Let the function P represent the population P(d), in thousands, of a colony of insect
d days after first being measured. A model for P is P(d) = 10. (1.08)".
Answers
Answer:
(c) and (e) are true
Step-by-step explanation:
Given
[tex]P(d) = 10. (1.08)^d[/tex]
See attachment for complete question
Required
Which of the options is true
(a) 1080 insects on day 1
This implies that d = 1
So, we have:
[tex]P(1) = 10* (1.08)^1[/tex]
[tex]P(1) = 10* 1.08[/tex]
[tex]P(1) = 10.8[/tex]
(a) is incorrect because [tex]P(1) \ne 1080[/tex]
(b) 10800 insects after a week
This implies that [tex]d = 7[/tex]
So, we have:
[tex]P(7) = 10* (1.08)^7[/tex]
[tex]P(7) = 10* 1.71382426878[/tex]
[tex]P(7) = 17.14[/tex]
(b) is incorrect because [tex]P(7) \ne 10800[/tex]
(c): Growth factor per day is 1.08
An exponential factor is represented as:
[tex]y = ab^x[/tex]
Where
b is the growth factor
By comparison:
[tex]b = 1.08[/tex]
Hence, (c) option is true
(d): Growth factor per week is 1.08*7
In (c), we have:
[tex]b = 1.08[/tex] as the daily growth factor
So, the growth factor for n days is:
[tex]Factor = 1.08^n[/tex]
Substitute 7 for n i.e. 7 days
[tex]Factor = 1.08^7[/tex]
So, the growth factor for 7 days is: [tex]1.08^7[/tex] not [tex]1.08*7[/tex]
Hence, (d) option is true
(e): Growth factor per week is 1.08*7
In (c), we have:
[tex]b = 1.08[/tex] as the daily growth factor
For hourly rate, we have:
[tex]Factor = 1.08^\frac{1}{24}[/tex]
Hence, (e) option is true
Related Questions
Evaluate the expression. Can someone show me how this is done with fractions on 7 and 9
Answers
Answer:
Number 7 is; -1/7776
number nine is :| −8/ 3 | or 2.666667
Step-by-step explanation:
-1/6)^5=1^5/6^5
=-1/^5/6/5
1^5=1
=-1/6^5
6^5=7776
=-1/7776
|(− 1/ 3 )(110+9−2)|
=| −1/ 3 (110+9−2)|
=| −1/ 3 (1+9−2)|
=| −1/ 3 (10−2)|
=| −1 /3 (8)|
=| −8 /3 | =2.666667
Hope this helped!!!!
How do I answer this and I need explanation pls
Answers
Answer:
65 degrees
Step-by-step explanation:
1) Find the value of x
The sum of all the interior angles of a triangle is always 180 degrees. Knowing this, we can construct the following equation:
[tex](2x-5)+(115-x)+x=180[/tex]
Open up the parentheses
[tex]2x-5+115-x+x=180[/tex]
The two x's cancel out
[tex]2x-5+115=180\\2x+110=180[/tex]
Subtract 110 from both sides
[tex]2x+110-110=180-110\\2x=70[/tex]
Divide both sides by 2
[tex]2x/2=70/2\\x=35[/tex]
Therefore, x is equal to 35.
2) Find the value of <C
[tex]C=2x-5[/tex]
Plug 35 into the equation as x
[tex]C=2(35)-5\\C=70-5\\C=65[/tex]
Therefore, the value of angle C is 65 degrees.
I hope this helps!
A researcher studying public opinion of proposed Social Security changes obtains a simple random sample of 50 adult Americans and asks them whether or not they support the proposed changes. To say that the distribution of the sample proportion of adults who respond yes, is approximately normal, how many more adult Americans does the researcher need to sample in the following cases? (a) 20% of all adult Americans support the changes (b) 25% of all adult Americans support the changes
Answers
Hence, the study would require at least 385 more adult Americans to be sampled as the degree of inaccuracy is E. (e.g., 0.05).
What is proportionality ?In mathematics, proportionality is the connection between two factors that maintains a fixed ratio called scale factor. Or, to put it another way, if one variable is increased or divided by a specific number, the second variable will also be doubled or divided by that identical number, maintaining their proportionality. Calculus, algebra, and geometry are three areas of mathematics where this idea is frequently applied.
given
(a) If 20% of adult Americans favour the suggested reforms, the sample size needed at the very least is:
n = [(zα/2)² * p * (1-p)] / E²
where z/2 is the standard normal distribution's critical value for the chosen degree of confidence (e.g., 1.96 for a 95% confidence level).
The population proportion is p. (0.2 in this case)
The degree of inaccuracy is E. (e.g., 0.05)
When we enter the values, we obtain:
n = [(1.96)² * 0.2 * (1-0.2)] / 0.05²
n = 1536.64
Thus, the study would require at least 1537 more adult Americans to be sampled.
(b) The minimal sample size needed if the proposed modifications are
supported by 25% of all adult Americans is:
n = [(zα/2)² * p * (1-p)] / E²
where:
The standard normal distribution's critical value, z/2, depends on the desired level of confidence (e.g., 1.96 for a 95% confidence level).
The population proportion is p. (0.25 in this case)
The degree of inaccuracy is E. (e.g., 0.05)
When we enter the values, we obtain:
n = [(1.96)² * 0.25 * (1-0.25)] / 0.05² \sn = 384.16
Hence, the study would require at least 385 more adult Americans to be sampled as the degree of inaccuracy is E. (e.g., 0.05).
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Find the co-ordinates of the point where the line y = 3x - 8 crosses the y-axis.
Answers
Explanation: In y=mx + b, m represents the slope of the line and b represents the y intercept, since b is -8, it will cross the y-axis at (0,-8)
Please help :) Giving brainliest.
Answers
Answer:
D
Step-by-step explanation:
A sequence is defined by the formula f(n+1)=f(n)-3. If f(4)=22, what is f(1)?
A. 10
B. 13
C. 31
D. 34
Answers
9514 1404 393
Answer:
C. 31
Step-by-step explanation:
The recursive definition tells us the 4th term is 22 and the common difference is -3. This lets us write an explicit formula for the n-th term:
f(n) = f(4) +d(n -4)
f(n) = 22 -3(n -4) = 34 -3n
Substituting n=1 into this formula, we get ...
f(1) = 34 -3(1) = 31
The first term is f(1) = 31.
Answer:
31
Step-by-step explanation:
Find the 43rd term of the sequence
-3.0,-2.5,-2.0,-1.5
Answers
Answer:
19.5
Step-by-step explanation:
The 43rd term of the sequence is 19.5
How can I get the answer for c
Answers
125 and c are supplementary angles which means they add up to 180
5th grade math. correct answer will be marked brainliest
Answers
Answer:
2 over 15 I think. I might be wrong. I rarely deal with fractions anymore.
a bottle of soft drinks costs $2. the commission paid on one bottle is 2% of the cost price.find the commission on 24 bottles of soft drinks
Answers
Answer:
$0.96
Step-by-step explanation:
First, find the cost of the 24 bottles, by multiplying 24 by 2
24(2)
= 48
Find the commission by finding 2% of 48
48(0.02)
= 0.96
So, the commission will be $0.96
The commission on 24 bottles of soft drinks is $0.96.
How to find the commission on 24 bottles of soft drinks?Given:
a bottle of soft drinks costs $2. the commission paid on one bottle stands at 2% of the cost price.
First, we want to estimate the cost of the 24 bottles, by multiplying 24
by 2
[tex]= 24*(2)[/tex]
= 48
To find the commission by estimating 2% of 48
commission = 48*(0.02)
commission = 0.96
So, the commission will be $0.96.
Therefore, the commission on 24 bottles of soft drinks is $0.96.
To learn more about algebra
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HEEEEEEEEEEEEEELLLLLLLLLLLLLLLLLLPPPPPPPPPPPPPPPPPP
Answers
Answer:
x = 12
Step-by-step explanation:
Given:
m<BCF = 4x°
m<CFE = 11x°
Required:
m<BCF and m<CFE
SOLUTION:
m<BCF + m<CFE = 180° (same side interior angles are supplementary)
Substitute
4x + 11x = 180
15x = 180
Divide both sides ny 15
15x/15 = 180/15
x = 12
The sales tax rate on a new vehicle is 6.5%. If the vehicle is $12,000, then how much will you be charged for sales tax
Answers
Please help me with this!
Answers
9514 1404 393
Answer:
y ≥ -2/3x +2
Step-by-step explanation:
The y-intercept of the boundary line is y=2.
The next grid intersection to the right appears to be the x-intercept at x=3, which represents a "rise" of -2 and a "run" of +3 from the y-intercept.
At this point, we know the slope (rise/run = -2/3) and the y-intercept (+2) of the boundary line. We see it is a solid line, and shading is above it. This means the inequality could be ...
y = mx + b . . . . . . . . . equation for a line with slope m and y-intercept b
y ≥ -2/3x +2 . . . . . equation for the graphed inequality
__
Alternate solution
We observe that the y-intercept is +2, and the x-intercept is +3. The equation of the boundary line can be written in intercept form as ...
x/x-intercept = y/y-intercept = 1
As noted above, the line is shaded where both x- and y-values are greater than or equal to those on the line. So, the "intercept form" of the inequality could be ...
x/3 +y/2 ≥ 1
Often, we don't like fractions, so we can multiply by 6 to put this in standard form:
2x +3y ≥ 6
_____
Additional comment
Any of these highlighted inequalities is "an inequality" that describes the graph. We don't know if you're required to write the inequality in a specific form.
PLEASE HELP ME ASAP WITH WORK!! I WILL GIVE BRIANLIEST!!
Ba) Xander needs to collect at least 120 cans for a food drive to earn
community service credit. He has already collected 64 items. Write and
solve an inequality to represent the number of cans, c, that Xander must
still collect.
8b) describe the graph of the solution set for the question above. Be sure to describe the circle and tell the direction on the arrow
Answers
Answer:
he needs to collect at least 56 more
Step-by-step explanation:
c+64[tex]\geq[/tex]120
c[tex]\geq[/tex]120-64
c[tex]\geq[/tex]56
Answer:56 more
Step-by-step explanation:
A kite flying in the air has a 78-string attached to it, and the string is pulled taut. The angle of elevation of the kite is 52°. Find the height of the kite. Round
your answer to the nearest tenth.
Answers
Answer:
sine 52 degrees = height / 78
height = 78 * sine 52
height = 78 * 0.78801
height = 61.46478 feet
rounded to nearest tenth 61.5 feet
Step-by-step explanation:
Question
Sam sells orange juice by the glass and each glass contains 250 milliliters of orange juice. Sam has 10
cartons that each contain 3.5 liters of orange juice. What is the greatest number of glasses of orange juice
that Sam can sell? (1 liter = 1,000 milliliters)
Answers
Answer:
14 glasses
Step-by-step explanation:
3.5 (liters) times 10 (cartons) = 35 (liters)
(1 liter = 1,000 milliliters)
(35 liters = 3,500 milliliters)
3,500 (liters) divided by 250 (milliliters) = 14 glasses
The greatest number of glasses of orange juice that Sam can sell will be 140 glass.
What are ratio and proportion?A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.
Sam sells orange juice by the glass, and each glass contains 250 milliliters of orange juice.
Sam has 10 cartons that each contain 3.5 liters of orange juice.
Then the total amount of orange juice will be
Total amount = 10 x 3.5
Total amount = 35 liters
We know that one liter is equal to 1000 milliliters.
Then the total amount of the orange juice in milliliters will be
Total amount = 35 x 1000
Total amount = 35,000 milliliters
Then the greatest number of glasses of orange juice that Sam can sell will be
Total number of glass = 35,000 / 250
Total number of glass = 140 glass
The greatest number of glasses of orange juice that Sam can sell will be 140 glass.
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PLEASE HELP!!!!!!!!!!! Yelena has a toy in the shape of a cube. Each side of the cube measures 7 cm. What is the volume of the toy?
Answers
Answer:
7³ = 343
Step-by-step explanation:
a cube is equilateral
Find the 97th of the arithmetic sequence 25, 29, 33, ...
Answers
Answer:
If im not wrong is 409
Step-by-step explanation:
have a nice day :)
Find the midpoint of BD.
B (0, a)
C С
А
D (a,0)
Enter the value that [?]
belongs in the green box.
Midpoint Formula: M = (4x2.979)
들
2
Enter
Answers
Answer:
A
Step-by-step explanation:
(0.5a, 0.5a) is the midpoint of the line BD and a is the value that belongs in the green box.
What is a midpoint?The midpoint of a line segment is a point that lies exactly halfway between two points.
Consider the points B(0,a) and D(a,0).
The general form of midpoint formula is given by
Midpoint = ( (x₁ + x₂)/2 , (y₁ + y₂)/2)
Here, x₁ = 0, x₂=a and y₁ = a, y₂ = 0
Therefore, the value that belongs in the green box is given by
(x₁ + x₂)/2 = (0+a)/2 = a/2 = 0.5a
(y₁ + y₂)/2 = (a+0)/2 = a/2 = 0.5a
The midpoint is given by
Midpoint = ( (x₁ + x₂)/2 , (y₁ + y₂)/2) = (0.5a, 0.5a)
Hence, the value that belongs in the green box is a and the midpoint of the line BD is (0.5a, 0.5a).
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the model below is shaded to represent an expression. which expression represents the model? PLS HELPPPPP
Answers
Answer:C
Step-by-step explanation:
The expression that most adequately expresses the model would be:
C). 3 × 2/5
What is a fraction?A fraction is described as an expression employed to denote a segment or section belonging to a larger whole.
In the given question, it can be observed that the model contains 10 parts in total with a division of 5 each into 2 parts.
Since the division of 2 is made thrice, it gives 3 × 2/5 which makes the third option the correct one.
Thus, option C is the correct answer.
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The cost of an item is $75. What will the total cost be with 9% tax?
Answers
Answer:
81.75
Step-by-step explanation:
75*1.09 = 81.75
Answer:$81.75
Step-by-step explanation:
9% of 75 is 6.15, add that to 75 and the answer is 81.75
For the polynomial x^3-7x^2+12x-6, 1 is a zero. Express g(x) as a product of linear factors.
Answers
Answer:
(x–1)(x²–6x+6)
Explanation:
Given that 1 is a zero, we can use synthetic division to compute the factor.
If 1 is a zero (x–1) is a factor.
Here is the process:
| 1 | 1 -7 12 -6
↓ +(1) +(-6) +(6)
↓ ↓ ↓
1 -6 6 0
→ [1]x² + [-6]x + [6]1 + [0]/x–1 =
x² – 6x + 6.
Therefore the factors are (x–1)(x²–6x+6)
Elimination 5x -6y = -17. -3x -5y = -7
Answers
Answer:
x = -1 and y = 2
Step-by-step explanation:
3(5x - 6y = -17)
5(-3x - 5y = -7)
----------------------- Add the two equations together
-43y = -86
y = 2
5x - 6(2) = -17 Substitute y with 2 in the first equation to get the value of x
x = -1
Answer:
x = -1
y = 2
Step-by-step explanation:
5x - 6y = -17
-3x - 5y = -7
I will eliminate variable x first:
Multiply the first equation by 3
15x - 18y = -51
Multiply the second equation by 5
-15x - 25y = -35
Now subtract the second equation from the first equation:
15x - 18y = -51
-15x - 25y = -35
0x - 43y = -86
-43y = -86
Divide both sides by -43
Negative + Negative = Positive
y = 2
Now eliminate variable y:
Multiply the first equation by 5
25x - 30y = -85
Multiply the second equation by -6 (Negative switches all of the signs)
18x + 30y = 42
43x + 0y = -43
43x = -43
Divide both sides by 43
x = -1
Check work:
5(-1) - 6(2) = -17
-5 - 12 = -17
-17 = -17
Correct
-3(-1) - 5(2) = -7
3 - 10 = -7
-7 = -7
Correct
A water station table at a marathon starts with 200 plastic cups on it. Every minute, 15 cups are taken from the table. How many minutes could have passed if there are fewer than 50 cups on the table?
Answers
Answer:
is dancing with the circus grows and the mongooses you join us for the circus grows and the mongooses you join us for the circus grows and the mongooses you
Find the exact value of x. Do the side lengths form a Pythagorean triple?
Answers
Answer: Square root (52), No
Step-by-step explanation:
Answer:
Step-by-step explanation:
4^2 + 6^2 = x^2
sqrt 52 = x
x= 7.211
No, it is not a pythagorean triple because x is not a whole number.
What is the value of the expression below when x equals 4? 13 + 13x
Answers
Answer:
the answer is 50
Step-by-step explanation:
13+52
65
hope this helps
Please help me with this answer
Thank you!
Answers
What is the measure of B ?
Answers
Answer: if you add then all up you get 75 so it could be A or D I don't know if it want the volume and the volume is 75 hope this helped
Step-by-step explanation:
pleas make brainly
someone please help. this is the rest of my points. and it's worth 50% of my grade
Answers
Answer:
a=52
b=128
r=s=100
Step-by-step explanation:
please help will get brainliest
(the figure is not drawn to scale)
which one?
154 cm2
217 cm2
308 cm2
5488 cm2
Answers
V =14 V-6=8 - =22
K+K=14
22 x 14 =308