Answer:
(a) 0.0225
(b) 0.225
Step-by-step explanation:
It is given that 15% of total population is allergic to pollenallergic to pollen.
Thus, Probability of an individual s/he has allergy is 0.15
Thus, The probability that two person is selected and both has allergy is 0.15 × 0.15 = 0.0225
And the Probability that at least one person is suffered from allergy from that two person = P(allergic and non-allergic) + P(non-allergic and allergic)
⇒ 0.15 × (1 - 0.15) + (1 - 0.15) × 0.15
⇒ 0.15 × 0.85 + 0.85 × 0.15 = 0.225
What is the value of the 11th term of the sequence 1, -2, 4, -8, ...?
4,096
1,024
-2,048
-1,024
How many zeros are there at the end of 100!?
Final answer:
The number of zeros at the end of 100! is determined by counting the multiples of 5 in the factorization, including higher powers like 25. The result is a total of 24 zeros at the end of 100!.
Explanation:
To determine how many zeros are at the end of the factorial of 100 (100!), we need to know how many times the number 10 can be factored within that number. Since 10 is the product of 2 and 5, we should count the number of 2s and 5s in the prime factorization of 100!. The number of zeros at the end of 100! will equal the smaller of these two counts. However, because there are more 2s than 5s in the prime factorization, we only need to count the number of 5s as every 5 will have a corresponding 2 to form a 10.
For 100!, we count how many multiples of 5 there are within that range, including the multiples of 25 (since 25 includes an extra 5), and possibly higher powers of 5 if applicable. For example, 5 is counted once, 25 is counted twice (as 25 = 5×5), and so on.
Therefore, the number of zeros at the end of 100! equals the sum of the integer division of 100 by 5, plus the integer division of 100 by 25, and so on for any higher powers of 5. However, since 100 < 125, we do not need to consider any higher powers than 25.
We calculate:
100 ÷ 5 = 20,
100 ÷ 25 = 4.
Adding these together (20 + 4), we find that there are 24 zeros at the end of 100!.
Find the first five terms of the sequence described by the following recursive formula: an = an – 1 + an – 2 where a1 = 1.2 and a2 = 2.3
1.2, , , ,
Find the first six terms of the sequence described by the following recursive formula:
an = an – 1 + an – 2
where a3 = -5 and a4 = 3
,
,
,
,
,
The recursive formula an = an – 1 + an – 2 describes a sequence where each term is the sum of the two previous terms. To find the first five or six terms, we substitute the given initial conditions into the formula and repeatedly apply it to find subsequent terms.
Explanation:The recursive formula an = an – 1 + an – 2 describes a sequence where each term is the sum of the two previous terms. To find the first five terms, we begin with a1 = 1.2 and a2 = 2.3. Then we use the formula to find the next terms:
a3 = a2 + a1 = 2.3 + 1.2 = 3.5a4 = a3 + a2 = 3.5 + 2.3 = 5.8a5 = a4 + a3 = 5.8 + 3.5 = 9.3So the first five terms of the sequence are 1.2, 2.3, 3.5, 5.8, and 9.3.
Similarly, to find the first six terms of the sequence with a3 = -5 and a4 = 3, we use the formula:
a5 = a4 + a3 = 3 + (-5) = -2a6 = a5 + a4 = -2 + 3 = 1So the first six terms of this sequence are -5, 3, -2, 1, -1, and 0.
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Which one of the binomials is a factor of this trinomial?
x^2-13x+40
A. x-8
B. x+8
C. x-4
D. x+4
For what values of x does f(x)= x^2 +9x +20 reach its minimum value?
The minimum value of the quadratic function f(x)= [tex]x^2[/tex] +9x +20 is achieved at x = -4.5, calculated using the vertex formula -b/2a.
Explanation:The function f(x)= [tex]x^2[/tex] +9x +20 is a quadratic function. The minimum value of a quadratic function is achieved at the vertex. The x-coordinate of the vertex can be found using the formula -b/2a, where a and b are coefficients of [tex]x^2[/tex] and x respectively in the standard form a[tex]x^2[/tex] + bx + c. Here, a=1 and b=9.
So, by applying the formula, the value of x will be -b/2a = -9/(2*1) = -4.5. Hence, the function achieves its minimum value when x = -4.5.
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Graph y = log8^x and its inverse
Answer:
Third one will be correct.
Step-by-step explanation:
Given : y =[tex]log_{8}(x)[/tex].
To find : Graph and its inverse.
Solution : We have given that
y =[tex]log_{8}(x)[/tex].
For x - intercept , y =0.
y = 0
0 =[tex]log_{8}(x)[/tex].
x = 1
(1,0)
Inverse of y =[tex]log_{8}(x)[/tex].
Interchange the x and y.
x = [tex]log_{8}(y)[/tex].
Solving for y
y = [tex]8^{x}[/tex].
Then For x = 0
y = [tex]8^{0}[/tex].
y = 1
For inverse ( 0 ,1)
Then we can see from given graphs Third one will be correct.
Therefore, Third one will be correct.
a restaurant offers 3 kinds of bread 4 kinds of meat and 3 kinds of cheese
Answer:
36 combos
Step-by-step explanation:
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You buy a commemorative coin for $110. Each year, t, the value V of the coin increases by 4%
Part a: Write a function that can be used to find the coin’s value after t years.
Part b: If the coin’s value continues to grow 4% per year, what will the approximate value be in 8 years? Round to two decimal places.
Answer:
$136.86
Step-by-step explanation:
True or False.
A binomial is also a polynomial.
A purse contains dimes and nickels. The total value of all the coins is, at most, $2.50, and there are at least three of each coin. Which of the following systems correctly shows the system that describes the possible number of nickels (n) and dimes (d) in the purse?
<= That means greater than or equal to or less than or equal to
1.n >= 3
d >= 3
0.05n+0.1d <= 2.50
2. n <= 3
d <= 3
0.05+0.1d <= 2.50
3. n <= 3
d<= 3
n + d >= 2.50
4. n>=3
d >= 3
n + d <=2.50
A cubic centimeter of quartz, olivine, and gold weighs 2.5, 3.0, and 19.8 grams, respectively. this indicates that
To solve the problem we must know about density.
The different weight shows that the solids have different density.
Given to us
A cubic centimeter of quartz, olivine, and gold weighs 2.5, 3.0, and 19.8 grams.What are weight and mass?We know that weight is the product of mass and acceleration due to gravity, also, mass is the product of density and volume.
[tex]\rm{ weight = mass \times acceleration\ due\ to\ gravity[/tex]
[tex]\rm{ w = m \times g[/tex]
[tex]\rm{ Mass = density \times volume[/tex]
[tex]m = \rho \times v[/tex]
What is the relationship between weight and mass?In the three solids given, the acceleration due to gravity will be the same, also, it is already mentioned that the volume of the three materials is the same that is 1 cubic centimeter.
[tex]w = m \times g\\w = (\rho \times v) \times g\\\\w = \rho \times 1\ cm^3 \times 9.81[/tex]
Therefore, the only thing that can vary is the density of the solids. Hence, the different weight shows that the solids have different density, the more is the weight the more is the density of the solid.
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How is the graph of y = 8x^2 − 1 different from the graph of y = 8x^2?
Answer:
1 up⊕⊕⊕⊕⊕⊕⊕⊕
Step-by-step explanation:
If f(x)=5x-2 and g(x)=2x+1, find(f-g)(x)
Write the equation of a hyperbola with vertices (3, -1) and (3, -9) and co-vertices (-6. -5) and (12, -5).
Please Help!!!
which statement is true about the system x-3y = 5 and y = x - 7 ?
Triangle PIG was rotated to create triangle P'I'G'. Describe the transformation using details and degrees.
The value of a camcorder bought new for $2000 decreases 20% each year. Identify the function for the value of the camcorder. Does the function represent growth or decay?
A) V(t) = 2000(0.8)t; growth
B) V(t) = 2000(0.8)t; decay
C) V(t) = 2000(1.2)t; decay
D) V(t) = 2000(1.2)t; growth
Answer: V(t) = 2000(0.8)t; decay
Step-by-step explanation:
What is best definition of combining like terms
What can you conclude about the slope of the values in the table? Check all that apply.
The slope is 3.
The slope is 0.
The slope is undefined.
The graph will be a horizontal line.
The graph will be a vertical line.
The graph will have a line with a positive slope.
The conclusion that can be drawn from the slope of the values given in the table is:
3. Slope is undefined.
5. Graph is a vertical line.
First, let's determine the value of the slope by applying the slope formula using two points given from the table, say, (1000, 20) and (1000, 23):Slope formula = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]
Let,[tex](1000, 20) = (x_1, y_1)\\\\(1000, 23) = (x_2, y_2)[/tex]
Substitute:[tex]slope(m)=\frac{23 - 20}{1,000 - 1,000}\\\\slope (m) =\frac{3}{0}[/tex] (undefined)
Zero cannot divide 3 hence, the slope is undefined.Slope that are vertical have rise but no run, thus, their slope is undefined.(see attachment for image showing an example of how an undefined slope looks like on a graph.)
Therefore, the conclusion that can be drawn from the slope of values given in the table is:
3. Slope is undefined.
5. Graph is a vertical line.
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The longest side of an acute triangle measures 30 inches. The two remaining sides are congruent, but their length is unknown.What is the smallest possible perimeter of the triangle, rounded to the nearest hundredth?
what divides an angle into two congruent angles
2. The value of a Plasma TV bought new for $3,700 decreases 25% each year. Identify the function for the value of the television. Does the function represent growth, or decay?
V(t) = 3700(1.25)t; growth
V(t) = 3700(0.75)t; decay
V(t) = 3700(1.25)t; decay
V(t) = 3700(0.75)t; growth
Answer: V(t) = 3700(0.75)t; decay
Step-by-step explanation:
Write an equation for ab is congruent to segment bc
Answer:
[tex]\overline {ab}\cong \overline {bc}[/tex]
Step-by-step explanation:
We are asked to write an equation for the given statement.
Statement:
Segment 'ab' is congruent to segment 'bc'.
We know that segment is written by a bar on name of segment as: [tex]\overline {ab}[/tex] and [tex]\overline {bc}[/tex].
Congruent sign is [tex]\cong[/tex]
Therefore, our required equation would be: [tex]\overline {ab}\cong \overline {bc}[/tex]
The formula is used to find the area of a parallelogram. if the base of a parallelogram is doubled and its height is doubled, how does this affect the area?
Choose the correct simplification of the expression (7x − 3)(4x2 − 3x − 6).
28x3 − 33x2 − 33x − 18
28x3 + 33x2 − 33x + 18
28x3 − 51x2 − 33x + 18
28x3 − 33x2 − 33x + 18
a b c d
Answer:
The expression (7x − 3) × (4x² − 3x − 6) is equivalent to 28x³ - 33x² - 33x + 18 .
Step-by-step explanation:
As given the expression in the question be as follow .
= (7x − 3) × (4x² − 3x − 6)
= 7x × (4x²- 3x - 6) - 3 × (4x² - 3x - 6)
Now open the bracket
= 7x × 4x² + 7x × -3x + 7x × -6 -3 × 4x² -3 × -3x - 3 × -6
= 28x³ -21x² -42x -12x² + 9x +18
= 28x³ -21x² - 12x² -42x + 9x + 18
= 28x³ - 33x² - 33x + 18
Therefore the expression (7x − 3) × (4x² − 3x − 6) is equivalent to 28x³ - 33x² - 33x + 18 .
HELP ROUND 479065.389037 TO THE NEAREST THOUSAND
Convert 28.7251° to degrees, minutes, and seconds. Round to the nearest second.
28.7251 =
28 degrees
then take the decimal and multiply by 60 to get the minutes
so 0.7251 *60 = 43.506, use the whole number (43)
so now you have 28 degrees, 43 minutes
now take the remaining decimal ( 0.506) and multiply by 60
0.506*60= 30.36
when you have a decimal left over for the seconds, keep that as is.
so you now have 28 degrees, 43 minutes and 30.36 seconds
use ' for minutes and " for seconds
28 degrees 43' 30.36"
rounded to the nearest second would be 28 degrees 43 minutes and 30 seconds
Find the sum of the following infinite geometric series, if it exists.
1.02 + 2.04 + 4.08 + 8.16 +…
20
Does not exist
22
24
We can see that for every increment, the number gets doubled positively. Since we are looking for the value when the repetition is made infinite, therefore the value at that point would also be infinite. Since infinite is imaginary, therefore the correct answer is:
Does not exist
The frequency table shows the results of a survey comparing weekly gasoline costs to the average number of miles a car can drive on a gallon of gasoline. Marcel converts the frequency table to a conditional relative frequency table by row. Which value should he use for Y? Round to the nearest hundredth. 0.19 0.45 0.82 0.90
Answer:
Its D on Ed2022
Step-by-step explanation:
A certain forest covers an area of 1800 km2. Suppose that each year this area decreases by 8.5%. What will the area be after 14 years? Use the calculator provided and round your answer to the nearest square kilometer.
[tex]519km^{2}[/tex] will be the area after [tex]14[/tex] years.
What is area?
Area is the quantity that expresses the extent of a region on the plane or on a curved surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object.
According to questions, a certain forest covers an area of [tex]1800[/tex] [tex]km^{2}[/tex]. Each year this area decreases by [tex]8.5[/tex]%.
We have to find the area after 14 years.
Area after 14 years can be found using the below formula
[tex]A=I(1-r)^{t}[/tex]
[tex]=1800(1-0.085)^{14}[/tex]
[tex]=1800[/tex]×[tex]0.288[/tex]
[tex]=519km^{2}[/tex]
Hence, [tex]519km^{2}[/tex] will be the area after [tex]14[/tex] years.
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