Answer:
Ok so we have a set of 8 numbers {1,2,...,8}
a) 5 and 8 are picked.The probability here is:
In the first selection we can pick 5 or 8, so we have two possible outcomes out of 8 total outcomes, then the probability for the first selection is:
P = 2/8 = 1/4.
Now, if one of those numbers was picked in the first selection, only one outcome is possible in this second selection, (if before we picked a 5, here we only can pick an 8)
Then the probability is:
P = 1/8
The joint probability is equal to the product of the individual probabilities, so here we have:
P = (1/4)*(1/8) = 1/32 = 0.003
b) The numbers match:
In the first selection we can have any outcome, so the probability is:
P = 8/8 = 1
Now, based on the previous outcome, in the second selection we can have only one outcome, so here the probability is:
P = 1/8 = 0.125
The joint probability is p = 1/8
c) The sum is smaller than 4:
The combinations are:
1 - 1
1 - 2
2 - 1
We have 3 combinations, and the total number of possible combinations is:
8 options for the first number and 8 options for the second selection:
8*8 = 64
The probabilty is equal to the number of outcomes that satisfy the sentence divided by the total numberof outcomes:
P = 3/64 = 0.047
Using the probability concept, it is found that there is a:
i. 0.03125 = 3.125% probability that 5 and 8 are picked.
ii. 0.125 = 12.5% probability that both numbers match.
iii. 0.046875 = 4.6875% probability that the sum of the two numbers picked is less than 4.
A probability is the number of desired outcomes divided by the number of total outcomes.
In this problem, two integers are chosen from a set of 8, hence, there are [tex]8^2 = 64[/tex] total outcomes.
Item i:
Two outcomes result in 5 and 8 being picked, (5,8) and (8,5), hence:
[tex]p = \frac{2}{64} = 0.03125[/tex]
0.03125 = 3.125% probability that 5 and 8 are picked.
Item ii:
8 outcomes result in both numbers matching, (1,1), (2,2), ..., (8,8), hence:
[tex]p = \frac{8}{64} = 0.125[/tex]
0.125 = 12.5% probability that both numbers match.
Item ii:
Three outcomes result in a sum of less than 2, (1,1), (1,2), (2,1), hence:
[tex]p = \frac{3}{64} = 0.046875[/tex]
0.046875 = 4.6875% probability that the sum of the two numbers picked is less than 4.
A similar problem is given at https://brainly.com/question/15536019
PLEASE HELP!!! QUICKLY
Practice
Question 1: Choose the number that will complete this Pythagorean triple.
15, 17
Question 2: Choose the number that will complete this Pythagorean triple.
9,
41
Question 3: Choose the number that will complete this Pythagorean triple.
12, 35,
Reset
Submit
Answer:
1. = 8
2. =40
3. =37
Step-by-step explanation:
1. x = √(17² - 15²) = 8
2. x =√(9² +41²) = 40
3. x =√(12² + 35²) = 37
please mark brainliest
What is the base of the expression 11^12? A. 3 B. 11 C. 12 D. 21
An exponential has the base at the bottom, or the lower portion. Think of "basement" to help remember this. The exponent is the number up top, so 12 is the exponent.
Answer:
The person above me is correct ( :
Step-by-step explanation:
B
In a box-and-whisker plot, the interquartile
range is a measure of the spread of the
middle half of the data. Find the interquartile
range for the data set: 10, 3, 7, 6, 9, 12, 13.
Answer:
I believe the interquarrile range is 5
what is that is the derivative of
x^2-x+3 at the point
x=5
What value of x where
x²-x+3
a minimum?
Answer:
see explanation
Step-by-step explanation:
differentiate using the power rule.
[tex]\frac{d}{dx}[/tex]( a[tex]x^{n}[/tex] ) = na[tex]x^{n-1}[/tex] , thus
[tex]\frac{d}{dx}[/tex](x² - x + 3 ) = 2x - 1
x = 5 → 2(5) - 1 = 10 - 1 = 9
To find the value of x for minimum , equate [tex]\frac{d}{dx}[/tex] to zero
2x - 1 = 0 , then
2x = 1 and
x = [tex]\frac{1}{2}[/tex]
Marguerite wants to rent a carpet cleaner. Company A rents a carpet cleaner for $15 per day. Company B rents a carpet cleaner for $100 per week, with a one-time fee of $5. The following functions represent the rate structures of the two rental companies: x = the number of weeks Company A f(x) = 15(7x) Company B g(x) = 100x + 5 The function h(x) = f(x) – g(x) represents the difference between the two rate structures. Determine which statements about h(x) and about renting a carpet cleaner are true. Check all that apply. If Marguerite rents for 2 weeks, it will cost her more if she rents from Company B. If Marguerite rents for 2 weeks, it will cost her less if she rents from Company B. If Marguerite rents for 1 week, it will cost her the same at either company. If Marguerite rents for 1 week, it will cost her more if she rents from Company A. h(x) = 5x – 5 h(x) = 5x + 5
Answer:
see below
Step-by-step explanation:
Company A f(x) = 15(7x)
Company B g(x) = 100x + 5
If Marguerite rents for 2 weeks, it will cost her more if she rents from Company B
A = 105(2) = 210
B = 100(2) + 5 = 205 B costs less False
f Marguerite rents for 2 weeks, it will cost her less if she rents from Company B
A = 105(2) = 210
B = 100(2) + 5 = 205 B costs less True
If Marguerite rents for 1 week, it will cost her the same at either company
A = 105(1) = 105
B = 100(1) +5 = 105 True
If Marguerite rents for 1 week, it will cost her more if she rents from Company A
A = 105(1) = 105
B = 100(1) +5 = 105 False
h(x) = 5x – 5
h(x) = f(x) – g(x)
=15(7x) - ( 100x + 5)
= 105x - 100x -5
= 5x-5 True
h(x) = 5x + 5 False
Answer:
If Marguerite rents for 2 weeks, it will cost her less if she rents from Company B.
If Marguerite rents for 1 week, it will cost her the same at either company.
h(x) = 5x - 5.
Step-by-step explanation:
Company A: f(x) = 15(7x)
Company B: g(x) = 100x + 5
h(x) = f(x) - g(x)
So, the function h(x) is the difference between Company A's rental and Company B's rental.
h(x) = (15(7x)) - (100x + 5)
= (105x) - (100x + 5)
= 105x - 100x - 5
= 5x - 5
h(x) = 5x - 5.
Let's say that Marguerite rents for 1 week. In Company A, that will cost her 15 * 7 = 105. In Company B, it will cost her 100 + 5 = 105. So, if Marguerite rents for 1 week, it will cost her the same at either company.
Let's say that Marguerite rents for 2 weeks. In Company A, that will cost her 15 * 7 * 2 = 30 * 7 = 210. In Company B, it will cost her 100 * 2 + 5 = 200 + 5 = 205. So, if Marguerite rents for 2 weeks, it will cost her less if she rents from Company B.
Hope this helps!
1. for what constant k must f(k) always equal the constant term of f(x) for any polynomial f(x) 2. If we multiply a polynomial by a constant, is the result a polynomial? 3. if deg(f+g) is less than both deg f and deg g, then must f and g have the same degree?
Answer:
1. k=0
2. yes, result is still a polynomial.
3. yes, f and g must have the same degree to have deg(f+g) < deg(f) or deg(g)
Step-by-step explanation:
1. for what constant k must f(k) always equal the constant term of f(x) for any polynomial f(x)
for k=0 any polynomial f(x) will reduce f(k) to the constant term.
2. If we multiply a polynomial by a constant, is the result a polynomial?
Yes, If we multiply a polynomial by a constant, the result is always a polynomial.
3. if deg(f+g) is less than both deg f and deg g, then must f and g have the same degree?
Yes.
If
deg(f+g) < deg(f) and
deg(f+g) < deg(g)
then it means that the two leading terms cancel out, which can happen only if f and g have the same degree.
Suppose you invest $15,000 at the age of 35, and agree to start receiving
payments at the age of 45. At age 41, you decide you want to withdraw $5000
from your account. What is the IRS fee you will have to pay? Remember, the
IRS charges 10% if you withdraw before you are 59.5.
A. $500.00
B. $750.00
C. $50.00
D. $250.00
Answer:
A. $500.00
Step-by-step explanation:
IRS popularly known as Internal revenue service charges an IRS fee under the authority of the Federal Law and policy agencies. This implementation of IRS fee is to recuperate the cost of rendering a service to the masses.
From the given information in the question:
Suppose you invest $15,000 at the age of 35 and agree to start receiving payments at the age of 45.
At age 41, you decide you want to withdraw $5000 from your account.
Since the investor is still 41 years of age ; IRS will charge 10% of the withdrawal amount.
IRS fee = 10% of $5000
IRS fee = 0.1 × $5000
IRS fee = $500
A researcher compares the effectiveness of two different instructional methods for teaching anatomy. A sample of 146 students using Method 1 produces a testing average of 51.6. A sample of 180 students using Method 2 produces a testing average of 62.7. Assume the standard deviation is known to be 9.42 for Method 1 and 14.5 for Method 2. Determine the 98% confidence interval for the true difference between testing averages for students using Method 1 and students using Method 2. Step 1 of 2: Find the critical value that should be used in constructing the confidence interval.
Answer:
The confidence interval is [tex]-11.34 < \mu_1 -\mu_2 < -10.86[/tex]
Step-by-step explanation:
From the question we are told that
The first sample size is [tex]n_1 = 146[/tex]
The second sample size is [tex]n_2 = 180[/tex]
The first sample mean is [tex]\= x_1 = 51.6[/tex]
The second sample mean is [tex]\= x_2 = 62.7[/tex]
The first standard deviation is [tex]\sigma _1 = 9.42[/tex]
The second standard deviation is [tex]\sigma _2 = 14.5[/tex]
Given that the confidence level is 98% then the significance level is mathematically evaluated as
[tex]\alpha = (100 -98 )\%[/tex]
[tex]\alpha = 2 \%[/tex]
[tex]\alpha = 0.02[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the z-table , the value is [tex]Z_{\frac{\alpha }{2} } = 2.33[/tex]
The reason we are obtaining critical value of
[tex]\frac{\alpha }{2}[/tex]
instead of
[tex]\alpha[/tex]
is because
[tex]\alpha[/tex]
represents the area under the normal curve where the confidence level interval (
[tex]1-\alpha[/tex]
) did not cover which include both the left and right tail while
[tex]\frac{\alpha }{2}[/tex]
is just the area of one tail which what we required to calculate the margin of error
NOTE: We can also obtain the value using critical value calculator (math dot armstrong dot edu)
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \sqrt{ \frac{\sigma_1^2}{n_1^2} + \frac{\sigma_2^2}{n_2^2} }[/tex]
substituting values
[tex]E = 2.33 * \sqrt{ \frac{9.42^2}{146^2} + \frac{14.5^2}{180^2} }[/tex]
substituting values
[tex]E = 2.33 * \sqrt{ \frac{9.42^2}{146^2} + \frac{14.5^2}{180^2} }[/tex]
[tex]E = 0.2405[/tex]
The 98% confidence interval is mathematically represented as
[tex](\= x _ 1 - \= x_2 ) - E < \mu_1 -\mu_2 < (\= x _ 1 - \= x_2 ) + E[/tex]
substituting values
[tex](51.6 - 62.7) - 0.2405 < \mu_1 -\mu_2 < (51.6 - 62.7) + 0.2405[/tex]
[tex]-11.34 < \mu_1 -\mu_2 < -10.86[/tex]
Find the indicated sum for each sequence. S9 of –9, 36, –144, 576, ... A –585 B –471,861 C 1,887,435 D –471,852
=====================================================
Explanation:
This is a geometric sequence because each new term is found by multiplying the last term by -4.
The common ratio is r = -4. The first term is a = -9. We want to sum up n = 9 terms.
Use the geometric nth partial sum formula below to plug in the terms mentioned
[tex]S_n = \frac{a*(1-r^n)}{1-r}\\\\S_9 = \frac{-9*(1-(-4)^9)}{1-(-4)}\\\\S_9 = \frac{-9*(1-(-262144))}{1+4}\\\\S_9 = \frac{-9*(1+262144)}{1+4}\\\\S_9 = \frac{-9*(262145)}{5}\\\\S_9 = \frac{-2359305}{5}\\\\S_9 = -471,861\\\\[/tex]
Answer:
-471,861
Step-by-step explanation:
"An engineer designed a valve that will regulate water pressure on an automobile engine. The engineer designed the valve such that it would produce a mean pressure of 4.1 pounds/square inch. It is believed that the valve performs above the specifications. The valve was tested on 260 engines and the mean pressure was 4.2 pounds/square inch. Assume the standard deviation is known to be 0.9. A level of significance of 0.02 will be used. Determine the decision rule. Enter the decision rule."
Answer:
H₀ is accepted, we don´t have evidence to claim valves produces more than 4,1 pounds/square inch
Step-by-step explanation:
Normal Distribution
Population mean μ₀ = 4.1
Population standard deviation σ = 0,9
Sample size n = 260
Sample mean μ = 4,2
Level of significance 0,02 α = 0,02 form z-table we find z score
z(c) = 2,05 (critical value)
Test hypothesis
Null hypothesis H₀ μ = μ₀
Alternative hypothesis Hₐ μ > μ₀
Is a one tail-test ( to the right. Values have a mean over the population mean)
z(s) = ( μ - μ₀ )/ σ /√n
z(s) = 4,2 - 4,1 / 0,9/√260
z(s) = 0,1 *16,1245 / 0,9
z(s) = 1,7916
To compare z(s) and z(c)
z(s) < z(c)
Then z(s) is in the acceptance region, we accept H₀
In circle O, radius OQ measures 9 inches and arc PQ measures 6π inches. Circle O is shown. Line segments P O and Q O are radii with length of 9 inches. Angle P O Q is theta. What is the measure, in radians, of central angle POQ?
Answer:
2π/3 radStep-by-step explanation:
To get theta, we will apply the formula for calculating the length of an arc as shown;
Length of an arc = theta/360 * 2πr
theta is the central angle (required)
r is the radius of the circle
Given r = 9 inches and length of the arc PQ = 6π in
Substituting this given values into the formula to get the central angle theta;
6π = theta/360 * 2πr
Dividing both sides by 2πr
theta/360 = 6π/2πr
theta/360 = 3/r
theta/360 = 3/9
theta/360 = 1/3
cross multiplying;
3*theta = 360
theta = 360/3
theta = 120°
Since 180° = π rad
120° = x
x = 120π/180
x = 2π/3 rad
Hence the measure of the central angle in radians is 2π/3 rad
Circle the numbers divisible by 2.
320;5,763; 9,308; 5,857;3,219; 5,656; 83,001;53,634
Subtract the rational expressions: (x/x+2)-(2/x)
In how many ways can 13 people be divided into four groups with 3, 6, 2 and 2 people respectively?
Answer:
6227020800
Step-by-step explanation:
There are 13 ways to choose the first person in the first group, 12 ways to choose the second person in the first group and so on until we get 1 way to choose the second person in the last group so the answer is 13 * 12 * 11 * ... * 3 * 2 * 1 = 13! = 6227020800.
Assume that y varies directly with x, then solve.
If y=6 when x= 2/3 find x when y=12.
х: /
2×y = 2×6= 12 so 2×x = 2×23 = 43 = 113
Step-by-step explanation:
Is this what you are looking for?
Find the unknown side length, x. Write your answer in simplest radical form.
Answer:
Correct option: D
Step-by-step explanation:
In the figure we have a right triangle, that is, one of the angles is a 90° angle. Therefore, we can use the Pythagoras' theorem to find the relation between the sides of the triangle:
[tex]a^2 = b^2 + c^2[/tex]
Where b and c are cathetus of the triangle (sides adjacent to the 90° angle) and a is the hypotenuse (opposite side to the 90° angle).
So in our case, we have that x is the hypotenuse, and 40 and 42 are cathetus, so we have:
[tex]x^2 = 40^2 + 42^2[/tex]
[tex]x^2 = 1600 + 1764[/tex]
[tex]x^2 = 3364[/tex]
[tex]x = 58[/tex]
So the correct option is D.
If y>0, which of these values of x is NOT in the domain of this equation? y=x2+7x
Answer:
[tex]\boxed{\sf \ \ \ [-7,0] \ \ \ }[/tex]
Step-by-step explanation:
Hello
[tex]y=x^2+7x=x(x+7) >0\\<=> x>0 \ and \ x+7 >0 \ \ or \ \ x<0 \ and \ x+7<0\\<=> x>0 \ \ or \ \ x<-7\\[/tex]
So values of x which is not in this domain is
[tex]-7\leq x\leq 0[/tex]
which is [-7,0]
hope this helps
The number of users on a website has grown exponentially since its launch. After 1 month, there were 120 users. After 4 months, there were 960 users. Find the exponential function that models the number of users x months after the website was launched. Write your answer in the form f(x)=a(b)x.
Answer:
f(x) = 60(2)ˣ
Step-by-step explanation:
f(x) = a(b)ˣ
After one month:
120 = a(b)¹
After four months:
960 = a(b)⁴
Divide the second equation by the first:
8 = b³
b = 2
Plug into either equation and find a.
120 = a(2)¹
a = 60
Therefore, f(x) = 60(2)ˣ.
Alex has built a garden shed in the shape shown.
(A) Alex plans to paint the outside of the shed, including the roof but not the floor. One can of paint can cover 6m^2 . How many cans of paint will Alex need.
(B)If one can of paint costs $25.50, what will the cost be including 13% tax.
Answer:
A) 22 cans required to paint
B) Including 13% tax, cost of painting = $633.93
Step-by-step explanation:
As we check the figure, we have a composite figure.
Cuboid on the base and a pyramid on the top of it.
To find the area to be painted, we have 4 rectangular faces of cuboid with dimensions 6m [tex]\times[/tex] 3m.
And 4 triangular faces of pyramid with Base = 6m and Height 5m.
So, total area to be painted = 4 rectangular faces + 4 triangular faces
Area of rectangle = Length [tex]\times[/tex] Width = 6 [tex]\times[/tex] 3 = 18 [tex]m^2[/tex]
Area of triangle = [tex]\frac{1}{2}\times Base \times Height =\frac{1}{2}\times 6 \times 5 = 15\ m^{2}[/tex]
Total area to be painted = 4 \times 18 + 4 \times 15 = 72 + 60 = 132 [tex]m^2[/tex]
A) Area painted by 1 can = 6 [tex]m^2[/tex]
Cans required to paint 132 [tex]m^2[/tex] = [tex]\frac{132}{6} = 22\ cans[/tex]
B)
Cost of 1 can = $25.50
Cost of 22 can = $25.50 [tex]\times[/tex] 22 = $561
Including tax of 13% = $561 + $561 [tex]\times \frac{13}{100}[/tex] = $561 + $72.93 = $633.93
So, the answers are:
A) 22 cans required to paint
B) Including 13% tax, cost of painting = $633.93
Help ! Inductive and deductive reasoning differ in which way? A) Conclusions drawn using deductive reasoning are always false, while conclusions drawn using inductive reasoning are always true. B) Conclusions drawn using inductive reasoning are always valid, while conclusions drawn using deductive reasoning may or may not be valid. C) Conclusions drawn using inductive reasoning are always false, while conclusions drawn using deductive reasoning are always true. D) Conclusions drawn using deductive reasoning are always valid, while conclusions drawn using inductive reasoning may or may not be valid.
Answer:
B) Conclusions drawn using inductive reasoning are always valid, while conclusions drawn using deductive reasoning may or may not be valid.
Step-by-step explanation:
Inductive reasoning uses logic and uses more evidence to draw conclusions. In deductive reasoning, WE decide whether a deductive statement is true by assessing the strength of the link between the premises and the conclusion. But some deductive reasoning may appear to make sense without pointing to a truth
Answer:
The answer is D. Conclusions drawn using deductive reasoning are always valid, while conclusions drawn using inductive reasoning may or may not be valid.
Step-by-step explanation:
I took the test
What is the degree of the polynomial?
Answer:
2
Step-by-step explanation:
The degree of this polynomial is 2, since a parabola is drawn. A parabola is a graph of a quadratic equation which has the highest degree of 2.
Two trains leave New York at the same time heading in opposite directions. Train A travels at 4/5 the speed of train one. After seven hours they are 693 miles apart. What was the speed of train A? Can you pls help me fast
=============================================
Work Shown:
x = speed of train A
y = speed of train B
"train A travels 4/5 the speed of train B" (I'm assuming "train one" is supposed to read "train B"). So this means x = (4/5)y
distance = rate*time
d = x*7
d = (4/5)y*7 = (28/5)y represents the distance train A travels
d = y*7 = 7y represents the distance train B travels
summing those distances will give us 693
(28/5)y + 7y = 693
5*( (28/5)y + 7y ) = 5*693
28y + 35y = 3465
63y = 3465
y = 3465/63
y = 55
Train B's speed is 55 mph
4/5 of that is (4/5)y = (4/5)*55 = 4*11 = 44 mph
Train A's speed is 44 mph
Find the equation of a line that contains the points (−2,2) and (−6,−5). Write the equation in slope-intercept form, using fractions when required.
Answer:
[tex]4y - 7x - 1 = 0[/tex]
[tex]m = \frac{y2 - y1}{x2 - x1?} [/tex]
[tex]m = \frac{ - 5 - 2}{ - 6 - - 2?} [/tex]
[tex]m = \frac{ - 7}{ - 4} [/tex]
[tex]m = \frac{7}{4} [/tex]
[tex]y = m(x - x1) + y1[/tex]
[tex]y = \frac{7}{4} (x + 2) + 2[/tex]
[tex]y = \frac{7}{4} x + \frac{7}{2} + 2[/tex]
[tex]y = \frac{7}{4} x + \frac{11}{2} [/tex]
[tex]4y = 7x + 22[/tex]
[tex]4y - 7x - 22 = 0[/tex]
The equation of the line passing through the point (-2,2) and (-6,-5) is,
y = (-7/4)x +(11/2).
What is an equation of the line?An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.
The general form of the equation of the line:-
y = mx + c
m = slope
c = y-intercept
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given that the equation of a line that contains the points (−2,2) and (−6,−5).
Calculate the slope of the line,
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
Slope = ( -5-2) / (-6 + 2 )
Slope= 7 / 4
The y-intercept is calculated as,
y = mx + c
2 = (-7/4) x 2 + c
c = 11 / 2
The equation will be written as,
y = mx + c
y = (7 / 4)x + (11/2)
Therefore, the equation of the line passing through the point (-2,2) and (-6,-5) is,
y = (-7/4)x +(11/2).
To know more about an equation of the line follow
https://brainly.com/question/18831322
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¿Qué interés produce s/ 72,000 al 5% anual en 1 año, 1 mes, 10 días?
Answer: 3,988.8
Usaremos la fómula: I = C * i * n
I = 72 000 * 0.05 * (1 año + 1 mes + 10 día)
I = 72 000 * 0.05 * (1 + 0.08 + 0.0028)
I = 72 000 * 0.05 * 1.108
3,988.8
Step-by-step explanation:
Podemos obtener el interés que produce un capital con la siguiente fórmula:
I = C * i * n
Ejemplo: Si queremos calcular el interés simple que produce un capital de 1.000.000 pesos invertido durante 5 años a una tasa del 8% anual. El interés simple se calculará de la siguiente forma:
I = 1.000.000 * 0,08 * 5 = 400.000
Si queremos calcular el mismo interés durante un periodo menor a un año (60 días), se calculará de la siguiente forma:
Periodo: 60 días = 60/360 = 0,16
I = 1.000.000 * 0,08 * 60/360 = 13.333
Espero te ayude :3
Given: F={(0, 1), (2, 4), (4, 6), (6, 8)} and G = {(2, 5), (4,7), (5, 8), (6,9). (7.5))
(F. G) (2) =
10
O 20
O 40
Answer:
(F·G)(2) = 20
Step-by-step explanation:
We assume you want (F·G)(2).
(F·G)(2) = F(2)·G(2)
F(2) = 4 . . . . from the ordered pair (2, 4)
G(2) = 5 . . . .from the ordered pair (2, 5)
So your product is ...
F(2)·G(2) = 4·5 = 20
(F·G)(2) = 20
There are 4 red balls and 6 green balls in a bag.
You reach in the bag and take out 3 balls without looking.
What is the probability that all three of the balls you take out are red?
[tex]\frac{1}{30}[/tex]
Step-by-step explanation:From the question, in the bag there are;
4 red balls
6 green balls
10 balls in total.
Now, reaching in the bag and taking out 3 balls without looking, the probability that all three balls are red, can be analyzed as follows;
All three red means;
The first ball is red,
The second ball is red and;
The third ball is red.
i. First you take out a ball from a total of 10 balls. The probability P⁰(R) of having a red ball is given as;
P⁰(R) = [tex]\frac{possible-space}{total-space}[/tex]
Since there are 4 red balls, the possible-space is 4
Also, since there are a total of 10 balls, the total-space is 10
P⁰(R) = [tex]\frac{4}{10} = \frac{2}{5}[/tex]
ii. Secondly, you take out a ball from a remaining total of 9 balls. The probability P¹(R) of still having a red ball is given as;
P¹(R) = [tex]\frac{possible-space}{total-space}[/tex]
Since there are 3 red balls remaining, the possible-space is 3
Also, since there are a remaining total of 9 balls, the total-space is 9
P¹(R) = [tex]\frac{3}{9} = \frac{1}{3}[/tex]
iii. Thirdly, you take out a ball from a remaining total of 8 balls. The probability P²(R) of still having a red ball is given as;
P²(R) = [tex]\frac{possible-space}{total-space}[/tex]
Since there are 2 red balls remaining, the possible-space is 2
Also, since there are a remaining total of 8 balls, the total-space is 8
P²(R) = [tex]\frac{2}{8} = \frac{1}{4}[/tex]
Therefore, the probability P(R) of taking out three red balls without looking is given by the product of the probabilities described above. i.e
P(R) = P⁰(R) x P¹(R) x P²(R)
P(R) = [tex]\frac{2}{5} * \frac{1}{3} * \frac{1}{4} = \frac{1}{30}[/tex]
In Sparrowtown, the use of landlines has been declining at a rate of 5% every year. If there are 20,000 landlines this year, how many will there be in 15 years? If necessary, round your answer to the nearest whole number.
Answer:
5,000
Step-by-step explanation:
If it decreases by 5% a year, it'll decrease by 75% in 15 years
i.e 1 year = 5%
15 years = x
Cross multiply
x = 75%
Therefore, since it decreases by 75%
100 - 75 x 20,000 = 5,000
100
Could someone please help me Thank you!!
Answer:
-5/3 -2/5
im pretty sure
Answer:
[tex]5^{7[/tex] or 78125
Step-by-step explanation:
5^2 ( 5^3 · 5^2 )
= 5^2 ( 5^5 ) = 5^7
or, 78125
hi there help me please
Hello!
Answer:
Choice 1.
Step-by-step explanation:
We can go through each answer choice and examine whether it represents the question:
1) This does not represent the question because 10% of 6 is 0.6. The question is asking to find a number that 6 = 10% of, not finding 10% of 6.
2) Correct because a number multiplied by 10%, or 0.1, should be equal to 6 to answer the question.
3) Correct because 6 is equivalent to 10% of the answer, which is stated in this answer choice.
4) Correct because 6 should be 10% of the answer.
Therefore, the incorrect choice would be Choice 1.
hich sequence of transformations could map △ABC to △XYZ? a reflection across line m and a dilation a dilation by One-fourth and a reflection across line m a rotation about C and a dilation a dilation by One-fourth and a translation
Answer:
a dilation by One-fourth and a translation
Step-by-step explanation:
For determining the sequence first we have to find out the scale factor which is shown below:
We can calculate the scale factor to obtain
[tex]= \frac{1.5}{6} \\\\ = \frac{1}{4}[/tex]
Now as we know that the triangle XYZ and the triangle ABC are similar to each other but in the triangle XYZ is smaller in size and it is a shift to upward and right
Therefore the last option is correct