{9}[/tex]
[tex]\bar x = \frac{964}{9}[/tex]
[tex]\bar x = 107.11[/tex]
Solving (b): The sample standard deviation
This is calculated as:
[tex]\sigma_x = \sqrt{\frac{\sum(x - \bar x)^2}{n-1}}[/tex]
So, we have:
[tex]\sigma_x = \sqrt{\frac{(97 - 107.11)^2 +.............+ (85- 107.11)^2 }{9-1}}[/tex]
[tex]\sigma_x = \sqrt{\frac{7720.8889}{8}}[/tex]
[tex]\sigma_x = \sqrt{965.1111125}[/tex]
[tex]\sigma_x = 31.07[/tex]
HELPPP PLEASEEE! I tried everything from adding to dividing, subtracting, multiplying but still no correct answer. Can someone help me out here please? I am not sure where to start either now. Thank you for your time.
You have some data points labeled by [tex]x[/tex]. They form the set {3, 5, 7}.
The mean, [tex]\bar x[/tex], is the average of these values:
[tex]\bar x = \dfrac{3+5+7}3 = \dfrac{15}3 = 5[/tex]
Then in the column labeled [tex]x-\bar x[/tex], what you're doing is computing the difference between each data point [tex]x[/tex] and the mean [tex]\bar x[/tex]:
[tex]x=3 \implies x-\bar x = 3 - 5 = -2[/tex]
[tex]x=5 \implies x-\bar x = 5-5 = 0[/tex]
[tex]x=7 \implies x-\bar x = 7 - 5 = 2[/tex]
These are sometimes called "residuals".
In the next column, you square these values:
[tex]x=3 \implies (x-\bar x)^2 = (-2)^2 = 4[/tex]
[tex]x=5 \implies (x-\bar x)^2 = 0^2 = 0[/tex]
[tex]x=7 \implies (x-\bar x)^2 = 2^2 = 4[/tex]
and the variance of the data is the sum of these so-called "squared residuals".
Suppose f(x,y,z) = x2 + y2 + z2 and W is the solid cylinder with height 7 and base radius 2 that is centered about the z-axis with its base at z = −2. Enter θ as theta.
A) As an iterated integral, ∭WfdV = ∫BA∫DC∫FE dzdrdθ with limits of integration.
B) Evaluate the integral.
In cylindrical coordinates, W is the set of points
W = {(r, θ, z) : 0 ≤ r ≤ 2 and 0 ≤ θ ≤ 2π and -2 ≤ z ≤ 5}
(A) Then the integral of f(x, y, z) over W is
[tex]\displaystyle\iiint_W(x^2+y^2+z^2)\,\mathrm dV = \int_0^{2\pi}\int_0^2\int_{-2}^5r(r^2+z^2)\,\mathrm dz\,\mathrm dr\,\mathrm d\theta[/tex]
(B)
[tex]\displaystyle \int_0^{2\pi}\int_0^2\int_{-2}^5r(r^2+z^2)\,\mathrm dz\,\mathrm dr\,\mathrm d\theta = 2\pi \int_0^2\int_{-2}^5(r^3+rz^2)\,\mathrm dz\,\mathrm dr \\\\\\= 2\pi \int_0^2\left(zr^3+\frac13rz^3\right)\bigg|_{z=-2}^{z=5}\,\mathrm dr \\\\\\= 2\pi \int_0^2\left(\frac{133}3r+7r^3\right)\,\mathrm dr \\\\\\= 2\pi \left(\frac{133}6r^2+\frac74r^4\right)\bigg|_{r=0}^{r=2} \\\\\\= 2\pi \left(\frac{110}3\right) = \boxed{\frac{220\pi}3}[/tex]
