Answer:
Hypotenuse=10 miles.
Short leg=6 miles.
Step-by-step explanation:
Set up triangle, leg 8 miles, hypotenuse x miles, short leg x-4 miles.Input into Pythagoras theorem.Simplify.The probability that a patient recovers from a disease is 0.3.
If 6 people are known to have contacted the disease, what is the probability that at least 4 survive?
Answer:
0.07047
Step-by-step explanation:
at least 4 people survive is
4 people survive and 2 don't +
5 people survive and 1 doesn't +
all 6 people survive
the probability of 4 people to survive is the product of the individual probabilities :
0.3×0.3×0.3×0.3 = 0.3⁴ = 0.0081
times the probability 2 don't survive
0.7×0.7 = 0.49
0.0081×0.49 = 0.003969
now, the chance that 4 out of 6 survive is that probabilty times how many times we can select 4 out of 6.
to select 4 out of 6 is
[tex] \binom{6}{4} [/tex]
= 6! / (4! × (6-4)!) = 6! / (4! × 2!) = 6×5/2 = 30/2 = 15
so, the probability of having 4 survivors is
15×0.003969 = 0.059535
the probability of 5 people surviving is 0.3⁵ times one not
0.3⁵×0.7 = 0.001701
we have 6 over 5 combinations to pick 5 out of 6 = 6.
so, in total for 5 survivors we get
6×0.001701 = 0.010206
and the probabilty of all 6 surviving is
0.3⁶ = 0.000729
so, the probability of at least 4 out of 6 surviving is
0.059535 +
0.010206 +
0.000729
---------------
0.070470
Use the given degree of confidence and sample data to construct a confidence interval for the population mean μ. Assume that the population has a normal distribution. A laboratory tested twelve chicken eggs and found that the mean amount of cholesterol was 185 milligrams with s = 17.6 milligrams.
Required:
Construct a 95% confidence interval for the true mean cholesterol content of all such eggs.
Answer:
CI ≈ (173.8 < μ < 196.2)
Step-by-step explanation:
We are told that laboratory tested twelve chicken eggs. Thus;
n = 12
Mean; x¯ = 185 mg
S.D; s = 17.6 mg
DF = n - 1 = 12 - 1 = 11
We have a 95% confidence level. Thus; α = 0.05
Since n < 30, we will use t-sample test.
Thus, from t-table attached at 95% Confidence level and DF = 11, we have;
t = 2.201
Thus,formula for Confidence interval is;
CI = (x¯ - t(s/√n)) < μ < (x¯ + t(s/√n))
CI = (185 - 2.201(17.6/√12)) < μ < (185 + 2.201(17.6/√12))
CI = (185 - 11.1825) < μ < (185 + 11.1825)
CI = (173.8175 < μ < 196.1825)
CI ≈ (173.8 < μ < 196.2)
(x+1).(x/2 +2).(x/3+3).(x/4+4).(x/5+5)
Answer:
Please see the attached picture below to understand the steps I've typed to get to the final solution.
8/9 - Evaluating Algebraic Expressions
5. Which is equivalent to 4x - (y + x) + 2, if x = 5 and y=-3?
O 20
-20
-15
O 15
9514 1404 393
Answer:
(a) 20
Step-by-step explanation:
Put the numbers in place of the corresponding letters and do the arithmetic.
4(5) -((-3) +5) +2 = 20 -2 +2 = 20
PLease Help! I will give you the brainiest and a lot of points
A survey of 104 college students was taken to determine the musical styles they liked. Of those, 22 students listened to rock, 23 to classical, and 24 to jazz. Also, 10 students listened to rock and jazz, 8 to rock and classical, and 8 to classical and jazz. Finally, 6 students listened to all three musical styles. Construct a Venn diagram and determine the cardinality for each region. Use the completed Venn Diagram to answer the following questions.
a. How many listened to only rock music?
n(only rock)
b. How many listened to classical and jazz, but not rock?
n(classical and jazz, not rock)
c. How many listened to classical or jazz, but not rock?
n(classical or jazz, not rock)
d. How many listened to music in exactly one of the musical styles?
n(exactly one style)
e. How many listened to music in exactly two of the musical styles?
n(exactly two styles)
f. How many did not listen to any of the musical styles?
n(none)
Answer:
A. 22
B. 8
C. 23 + 24
D. 22 + 23 + 24
E. 8 + 8 + 10
F. 104 - (sum of all the given numbers) = 3
Please help it’s due today
Answer:
67 degrees
Step-by-step explanation:
23 + 90 = 113
180 - 113 = 67
Please Help Polygons
Step-by-step explanation:
5.25....................
5 pencils for 15 dollers how much for each pencil
5 pencils = 15 dollors
1 pencil = 15/5 dollors
therefore 1 pencil = 3 dollors...
Answer:
Each pencil would cost $3.00
Step-by-step explanation:
If 5 costs $15, to find the cost of one you divide 15 by 5
15 ÷ 5 = 3
Samuel had 12 red marbles , 15 blue marbles , and 13 green marbles . Which fraction represents the number of red marbles he has
Answer:
12/40 or simplified it would be 3/10
Step-by-step explanation:
Find the fractal dimension of the object.
Answer:
maaqqqf aku ngak tau soal jawaban in
Write the point-slope form of an equation of the line through the points (-4, 7) and (5,-3).
0
A. Y+4= -1; (1 – 7)
B.Y-5 = = 10 (x+3)
OC. y +3 = = 10 (2+5)
D. y - 7= -5° (x+4)
Answer:
Step-by-step explanation:
There are two possible equations, but neither matches the the choices you listed. The choices seem to have several typographical errors.
Point-slope form of an equation of the line through the points (-4, 7) and (5,-3) is y - 7 =(-10/9)(x + 4).
How to estimate the point-slope form of an equation of the line through the points (-4, 7) and (5,-3)?Slope
[tex]$= \frac{y_{2} -y_{1}}{x_{2} -x_{1}}[/tex]
= (-3 - 7) / (5 - (-4))
= -10/9
The point-slope equation for the line of slope -(10/9) that passes through the point (5, -3).
y + 3 = (-10/9)(x - 5)
Point slope equation for the line of slope -(10/9) that passes through the point (-4, 7)
Point-slope form of an equation of the line through the points (-4, 7) and (5,-3) is y - 7 = (-10/9)(x + 4).
Therefore, the correct answer is y - 7 = (-10/9)(x + 4).
To learn more about the equation of a line refer to:
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1. On the set of axes below, graph . State the roots of
Is this question complete?
Express 5 cm in metre and kilometre.in decimals........................ ncert maths class 7 pls
will be marked as brainliest trust me
Answer:
Converting into metre (1m=100cm)= 5/100=0.05m.. Converting into km. (1km=100000cm). so 5 cm=5/100000=0.00005km.
Answer:
5cm in meters = 0.05 metre
5cm in kilometres = 0.00005km
1106.666667 To the nearest whole number
Answer:
1107.
You are rounding up because the number in the tenths slot is over 5.
Functions f and g are defined for all real
numbers. The function f has zeros at -2, 3, and 7:
and the function g has zeros at -3, -1, 4, and 7.
How many distinct zeros does the product
function f g have?
9514 1404 393
Answer:
6
Step-by-step explanation:
The number of distinct zeros in the product will be the union of the sets of zeros. Duplicated values are not distinct, so show in the union of sets only once.
F = {-2, 3, 7}
G = {-3, -1, 4, 7}
F∪G = {-3, -2, -1, 3, 4, 7} . . . . . . a 6-element set
The product has 6 distinct zeros.
_____
As you may notice in the graph, the duplicated zero has a multiplicity of 2 in the product.
Solve this inequality:
-9 > 3b + 6
Answer:
- 5 > b
Step-by-step explanation:
- 9 > 3b + 6
- 9 - 6 > 3b
- 15 > 3b
Divide 3 on both sides,
- 5 > b
Answer:
-5 >b
Step-by-step explanation:
-9 > 3b + 6
Subtract 6 from each side
-9-6 > 3b + 6-6
-15 > 3b
Divide each side by 3
-15/3 > 3b/3
-5 >b
2. What amount of money must Kurt Blixen invest at 4.75% to have it earn $10,000 in 90 days?
Kurt Blixen must invest $85,2296.94.
Given the following data;
Interest rate = 4.75%Simple interest = $10,000Time = 90 daysTo find how much money Kurt Blixen must invest;
Mathematically, simple interest is given by the formula;
[tex]S.I = \frac{PRT}{100}[/tex]
Where:
S.I is the simple interest.P is the principal amount.R is the interest rate.T is the time measured in years.First of all, we would convert the time in days to years.
Conversion:
365 days = 1 year
90 days = x year
Cross-multiplying, we have;
[tex]365 * x = 90\\\\x = \frac{90}{365}[/tex]
x = 0.247 year
Making P the subject of formula;
[tex]P = \frac{S.I(100)}{RT}[/tex]
Substituting the values into the formula, we have;
[tex]P = \frac{10000(100)}{4.75*0.247}\\\\P = \frac{1000000}{1.1733}[/tex]
P = $85,2296.94
Therefore, Kurt Blixen must invest $85,2296.94.
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[tex]\sqrt{25}[/tex]=?
[tex]Hello[/tex] [tex]There[/tex]
The answer is...
[tex]5.[/tex]
[tex]HopeThisHelps!![/tex]
[tex]AnimeVines[/tex]
How many numbers multiple of 3 are in the range [2,2000]?
Answer: so there are 666 multiples of 3 between 2 and 2000.
Step-by-step explanation:
the smallest number = 3 which is 3*1. The largest number is = 1998 = 3*666
multiples of 3 between {2,2000} = 666-1+1 = 666
Use the distributive property to find the product of the rational number.
5/2 (- 8/5 + 7/5)
9514 1404 393
Answer:
-1/2
Step-by-step explanation:
The factor outside parentheses multiplies each term inside.
5/2(-8/5 +7/5)
= (5/2)(-8/5) +(5/2)(7/5)
= -8/2 +7/2 = -1/2
Give a vector parametric equation for the line through the point (−2,−4,0) that is parallel to the line ⟨−2−3t,1−4t,−5t⟩:
The tangent vector for the given line is
T(t) = d/dt ⟨-2 - 3t, 1 - 4t, -5t⟩ = ⟨-3, -4, -5⟩
On its own, this vector points to a single point in space, (-3, -4, -5).
Multiply this vector by some scalar t to get a whole set of vectors, essentially stretching or contracting the vector ⟨-3, -4, -5⟩. This set is a line through the origin.
Now translate this set of vectors by adding to it the vector ⟨-2, -4, 0⟩, which correspond to the given point.
Then the equation for this new line is simply
L(t) = ⟨-3, -4, -5⟩t + ⟨-2, -4, 0⟩ = ⟨-2 - 3t, -4 - 4t, -5t⟩
The vector parametric equation for the line through the point is [tex]r = (-2, \ -4, \ 0) +(-3, \ -4, \ -5)t\\\\[/tex].
GivenGive a vector parametric equation for the line through the point (−2,−4,0) that is parallel to the line ⟨−2−3t,1−4t,−5t⟩.
What is a parametric equation vector?Parametric equations of the line segment are defined by its endpoints.
To find the vector equation of the line segment, we’ll convert its endpoints to their vector equivalents.
Two lines are parallel if they have the same direction, and in the parametric form, the direction of a line is always the vector of constants that multiply t (or the parameter).
The vector equation of a line is given by:
[tex]\rm v = r_0+tv[/tex]
Where v is the direction vector and [tex]\rm r_0[/tex] is a point of the line.
The tangent vector for the given line is
T(t) = d/dt ⟨-2 - 3t, 1 - 4t, -5t⟩ = ⟨-3, -4, -5⟩
Here,
[tex]\rm r_0 = (-2,-4,0) \ and \ v=(-3, \ -4, \ -5)t\\\\[/tex]
Then,
[tex]r = (-2, \ -4, \ 0) +(-3, \ -4, \ -5)t\\\\[/tex]
x = -2-3t, y = -4-4t, and z = 0-5t
To know more about the Parametric equation click the link given below.
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Please answer ASAP!!!!
Answer:
0
Step-by-step explanation:
0
Help please ……………….zzzz
1) I think 15 choose (d)
2) The choose (C) -4fg+4g
3) The choose (d) 3xy/2
4) The choose (a) ab/6
5) The choose (C) 2p+4q-6
6)
[tex]\pi {r}^{2} h = 3.14 \times {3}^{2} \times 1.5 = 42.39 {m}^{3} = 42.390 {m}^{3} [/tex]
Point 6 I think there is an error because the unit m must be m³ because it is r² (m²) and h(m) becomes m³.
I hope I helped you^_^
Evaluate the expression when x = 12/7
The value of the expression when x equals is ???
PLEASE HELP!!
Answer:
82
Step-by-step explanation:
1/3( x+9/7) + 3^4
Let x = 12/7
1/3( 12/7+9/7) + 3^4
PEMDAS says parentheses first
1/3( 21/7) + 3^4
1/3(3) +3^4
Then exponents
1/3(3)+81
Then multiply
1+81
82
I need help figuring out this equation
270 degrees is at the bottom of the unit circle, and it splits the 3rd and 4th quadrants.
Its terminal point is (0, -1).
Hope this helps!
Answer:
A. (0, -1)
Step-by-step explanation:
This question requires a chart to answer. The chart is inserted in the answer.
270 degrees is all the way at the bottom, at South which shows that 270 degrees is at (0, -1).
Meaning, the answer is A, (0, -1).
Hope this helped.
You need 675 mL of a 90% alcohol solution. On hand, you have a 25% alcohol mixture. How much of the 25% alcohol mixture and pure alcohol will you need to obtain the desired solution?
Answer:
90 ml of the 25 percent mixture and 585 of pure alcohol
Step-by-step explanation:
Firstly, you should find the quantity of alcohol in the desired mixture.
675:100*90= 675*0.9= 607.5
Firstly, define all the 25 percents mixure as x, the pure alcohol weight is y.
1. x+y= 675 (because the first and the second liquid form a desired liquid).
Then find the equation for spirit
The first mixture contains 25 percents. It is x/100*25= 0.25x
When the second one consists of pure alcohol, it contains 100 percents of spirit, so it is x.
2. 0.25x+y=607.5
Then you have a system of equations ( 1.x+y= 675 and 2. 0.25x+y= 607.5)
try 2-1 to get rid of y
x+y- (0.25x+y)= 675-607.5
0.75x= 67.5
x= 90
y= 675-x= 675-90= 585
It means that you need90 ml of the 25percents mixture and 585 0f pure alcohol
find the squre of 17
[tex] \sqrt{17} [/tex]
A runner sprinted for 414 feet. How many yards is this?
Answer:
138 yards
Step-by-step explanation:
1 feet is (1/3) yard
414 feet is (1/3)*414=138 yards
For the following function, one zero is given. Find all other zeros.
f(x)=x3-7x2+17x-15; 2-i
Answer:
1,-3,-5
Step-by-step explanation:
Given:
f(x)=x^3+7x^2+7x-15
Finding all the possible rational zeros of f(x)
p= ±1,±3,±5,±15 (factors of coefficient of last term)
q=±1(factors of coefficient of leading term)
p/q=±1,±3,±5,±15
Now finding the rational zeros using rational root theorem
f(p/q)
f(1)=1+7+7-15
=0
f(-1)= -1 +7-7-15
= -16
f(3)=27+7(9)+21-15
=96
f(-3)= (-3)^3+7(-3)^2+7(-3)-15
= 0
f(5)=5^3+7(5)^2+7(5)-15
=320
f(-5)=(-5)^3+7(-5)^2+7(-5)-15
=0
f(15)=(15)^3+7(15)^2+7(15)-15
=5040
f(-15)=(-15)^3+7(-15)^2+7(-15)-15
=-1920
Hence the rational roots are 1,-3,-5 !
[18].Simplify (TTE): x(2x+y+5) - 2(x²+xy+5) + y(x + y)
Answer:
[tex]x(2x+y+5) - 2(x\²+xy+5) + y(x + y) = 5x -10 + y\²[/tex]
Step-by-step explanation:
Given
[tex]x(2x+y+5) - 2(x\²+xy+5) + y(x + y)[/tex]
Required
Simplify
We have:
[tex]x(2x+y+5) - 2(x\²+xy+5) + y(x + y)[/tex]
Open brackets
[tex]x(2x+y+5) - 2(x\²+xy+5) + y(x + y) = 2x\²+xy+5x - 2x\²-2xy-10 + xy + y\²[/tex]
Collect like terms
[tex]x(2x+y+5) - 2(x\²+xy+5) + y(x + y) = 2x\²- 2x\²+xy-2xy+ xy+5x -10 + y\²[/tex]
[tex]x(2x+y+5) - 2(x\²+xy+5) + y(x + y) = 5x -10 + y\²[/tex]
