The population size after four days is 121.
Given that,
a population of protozoa with a constant relative growth rate of 0.8603 per member per day
let P be the population size and let t be the time interval then the given system modeled by the differential equation
[tex]\frac{dP}{dt}[/tex] = 0.8603
by solving the separable equation and expifying both sides we get,
P = A [tex]e^{0.8603t}[/tex]
From the condition that on day zero the population consist of four members,
i.e. P(0) = 4, A = 4
Therefore population size after four days is
P(4) = 4[tex]e^{4(0.8603)}[/tex]
= 4 [tex]e^{3.441}[/tex]
= 4 × 30.295
P(4) = 121.2
nearest whole number is 121
i.e P(4) = 121
Hence the population size after four days is 121.
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A study was conducted to compare the proportion of drivers in boston and new york who wore seat belts while driving. Data were collected, and the proportion wearing seat belts in boston was 0. 581 and the proportion wearing seat belts in new york was 0. 832.
z = -2.51 is the required test statistic.
What is the test statistic?A statistic employed in statistical hypothesis testing is known as a test statistic.
A test statistic, which can be thought of as a numerical summary of a data set that condenses the data into a single value that can be used to conduct the hypothesis test, is how a hypothesis test is commonly expressed.
The probability value, or p-value, indicates the likelihood that your data could have been true under the null hypothesis.
This is accomplished by estimating the probability of your test statistic, which is the figure obtained from a statistical analysis of your data.
So, we have to use: Ha: pB < pNY
This implies that the alternative thesis is revised as follows:
Ha: pB - pNY < 0
In contrast to the null hypothesis:
H₀: pB - pNY = 0
This is the test statistic:
z = X - μ/a
Now, pB = 0.581, pNY = 0.832.
It follows that: X = 0.581 - 0.832 = -0.251
The test for the null hypothesis is 0.
This follows to: μ = 0
Standard deviation: 0.1
This follows to: s = 0.1
Test statistic:
z = X - μ/a
z = -0.251-0/0.1
z = -2.51
Therefore, z = -2.51 is the required test statistic.
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Complete question:
A study was conducted to compare the proportion of drivers in Boston and New York who wore seat belts while driving. Data were collected, and the proportion wearing seat belts in Boston was 0.581 and the proportion wearing seat belts in New York was 0.832. Due to local laws at the time the study was conducted, it was suspected that a smaller proportion of drivers wear seat belts in Boston than New York.
Find the test statistic for this test using Ha: pB < pNY. (Use standard error = 0.1.)
Find the Laplace transform F(s) = L{f(t)} of the function f(t) = sin^2 (wt), defined on the interval t >= 0. F(s) = L {sin^2 (wt)} = For what values of S does the Laplace transform exist
The laplace transform of f(t) is [tex]F(s)=\frac{1}{2s}-\frac{2w}{2(s^2+4w^2)}[/tex] and it's values exists for [tex]s=w\pm\sqrt{3}wi[/tex].
Given,
[tex]f(t)=sin^2(wt)\\\\\therefore sin^2x=\frac{1-cos2x}{2}\\\\f(t)=\frac{1-cos2wt}{2}[/tex]
applying laplace transform on both sides,
[tex]L[f(t)]=L[\frac{1-cos2wt}{2}]\\\\F(s)=\frac{1}{2s}-\frac{2w}{2(s^2+4w^2)}[/tex]
The range for values of s for which F(s) exists is when F(s)≥0
[tex]\frac{1}{2s}-\frac{2w}{2(s^2+4w^2)} \geq0\\\\\frac{1}{2s} \geq\frac{2w}{2(s^2+4w^2)}\\\\2(s^2+4w^2) \geq 2sw\\\\s^2-2sw+4w^2 \geq0[/tex]
using formula to find roots,
[tex]s=\frac{-(-2w)\pm\sqrt{(-2w^2)-4(4w^2)}}{2}\\\\s=\frac{-(-2w)\pm\sqrt{(12w^2}}{2}\\\\s=w\pm\sqrt{3}wi[/tex]
Thus, the laplace transform of f(t) is [tex]F(s)=\frac{1}{2s}-\frac{2w}{2(s^2+4w^2)}[/tex] and it's values exists for [tex]s=w\pm\sqrt{3}wi[/tex].
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For what type of variable does it make sense to construct a confidence interval about a population​ proportion?.
A qualitative variable with two possible outcomes (Option D) is necessary to build a confidence interval for the population proportion.
Given,
We must determine the kind of variable needed in the given problem to build a confidence interval for a population proportion.
Considering that;
The percentage of the entire population that possesses a specific quality is known as the population proportion (which is qualitative in nature). Therefore, a qualitative variable with two alternative outcomes must be used to generate the confidence interval for the population proportion.
Therefore, the nature of the various types of variables is used to choose the correct option. A qualitative variable with two possible outcomes (Option D) is necessary to build a confidence interval for the population proportion.
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Question is incomplete. Completed question is given below;
What type of variable is required to construct a confidence interval for a population proportion?
A. Quantitative
B. Qualitative with any number of possible outcomes
C. Continuous
D. Qualitative with 2 possible outcomes
E. Discrete
F. Qualitative with 3 or more possible outcomes
A pyramid has a square base with edges that measure 6 meters, and a slant height of 7. 5 meters. What is its surface area? 270 45 126 102.
The surface area of the given pyramid 126 m².
What do you mean by surface area?
A solid object's surface area is a measurement of the overall space that the object's surface takes up.
According to data in the given question,
We have the given information:
A pyramid has a square base with edges that measure 6 meters, and a slant height of 7.5 meters.
Now, we need to determine the surface area of given pyramid,
The formula for a pyramid's surface area with a square base is:
[tex]SA=b^{2}+2*(bs)[/tex]
Where b is the base length and s is the slant height.
We have the following information for the stated situation,
b= 6 m
s= 7.5 m
Then, we will putting the given values in the above formula,
[tex]SA=b^{2}+2*(bs)[/tex]
[tex]SA=6^{2}+2*(6*7.5)\\SA=36+90\\SA=126m^{2}[/tex]
Therefore, the surface area is 126m².
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a piece of wire 10 m long is cut into two pieces. one piece is bent into an equilateral and the other is bent into a circle. how should the wire be cut so that the total area enclosed is (a) a maximum? (b) a minimum?
For maximum area the wire should be bent in the form of circle and for minimum area the wire should bent into equilateral triangle.
What is the area of any geometrical shape?
The area of a shape is the “space enclosed within the perimeter or within the boundary” of the given shape. We calculate the area for different shapes using math formulas.
Given that a piece of wire 10m long is cut into two pieces so now we have two wires with lengths of 5m and 5m.
One wire is bent into an equilateral so the perimeter of that triangle would be 3 m.
Perimeter = 3 m
3*side = 3 m
side = 1 m
Now the area of the equilateral triangle = [tex]A=\frac{\sqrt{3}}{4}\times (side)^2[/tex]
A = 0.4330 m² -----(I)
Now the circumference of the circle = 5 m
2π×r = 5
r = 5/2π
r = 0.7957 m.
Now the area of the circle = π×r²
= 3.14 × (0.7957)²
= 1.988 m² --------(II)
From (I) and (II), we can say that
Area of the equilateral triangle < Area of the circle
Hence, for maximum area the wire should be bent in the form of circle and for minimum area the wire should bent into equilateral triangle.
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10 degrees
below 0
Is it negative or positive or zero
Answer:
Step-by-step explanation:It's -10 degrees
Irina predicted that she would sell 75 books, but she actually sold 95 books. Which expression would find the percent error? Use the table below to help answer the question.
Answer:
21%
Step-by-step explanation:
Approximate number = 75
exact number = 95error
approximate number - exact number| ÷ exact number error = |(75-95)| / 95 = |20| / 95 = 0.21percentage of error = 0.21 x 100% = 21%
The answer should be correct! Hope it helps!!! Mark as Brainliest. It would make my day! Thank you :)
URGENT PLEASE HELP: Ryan planted flowers in a rectangular garden. The width of the garden is (x-8) feet and the length of the garden is 3 feet longer than the width. Write an expression for the area of the
garden.
An expression for the area of the garden is
(Type an expression using x as the variable.)
Answer:
-8 + 3 + x = x - 5
Step-by-step explanation:
This is because X does not have a value & both 8 & 3 are constants making them computable
he points (12,10) and (30,25) form a proportional relationship. Find the slope of the line through the points. Then use the slope to graph the line.
The slope of the two points passing through points (12,10) and (30,25) will be 5 / 6.
What is a slope?Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line. the slope is defined as the ratio of the rise to the run.
Given that points (12,10) and (30,25) form a proportional relationship.
The slope of the line passing through the two points will be calculated as,
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
Slope = ( 25-10 ) / ( 30-12 )
Slope = 15 / 18
Slope = 5 / 6
Therefore, the slope of the two points passing through points (12,10) and (30,25) will be 5 / 6.
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Nobody ANSERS MY QUESTONS pleas help me
Answer:
∠RPQ = 105
∠R = 45
Step-by-step explanation:
Question 1
By intersecting chord theorem ? = (175 + 35) / 2
? = (175 + 35) / 2
? = 210 / 2
? = 105
(See image below)
Question 2
By intersecting secant theorem ∠R = (140 - 50)/2
∠R = (140 - 50)/2
∠R = 90/2
∠R = 45
(See image below)
Intersecting chord theorem : Corresponding angle equals sum of corresponding arcs divided by two
Intersecting secant theorem : The inscribed angle equals major arc minus minor arc divided by two
Find the tenth term of the
sequence.
4, 3, 0, -5, - 12, ...
Answer:
-76
each term is being subtracted from the preceding the next odd number
My question is below!
Answer:
Below
Step-by-step explanation:
s = small box number volume = 6s
L = large box number volume = 15L
6s + 15 L =243
AND s = L +2
A recipe for cheesecake requires 3 cups of sugar per
batch.
A. Write an equation that can be used to determine y,
the number of cups of sugar required to make
cheesecake, based on x, the number of batches.
B. Use your equation to determine how many cups of
sugar are required to make 4 batches of cheesecake.
Pls hurry!!
Answer:
y = x × 3, 12
Step-by-step explanation:
If a recipe for cheesecake requires 3 cups of sugar per batch, we can use this equation:
y = x × 3
Using this, we can determine how many cups are needed when we need to make 4 batches.
y = 4 × 3 = 12
You need 12 cups of sugar for 4 batches.
5/3 x + 1/3 x = 40/3 + 8/3 x
6x-4y=18 -x-6y=7 solve
Answer:
Solution = (2, 1.5)
Step-by-step explanation:
Step 1: Solve for y in 6x - 4y = 18
1. 6x - 4y = 18 → -4y = -6x + 18 → y = 1.5x - 4.5
Step 2: Substitute 1.5x - 4.5 for y in -x - 6y = 7
2. -x - 6(1.5x - 4.5) = 7
Step 3: Solve for x
3. -x - 9x + 27 = 7 → -10x + 27 = -20 → -10x = -20 → x = 2
Step 4: Substitute 2 for x in -x - 6y = 7
4. -(2) - 6y = 7
Step 5: Solve for y
5. -2 - 6y = 7 → -6y = 9 → y = -1.5
Hope this helps you out :)
1. Write the slope-
intercept form
(y=mx+b) of the line
with a slope of -1/2and
one ordered pair (-6, 4).
amanda chicopee bought a new car and drove 8,000 miles in the first four months. at the same rate, how many miles will amanda drive in 3 years?
If Amanda stays on her current course, she will go 72,000 km in three years.
Given data,
In the first four months after purchasing a new car, Amanda Chicopee covered 8,000 kilometers. How many miles will Amanda log in three years if she continues on her path?
Here,
She drove 8000 km in 4 months.
⇒ In 1 month = 8000/4 = 2000 km
To find how many miles in 3 years,
⇒ In 36 months = 2000 * 36
= 72000 km
Hence, 72000 km will Amanda log in three years if she continues on her path.
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Ellis's backyard has a 6.25m by 6.25m patio. She would like to build a 1.5m wide extension around 3 sides of the patio. She will buy 0.25m b 0.25m tiles that come 25 to a package. How many packages does Ellis need to buy to build the extension?
Answer:
21
Step-by-step explanation:
The amount added to each of the 3 sides is a rectangle 6.25 m by 1.5 m.
Then there are two square corners added that each one is 1.5 m by 1.5 m.
Total added area = 3 × 6.25 m × 1.5 m + 2 × 1.5 m × 1.5 m
Total added area = 28.125 m² + 4.5 m²
Total added area = 32.625 m²
The area of each tile is:
0.25 m × 0.25 m = 0.0625 m²
A box of tiles has 25 tiles. The total area covered by a box of tiles is:
25 × 0.0625 m² = 1.5625 m²
The number of boxes need is:
32.625 m² / 1.5625 m² = 20.88
Since 20.88 boxes are needed, but she needs to buy full boxes, she needs 21 boxes of tiles.
Answer: 21
A landscape artist plans to draw a pair of mountains, so he takes some measurements and draws the figure below. (Note: the peaks are NOT right angles, and sides of the mountains are parallel). Find the measurement of x, y, and z. Explain your reasoning and show your work.
The angle measures in this problem are given as follows:
x = 88º. y = 55º.z = 37º.How to obtain the angle measures?The sides of the mountains are parallel, which means that the angles of these sides have the same measures, as follows:
y = 55º, as the measure on the first mountain is parallel to the measure of 55º in the second mountain.z = 37º, as the measure of 37º on the first mountain is parallel to the measure of z on the second mountain.Then the measure of x is obtained considering that angles x, y and z form a ray, that is, the sum of their measures is of 180º, hence:
x + y + z = 180
x + 55 + 37 = 180
x = 180 - (55 + 37)
x = 88º.
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caitlin won a bag full of money. she has 49 bills in all. she counts $1,430. there are twenty dollar bills and fifty dollar bills in the bag. how many of each bill does caitlin have?
Answer:
30 I think but I'm not positive
Step-by-step explanation:
Can someone please help me? I need help
BTW this is algebra 2
Answer:
Step-by-step explanation:
1. is .4444444 or 4/9
All you do for this is enter -2 as x for 4(3)^x
2. is x^24 or answer (4)
this is because you will multiply the exponents starting with -4 till you get 24.
-4 x -1 = 4
4 x 6 = 24
3. sorry I have to go for this one, plug in any number into x and experiment with the 4 answers till one of them gives you the same solution
Please help need this done asap
2. 2x-7=3 Addition Property
3. 2x=10 Division Property
4. x = 5
Answer:
I hope I helped
I have not been taught on this topic yet but I manage to answer the question if the answer is wrong it isn't my fault I haven't been taught yet.
I wish you a happy day
Step-by-step explanation:
1.)4x – 7 = 2x + 3
4x – 2x – 7 = 2x – 2x + 3 (subtraction property)
2x – 7 = 3
2x – 7 +7 = 3 + 7(addition property)
2x = 10(division property)
x = 5(reflexive property)
How can you balance the equation
Ba(C2O4) + K(IO3) → Ba(IO3)2 + K2(C2O4)
the big numbers in the parenthesis are supposed to be subscripts. Also the compound IO3 is supposed to be Iodine and oxygen separate I think.
The balanced equation is Ba(C₂O₄) + 2K(IO₃) → Ba(IO3)₂ + K₂(C₂O₄).
What is an equation?An equation is a combination of different variables, in which two expressions are equal to each other.
The given equation is,
Ba(C₂O₄) + K(IO₃) → Ba(IO3)₂ + K₂(C₂O₄)
Since, there are 2 atom of potassium on right side and also (IO₃) is two times.
To balance the equation, Coefficient of K(IO₃) should be 2.
The equation can be represented as,
Ba(C₂O₄) + 2K(IO₃) → Ba(IO3)₂ + K₂(C₂O₄)
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The Transportation Security Administration (TSA) is responsible for airport safety. On some flights, TSA officers randomly select passengers for an extra security check prior to boarding. One such flight had 76 passengers - 12 in first class and 64 in coach class. Some passengers were surprised when none of the 10 passengers chosen for screening were seated in first class. We can use a simulation to see if this result is likely to happen by chance. How would you use random digits to imitate one repetition of the process? What variable would you measure?
We will use certain constraints to imitate the repetition of the process as mentioned below
To simulate one repetition of the procedure using random digits, we shall perform as follows:
from a line of the random digits table, ten one and two-digit numbers could be selected with the following conditions;
1. skipping repeated numbers
2. skipping numbers from 77 to 99
here the numbers 01 to 12 i.e. first-class passengers in the group of selected random numbers are to be counted.
As we know, numbers represent first-class passengers while numbers to represent coach-class people.
Hence, using this we can use random digits
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customers is equally likely to report a food allergy, what is the probability that at least one customer will report a food allergy?
The probability that at least one client will disclose a food allergy will be 0.6323 when the percentage of customers who will disclose a food allergy is 0.08.
Given that.
The percentage of customers who will disclose a food allergy is 0.08
At Ying Ying's bakery, 121 people place orders on a single day.
We can utilize the binomial distribution if we believe that each of the 12 clients has an equal probability of reporting a food allergy.
Formula for Binomial probability distribution:
P(X=x)=ⁿCₓpˣ(1-p)ⁿ⁻ˣ
Where P(x)= probability of getting success in x trials,
n= sample size ,
p represents the probability that each event will succeed.
As stated, we have n=12
p=0.08
Let x signify that the client will disclose a food allergy.
Following that, the probability that at least one client will disclose a food allergy will be:
P(x≥1)=1-P(x<1)
=1-P(x=0)
=1-¹²C₀(0.08)⁰(1-0.08)¹²⁻⁰
=1-(1)(0.12)¹²
=1-0.3677
=0.6323
Therefore, the probability that at least one client will disclose a food allergy will be 0.6323 when the percentage of customers who will disclose a food allergy is 0.08.
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y varies directly as x. y = 18 when x = 5. Find x when y = 36.
Answer:
Step-by-step explanation:
y varies directly as x.
y = 18 , x = 5
y =36 then x also double,
x = 10
he fraction of defective integrated circuits produced in a photolithography process is being studied. a random sample of 300 circuits is tested, revealing 17 defectives. (a) use the data to test the hypothesis that the proportion is not 0.04. use ????α
The proportion is not equal to 0.04.
The test statistic
Z = 1.149
What is the random sample?
A simple random sample is a subset of a statistical population in which each member of the subset has an equal probability of being chosen.
Since the calculated value of Z = 1.149 is less than 1.96 at 5% (0.05) level of significance.
The null hypothesis is accepted
Hence the proportion is not equal to 0.04
Given data a random sample of 300 circuits is tested, revealing 17 defectives.
The proportion of success
P = 17 / 300 = 0.056
Null hypothesis:- H₀ = P ≠0.04
Alternative hypothesis:- H₁ = P =0.04
Q = 1-P = 1-0.04=0.96
Level of significance ∝ =0.05
The test statistic
[tex]z = \frac{p -P}{\sqrt{PQ/n} }[/tex]
now substitute all values, and we get
on calculation, Z = 1.149
Since the calculated value of Z = 1.149 is less than 1.96 at a 5% (0.05) level of significance.
The null hypothesis is accepted.
Hence the proportion is not equal to 0.04.
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what is the statement of |4×+12|=0
Step-by-step explanation:
4x+12=0
4x= -12
x = -3
.........
help me please/............................................ . . . . . . . . . . . .
The value of x=11 and the value of an angle ∠RDB=45°.
What is meant by an angle?In Euclidean geometry, an angle is the figure formed by two rays, known as the sides of the angle, that have a common termination, known as the vertex of the angle. These are referred to as dihedral angles. An angle can also be defined by two intersecting curves, which is the angle of the rays lying tangent to the respective curves at their point of intersection.
Angle can also refer to the measurement of an angle or a rotation. This measurement is the ratio of the length of a circular arc to its radius.
By using the secant-secant theorem,
(13x+7-60)/2=5x-10
13x-53=10x-20
3x-53=-20
3x=33
x=11
m ∠RDB=5(11)-10
=45°
Hence, the value of x=11 and the value of an angle ∠RDB=45°.
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An investigator wants to estimate caffeine consumption in high school students. How many students would be required to estimate the proportion of students who consume coffee? Suppose we want the estimate to be within 5% of the true proportion with 95% confidence.
Alpha = _____
Z = _____
p = _____
Effect Size = _____
n = _____
The value of alpha is 0.025. The Z-value is 1.96. The P(z) is 0.5. The effect size is 0.05. The Sample size for the study is 384.
What is confidence interval?An area created using fixed-size samples of data from a population (sample space) that follows a certain probability distribution is known as a confidence interval. A selected population statistic is built into the interval with a specified probability. An estimate's level of uncertainty is described by a confidence interval, which is a range of numbers. The 68-95-99.7 Rule states that 95% of values lie within two standard deviations of the mean, hence to get the 95% confidence interval, you add and subtract two standard deviations from the mean.
Here,
All the calculations attached in image.
z= 1.96
p = 0.5
q = 1-p = 0.5
E = 0.05
sample size =
(z^2).(pq)=(1.96^2).(0.5)(.0.5)
384.16,
round up
n for study =385
Alpha has a value of 0.025. There is a 1.96 Z-value. P(z) equals 0.5. The impact factor is 0.05. The Sample size for the study is 384.
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