Answer:
Initial amount (a)= 620
Growth factor (b)= 7.8
Step-by-step explanation:
620 is the initial amount and is multiplied by 7.8 x which is the growth factor.
a variable with an exponent is a perfect square if the exponent is divisible by____
Answer: 3
Step-by-step explanation:
Which of the following shows the graph of y = –(2)x – 1? On a coordinate plane, a curve is level at y = 0 in quadrant 2 and then decreases rapidly into quadrant 4. It crosses the y-axis at (0, negative 0.5). On a coordinate plane, a curve is level at y = negative 1 in quadrant 3 and then decreases rapidly into quadrant 4. It crosses the y-axis at (0, negative 2). On a coordinate plane, a curve is level at y = 1 in quadrant 3 and then decreases rapidly into quadrant 4. It crosses the y-axis at (0, 0).
Answer:
On a coordinate plane, a curve is level at y = -1 in quadrant 3 and then decreases rapidly into quadrant 4. It crosses the y-axis at (0, -2).
Step-by-step explanation:
y = -2 ^x -1
On a coordinate plane, a curve is level at y = – 1 in quadrant 3 and then decreases rapidly into quadrant 4. It crosses the y-axis at (0, -2). Option C is correct.
What is Cartesian coordinate plane?The Cartesian coordinate plane is a two-dimensional plane with infinite dimensions. On an endless 2d plane, any two-dimensional figure can be drawn. A location is assigned to each point on a Cartesian plane.
On a coordinate plane, a curve is level at y = – 1 in quadrant 3 and then decreases rapidly into quadrant 4. It crosses the y-axis at (0, -2).
Hence, option C is correct.
To learn more about the Cartesian plane, refer;
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solve for inequality
ᶜ⁄₋₃ ≥ 3
Answer:
c ≤ -9
Step-by-step explanation:
c / -3 ≥ 3
c ≤ -9
Remember, we flip the sign of the inequality by multiplying / dividing by a negative number.
Answer:
c ≤ -9
Step-by-step explanation:
c / -3 ≥ 3
c ≤ -9
what is the sum of 1 2/5 and 5 3/4
Answer:
[tex]7\frac{3}{20}[/tex]
Step-by-step explanation:
Hey there!
Well to add this we need to pu it in improper form.
7/5 + 23/4
Now we need to find the LCM.
5 - 5, 10, 15, 20, 25, 30
4 - 4, 8, 12, 16, 20, 24, 28
So the LCD is 20.
Now we need to change the 5 and 4 to 20.
5*4 = 20
7*4 = 28
28/20
4*5=20
23*5=115
115/20
Now we can add 28 and 115,
= 143/20
Simplified
7 3/20
Hope this helps :)
Answer:
[tex] \boxed{7 \frac{3}{20} }[/tex]Step-by-step explanation:
[tex] \mathrm{1 \frac{2}{5} + 5 \frac{3}{4} }[/tex]
Add the whole numbers and fractional parts of the mixed numbers separately
[tex] \mathrm{ = (1 + 5) + ( \frac{2}{5} + \frac{3}{4} })[/tex]
Add the numbers
[tex] \mathrm{=6 + ( \frac{2}{5} + \frac{3}{4} )}[/tex]
Add the fractions
[tex] \mathrm{=6 + (\frac{2 \times 4 + 3 - 5}{20} )}[/tex]
[tex] \mathrm{=6 + \frac{23}{20} }[/tex]
Convert the improper fractions into a mixed number
[tex] \mathrm{=6 + 1 \frac{3}{20} }[/tex]
Write the mixed number as a sum of the whole number and the fractional part
[tex] \mathrm {= 6 + 1 + \frac{3}{20} }[/tex]
Add the numbers
[tex] \mathrm{ = 7 + \frac{3}{20} }[/tex]
Write the sum of the whole number and the fraction as a mixed number
[tex] \mathrm{ = 7 \frac{3}{20} }[/tex]
Hope I helped
Best regards!
In triangle abc what is the value of cos b A 5/13 B 12/13 C 5/12 D 13/12
Answer:
[tex]\boxed{Option \ B}[/tex]
Step-by-step explanation:
In the triangle,
Hypotenuse = 13
Opposite = Perpendicular = 5
Adjacent = Base = 12
Now,
Cos B = [tex]\frac{Adjacent}{Hypotenuse}[/tex]
Cos B = 12/13
If the triangle is just like in the attached file!
Answer:
B) 12/13
Step-by-step explanation:
Determine which of the following statements is true. A: If V is a 6-dimensional vector space, then any set of exactly 6 elements in V is automatically a basis for V. B: If there exists a set that spans V, then dim V = 3. C: If H is a subspace of a finite-dimensional vector space V, then dim H ≤ dim V
Answer:
A. This statement A is false.
B. This statement A is false.
C. This statement is true .
Step-by-step explanation:
Determine which of the following statements is true.
From the statements we are being given , we are to determine if the statements are valid to be true or invalid to be false.
SO;
A: If V is a 6-dimensional vector space, then any set of exactly 6 elements in V is automatically a basis for V
This statement A is false.
This is because any set of exactly 6 elements in V is linearly independent vectors of V . Hence, it can't be automatically a basis for V
B. If there exists a set that spans V, then dim V = 3
The statement B is false.
If there exists a set , let say [tex]v_1 ...v_3[/tex], then any set of n vector (i.e number of elements forms the basis of V) spans V. ∴ dim V < 3
C. If H is a subspace of a finite-dimensional vector space V then dim H ≤ dim V is a correct option.
This statement is true .
We all know that in a given vector space there is always a basis, it is equally important to understand that there is a cardinality for every basis that exist ,hence the dimension of a vector space is uniquely defined.
SO,
If H is a subspace of a finite-dimensional vector space V then dim H ≤ dim V is a correct option.
x(x+3)(x+3)=0 Please I NEED HELP FAST! PLLLLLLLLLLLLLLLLLLLLLLLLLLEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEAAAAAAAAAAAAAAAAAAAAAAAAAAAAASSSSSSSSSSSSSSSSSSSSSSSSSSEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE!
Answer:
[tex]\boxed{x^3+6x^2+9x}[/tex]
Step-by-step explanation:
[tex]x(x+3)(x+3)[/tex]
Resolving the first parenthesis
[tex](x^2+3x) (x+3)[/tex]
Using FOIL
[tex]x^3+3x^2+3x^2+9x[/tex]
Adding like terms
[tex]x^3+6x^2+9x[/tex]
[tex]\text{If } \: a\cdot b \cdot c = 0 \text{ then } a=0 \text{ or } b =0 \text{ or } c=0 \text{ or all of them are equal to zero.}[/tex]
[tex]x(x+3)(x+3) =0[/tex]
[tex]\boxed{x_1 =0}[/tex]
[tex]x_2+3 =0[/tex]
[tex]\boxed{x_2 = -3}[/tex]
[tex]x_3+3 =0[/tex]
[tex]\boxed{x_3 = -3}[/tex]
4km in the ratio 9:4:7
Answer:
500km
Step-by-step explanation:
add all the proportions and then divide by 3. with conversion.
Using Pascal’s Theorem, expand the expression 〖(2x-y)〗^3
Answer:
(2x - y)³ = 8x³ - 12x²y + 6xy² - y³
Step-by-step explanation:
Pascal's Theorem uses a set of already known and easily obtainable numbers in the expansion of expressions. The numbers serve as the coefficients of the terms in the expanded expression.
For the expansion of
(a + b)ⁿ
As long as n is positive real integer, we can obtain the coefficients of the terms of the expansion using the Pascal's triangle.
The coefficient of terms are obtained starting from 1 for n = 0.
- For the next coefficients of terms are 1, 1 for n = 1.
- For n = 2, it is 1, 2, 1
- For n = 3, it is 1, 3, 3, 1
The next terms are obtained from the previous one by writing 1 and summing the terms one by one and ending with 1.
So, for n = 4, we have 1, 1+3, 3+3, 3+1, 1 = 1, 4, 6, 4, 1.
The Pascal's triangle is
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1
1 7 21 35 35 21 7 1
1 8 28 56 70 56 28 8 1
1 9 36 84 126 126 84 36 9 1
The terms can also be obtained from using the binomial theorem and writing the terms from ⁿC₀ all through to ⁿCₙ
So, for n = 3, the coefficients are 1, 3, 3, 1
Then the terms are written such that the sum of the powers of the terms is 3 with one of the terms having the powers reducing from n all through to 0, and the other having its powers go from 0 all through to n
So,
(2x - y)³ = [(1)(2x)³(-y)⁰] + [(3)(2x)²(-y)¹] + [(3)(2x)¹(-y)²] + [(1)(2x)⁰(-y)³]
= (1×8x³×1) + (3×4x²×-y) + (3×2x×y²) + (1×1×-y³)
= 8x³ - 12x²y + 6xy² - y³
Hope this Helps!!!
James is measuring the temperature (1) of a plate left sitting in the sun fort
hours. Which of the following is the most appropriate domain for h(0?
O A. All positive numbers
O B. Positive integers only
O C. All real numbers
O D. All integers
Answer:
O B. Positive integers only
Step-by-step explanation:
You have that the temperature of a plate is measured respect to the number of hours that the plate has been left in the sun.
In this case you have that the independent variable is the number of hours and the dependent variable is the temperature.
Due to James would like to know how is changing the temperature of the plate, per hour, the best domain for the function, that is, the best available values for the time on which the temperature of the plate is measured, are the positive integers only.
O B. Positive integers only
A company manufacturing oil seals wants to establish X and R control charts on the process. There are 25 preliminary samples of size 5 on the internal diameter of the seal. The summary data (in mm) are as follows:
sigma^25_i = 1 X_t = 1, 253.75, sigma^25_i = 1 R_i = 14.08
(a) Find the control limits that should be used on the X and R control charts. For n = 5, A2 = 0.577, D4 = 2.114, D3 = 0
(b) Assume that the 25 preliminary samples plot in control on both charts. Estimate the process mean and standard deviation.
Answer:
A ) i) X control chart : upper limit = 50.475, lower limit = 49.825
ii) R control chart : upper limit = 1.191, lower limit = 0
Step-by-step explanation:
A) Finding the control limits
grand sample mean = 1253.75 / 25 = 50.15
mean range = 14.08 / 25 = 0.5632
Based on X control CHART
The upper control limit ( UCL ) =
grand sample mean + A2* mean range ) = 50.15 + 0.577(0.5632) = 50.475
The lower control limit (LCL)=
grand sample mean - A2 * mean range = 50.15 - 0.577(0.5632) = 49.825
Based on R control charts
The upper limit = D4 * mean range = 2.114 * 0.5632 = 1.191
The lower control limit = D3 * mean range = 0 * 0.5632 = 0
B) estimate the process mean and standard deviation
estimated process mean = 50.15 = grand sample mean
standard deviation = mean range / d2 = 0.5632 / 2.326 = 0.2421
note d2 is obtained from control table
Jessie is adept at Imagining abstract concepts and applying advanced mathematical formulas while creating flowcharts for her programs. Jessle has strength in which
skill?
communication
Answer:
Design thinking skills
Step-by-step explanation:
The design thinking skills is observable in individuals who can effectively use Intuition to create prototypes of abstract objects.
Jessie thus shows that she possess design thinking skills by been able to imagine abstract concepts at the same and she applies advanced mathematical formulas which in turn provides solutions to problems.
In a poll conducted by the Gallup organization in April 2013, 48% of a random sample of 1022 adults in the U.S. responded that they felt that economic growth is more important than protecting the environment. We can use this information to calculate a 95% confidence interval for the proportion of all U.S. adults in April 2013 who felt that economic growth is more important than protecting the environment. Make sure to include all steps.
Answer:
The 95% confidence interval is [tex]0.449 < p < 0.48 + 0.511[/tex]
Step-by-step explanation:
From the question we are told that
The sample proportion is [tex]\r p = 0.48[/tex]
The sample size is [tex]n = 1022[/tex]
Given that the confidence level is 95% then the level of significance is mathematically evaluated as
[tex]\alpha = 100 - 95[/tex]
[tex]\alpha = 5 \%[/tex]
[tex]\alpha = 0.05[/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} } =Z_{\frac{0.05 }{2} }= 1.96[/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{\r p (1- \r p )}{n} }[/tex]
substituting values
[tex]E = 1.96* \sqrt{\frac{0.48 (1- 0.48 )}{1022} }[/tex]
[tex]E = 0.03063[/tex]
The 95% confidence interval is mathematically represented as
[tex]\r p - E < p < \r p + E[/tex]
substituting values
[tex]0.48 - 0.03063 < p < 0.48 + 0.03063[/tex]
[tex]0.449 < p < 0.48 + 0.511[/tex]
22,403 Check:
- 8,675
how i do this
Answer:
Hello!! :) The answer to your question is 13,728
Steps will be below.
Step-by-step explanation:
So we will subtract 22,403 and 8,675.
When we do that we will get 13,728
To check your answer we have to do the opposite of subtracting which will be adding.
This is how we check our work: the answer we got was 13,728...we have to take that answer and add it to 8,675 which will give us 22,403
(Both of the numbers are from the question)
At the bottom I attached a picture of how I did the subtracting and how I checked my work.
Sorry for my handwriting......if you can’t understand my handwriting, I attached another picture which is more clearer.
ANSWER TO YOUR QUESTION: 13,728
Brainliest would be appreciated! Thank you :3
Hope this helps! :)
Answer:
The answer is 13,728
Step-by-step explanation:
Check your work with addition.
Find the domain for the rational function f of x equals quantity x end quantity divided by quantity x minus 5 end quantity.
Answer:
All real numbers except for 5.
Step-by-step explanation:
[tex]f(x)=\frac{x}{x-5}[/tex]
The domain of rational functions is determined by the denominator. The denominator cannot equal zero since if they do, the function will be undefined.
Thus, we need to find the zero(s) of the denominator to determine the domain.
[tex]x-5=0[/tex]
[tex]x=5[/tex]
Therefore, the domain of the rational function is all real numbers except for 5.
In set builder notation, this is:
[tex]\{x|x\in \mathbb{R}, x\neq 5\}[/tex]
Compute the least-squares regression line for predicting y from a given the following summary statistics. Round final answers to four decimal places, as needed.
xbar = 8.8 sx = 1.5 sy = 1.8 ybar = 30.3
r = -0.84
Download data
Regression line equation: y = ______ + _______ x
Answer: Regression line equation: [tex]\hat{y}=-1.008x+39.1704[/tex]
Step-by-step explanation:
Equation of least-squares regression line for predicting y :
[tex]\hat{y}=b_1x+b_o[/tex]
, where [tex]\text{Slope} (b_1)=r\dfrac{s_y}{s_x}[/tex] , [tex]\text{intercept}(b_0)=\bar{y}-b_1\bar{x}[/tex]
Given: [tex]\bar{x}=8.8,\ s_x=1.5,\ s_y=1.8,\ \bar{y}=30.3,\ r=-0.84[/tex]
Then,
[tex]b_1=(-0.84)\dfrac{ 1.8}{ 1.5}\\\\\Rightarrow\ b_1=-1.008[/tex]
Now,
[tex]b_0=30.3-(-1.008)(8.8)=30.3+8.8704\\\\\Rightarrow\ b_0=39.1704[/tex]
Then, Regression line equation: [tex]\hat{y}=-1.008x+39.1704[/tex]
The equation 6x2 - 132 +5 -0 has solutions of the form
NVD
M
(A) Use the quadratic formula to solve this equation and find the appropriate integer values of N.M and D. Do not worry about simplifying the VD yet in this part of the problem.
N = ]:D
M
(B) Now simplify the radical and the resulting solutions. Enter your answers as a list of integers or reduced fractions, separated with commas. Example: -5/2-3/4
Preview
Answer:
(A)
[tex]N = -b = -(-13) = 13\\\\[/tex]
[tex]D =b^2 -4ac = (-13)^2 - 4(6)(5) = 169- 120 = 49[/tex]
[tex]M = 2a = 2(6) = 12[/tex]
(B)
[tex]$ x = (\frac{5}{3} , \: \frac{1}{2}) $[/tex]
Step-by-step explanation:
The given equation is
[tex]6x^2 - 13x + 5 = 0[/tex]
The solution is of the form as given by
[tex]$x=\frac{N\pm\sqrt{D}}{M}$[/tex]
(A) Use the quadratic formula to solve this equation and find the appropriate integer values of N, M and D. Do not worry about simplifying the VD yet in this part of the problem.
The quadratic formula is given by
[tex]$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$[/tex]
The equations of N, M and D are
[tex]N = -b[/tex]
[tex]D =b^2 -4ac[/tex]
[tex]M = 2a[/tex]
The values of a, b and c are
[tex]a = 6 \\\\b = -13 \\\\c = 5[/tex]
So,
[tex]N = -b = -(-13) = 13\\\\[/tex]
[tex]D =b^2 -4ac = (-13)^2 - 4(6)(5) = 169- 120 = 49[/tex]
[tex]M = 2a = 2(6) = 12[/tex]
(B) Now simplify the radical and the resulting solutions. Enter your answers as a list of integers or reduced fractions, separated with commas. Example: -5/2-3/4
N = 13
D = 49
M = 12
[tex]$x=\frac{13\pm\sqrt{49}}{12}$[/tex]
[tex]$x=\frac{13\pm7}{12}$[/tex]
[tex]$ x=\frac{13+7}{12} $[/tex] and [tex]$ x=\frac{13-7}{12} $[/tex]
[tex]$ x=\frac{20}{12} $[/tex] and [tex]$ x=\frac{6}{12} $[/tex]
[tex]$ x=\frac{5}{3} $[/tex] and [tex]$ x=\frac{1}{2} $[/tex]
[tex]$ x = (\frac{5}{3} , \: \frac{1}{2}) $[/tex]
Need Help with these (Giving brainiest if you can solve these)
Answer: try using sine for this equasion
Step-by-step explanation:
The world's largest university (by enrollment) is University A, followed by University B. If the enrollment in University A is 3.5 million more students than University B and their combined enrollment is 9.5 million students, find the enrollment for each university?
which of the following is equivalent to the expression below? log2-log14 A. LOG(1/7) B. LOG(-12) C. LOG 12 D. LOG 7
Answer:
The answer is option A.
Step-by-step explanation:
Using the properties of logarithms
that's
[tex] log(x) - log(y) = log( \frac{x}{y} ) [/tex]
log 2 - log 14 is
[tex] log(2) - log(14) = log( \frac{2}{14} ) [/tex]
Simplify
We have the final answer as
[tex] log( \frac{1}{7} ) [/tex]
Hope this helps you
Answer:
log ( 1/7)
Step-by-step explanation:
log2-log14
We know that log ( a/b) = log a - log b
log (2 /14)
log ( 1/7)
what is the length of bc in the right triangle below?
Answer: A) 15
Step-by-step explanation:
Because of Pythagorean Theorem, 9^2+12^2=BC^2. Thus, 81+144=BC^2. Thus, 225=BC^2. Thus, 15=BC.
Hope it helps, and ask if you want further clarification <3
What is the value of x in the diagram below?
A.
6
B.
4
C.
5
D.
3
Answer:
[tex]\boxed{3}[/tex]
Step-by-step explanation:
We can use ratios to solve since the sides are proportional.
[tex]\frac{18}{x} =\frac{48}{8}[/tex]
Cross multiply.
[tex]48x=18 \times 8[/tex]
Divide both sides by 48.
[tex]\frac{48x}{48} = \frac{18 \times 8}{48}[/tex]
[tex]x=3[/tex]
The value of x in the given triangle is 3.
What are similar triangles?Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles.
Given are two similar triangles,
Therefore, they have the same ratio of corresponding sides
18/48 = x/8
x = 3
Hence, The value of x in the given triangle is 3.
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The numbers of regular season wins for 10 football teams in a given season are given below. Determine the range, mean, variance, and standard deviation of the population data set.
2, 10, 15, 4, 11, 10, 15, 10, 2, 10
Answer:
a
[tex]R =13[/tex]
b
[tex]\= x =8.9[/tex]
c
[tex]var(x) = 16.57[/tex]
d
[tex]\sigma = 4.1[/tex]
Step-by-step explanation:
From the question we are given a data set
2, 10, 15, 4, 11, 10, 15, 10, 2, 10
The sample size is n = 10
The range is
[tex]R = maxNum - MinNum[/tex]
Where maxNum is the maximum number on the data set which is 15
and MinNum is the minimum number on the data set which is 2
So
[tex]R = 15 - 2[/tex]
[tex]R =13[/tex]
The mean is mathematically represented as
[tex]\= x = \frac{\sum x_i}{N}[/tex]
substituting values
[tex]\= x = \frac{2 + 10 + 15 + 4 + 11 + 10 + 15 + 10 + 2 + 10 }{10}[/tex]
[tex]\= x =8.9[/tex]
The variance is mathematically evaluated as
[tex]var(x) = \frac{\sum (x - \= x)^2}{N}[/tex]
substituting values
[tex]var(x) = \frac{(2 - 8.9 )^2 + (10 - 8.9 )^2 + (15 - 8.9 )^2 +(4 - 8.9 )^2 +(11 - 8.9 )^2 +(10 - 8.9 )^2 +(15 - 8.9 )^2 +(10 - 8.9 )^2 +} {10}[/tex] [tex]\frac{(2 - 8.9 )^2 +(10 - 8.9 )^2 }{10}[/tex]
[tex]var(x) = 16.57[/tex]
The standard deviation is [tex]\sigma = \sqrt{var(x)}[/tex]
substituting values
[tex]\sigma = \sqrt{16.57}[/tex]
[tex]\sigma = 4.1[/tex]
A recent study found that toddlers who have a diet high in processed foods may have a slightly lower IQ later in life. The conclusion came from a long-term investigation of 14,000 people whose health was monitored at 3,4,7, and 8 years of age.
a) One analysis found that of the 4000 children for which there were complete data, there was a significant difference in IQ between those who had had "processed" (i.e., junk) food and those who followed health-conscious diets in early childhood. Is this an experiment? Why or why not?
b) Discuss at least two explanatory factors that could conceivably confound the relationship between diet and IQ.
Answer:
A) it is not an experiment it is an observational study/analysis
B) i)Foods high in fats and sugar affects IQ (ii)Foods that contain the required classes of food affects IQ positively
Step-by-step explanation:
A) An analysis carried out on 400 children using the data derived from the long term investigation can not be said to be an experiment but an observational analysis this is because the complete data has been provided already from the long term investigation already. hence it can only be observed
B ) i) foods high in fats and sugar affects The IQ of children later in life as seen from the results of the observational study that children whom had processed foods had a significant negative difference in IQ when compared with children who had health-conscious diets
ii) following health conscious diets early in childhood will have a positive effect on one's IQ later in life .
What is the complete factorization of 36y2 − 1?
Answer:
36y² - 1
Factorize
We have the final answer as
[tex](y - \frac{1}{6} )(36y + 6)[/tex]
Hope this helps you
The slope of the line below is 5/7 Write a point-slope equation of the line
using the coordinates of the labeled point.
O A. y+2 --$(x+6)
O B. y-6--(x-2)
O C. y+6 -- (x + 2)
O D, y-2 - (x - 6)
Answer:
The option are incorrect because as its slope is only 5/7 the answer will never come like that.
Step-by-step explanation:
Here,
Given,
The dlope of a line is 5/7 and (6,2) is a point.
By one point formulae,
(y-y1)= m (x-x1).
or, (y-2)=5/7(x-1)
or, y = 5/7x -5/7+2
taking lcm of -5/7 and 2. we get,
or, y= 5/7 x -5+7/7
Therefore, the equation is y = 5/7 x -2/7.
Hope it helps..
Researchers recorded that a certain bacteria population declined from 800,000 to 500,000 in 6 hours after the administration of medication. At this rate of decay, how many bacteria would there have been at 24 hours? Round to the nearest whole number
Answer:
We can assume that the decline in the population is an exponential decay.
An exponential decay can be written as:
P(t) = A*b^t
Where A is the initial population, b is the base and t is the variable, in this case, number of hours.
We know that: A = 800,000.
P(t) = 800,000*b^t
And we know that after 6 hours, the popuation was 500,000:
p(6h) = 500,000 = 800,000*b^6
then we have that:
b^6 = 500,000/800,000 = 5/8
b = (5/8)^(1/6) = 0.925
Then our equation is:
P(t) = 800,000*0.925^t
Now, the population after 24 hours will be:
P(24) = 800,000*0.925^24 = 123,166
Answer:
122,070 bacteria.
Step-by-step explanation:AA0ktA=500,000=800,000=?=6hours=A0ekt
Substitute the values in the formula.
500,000=800,000ek⋅6
Solve for k. Divide each side by 800,000.
58=e6k
Take the natural log of each side.
ln58=lne6k
Use the power property.
ln58=6klne
Simplify.
ln58=6k
Divide each side by 6.
ln586=k
Approximate the answer.
k≈−0.078
We use this rate of growth to predict the number of bacteria there will be in 24 hours.
AA0ktA=?=800,000=ln586=24hours=A0ekt
Substitute in the values.
A=800,000eln586⋅24
Evaluate.
A≈122,070.31
At this rate of decay, researchers can expect 122,070 bacteria.
A magazine article states that the mean weight of one-year-old boys is the same as that of one-year-old girls. Does the confidence interval contradict this statement? The confidence interval this statement
Answer:
Yes, the confidence interval contradict this statement.
Step-by-step explanation:
The complete question is attached below.
The data provided is:
[tex]n_{1}=318\\n_{2}=297\\\bar x_{1}=25\\\bar x_{2}=24.1\\s_{1}=3.6\\s_{2}=3.8[/tex]
Since the population standard deviations are not provided, we will use the t-confidence interval,
[tex]CI=(\bar x_{1}-\bar x_{2})\pm t_{\alpha/2, (n_{1}+n_{2}-2)}\cdot s_{p}\cdot\sqrt{\frac{1}{n_{1}}+\frac{1}{n_{2}}}[/tex]
Compute the pooled standard deviation as follows:
[tex]s_{p}=\sqrt{\frac{(n_{1}-1)s_{1}^{2}+(n_{2}-1)s_{2}^{2}}{n_{1}+n_{2}-2}}=\sqrt{\frac{(318-1)(3.6)^{2}+(297-1)(3.8)^{2}}{318+297-2}}=2.9723[/tex]
The critical value is:
[tex]t_{\alpha/2, (n_{1}+n_{2}-2)}=t_{0.05/2, (318+297-2)}=t_{0.025, 613}=1.962[/tex]
*Use a t-table.
The 95% confidence interval is:
[tex]CI=(\bar x_{1}-\bar x_{2})\pm t_{\alpha/2, (n_{1}+n_{2}-2)}\cdot s_{p}\cdot\sqrt{\frac{1}{n_{1}}+\frac{1}{n_{2}}}[/tex]
[tex]=(25-24.1)\pm 1.962\times 2.9723\times \sqrt{\frac{1}{318}+\frac{1}{297}}\\\\=0.90\pm 0.471\\\\=(0.429, 1.371)\\\\\approx (0.43, 1.37)[/tex]
The 95% confidence interval for the difference between the mean weights is (0.43, 1.37).
To test the magazine's claim the hypothesis can be defined as follows:
H₀: There is no difference between the mean weight of 1-year old boys and girls, i.e. [tex]\mu_{1}-\mu_{2}=0[/tex].
Hₐ: There is a significant difference between the mean weight of 1-year old boys and girls, i.e. [tex]\mu_{1}-\mu_{2}\neq 0[/tex].
Decision rule:
If the confidence interval does not consists of the null value, i.e. 0, the null hypothesis will be rejected.
The 95% confidence interval for the difference between the mean weights does not consists the value 0.
Thus, the null hypothesis will be rejected.
Conclusion:
There is a significant difference between the mean weight of 1-year old boys and 1-year old girls.
6th grade math , helpp:D
Answer:
a) 30%
b) 45%
Step-by-step explanation:
a) Laura rolls it '4' 12/40 times, you need to convert that to a percent, so 12/40=6/20= 30% or 30/100
b) Basically the same thing: 18/40 = 45% or 45/100
Hope this helped XD
Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line.? y = 2 + sec(x), −π/3 ≤ x ≤ π/3, y = 4; about y = 2
Answer:
The volume of the solid is: [tex]\mathbf{V = \pi [ \dfrac{8 \pi}{3} - 2\sqrt{3}]}[/tex]
Step-by-step explanation:
GIven that :
[tex]y = 2 + sec \ x , -\dfrac{\pi}{3} \leq x \leq \dfrac{\pi}{3} \\ \\ y = 4\\ \\ about \ y \ = 2[/tex]
This implies that the distance between the x-axis and the axis of the rotation = 2 units
The distance between the x-axis and the inner ring is r = (2+sec x) -2
Let R be the outer radius and r be the inner radius
By integration; the volume of the of the solid can be calculated as follows:
[tex]V = \pi \int\limits^{\dfrac{\pi}{3}}_{\dfrac{-\pi}{3}} [(4-2)^2 - (2+ sec \ x -2)^2]dx \\ \\ \\ V = \pi \int\limits^{\dfrac{\pi}{3}}_{\dfrac{-\pi}{3}} [(2)^2 - (sec \ x )^2]dx \\ \\ \\ V = \pi \int\limits^{\dfrac{\pi}{3}}_{\dfrac{-\pi}{3}} [4 - sec^2 \ x ]dx[/tex]
[tex]V = \pi [4x - tan \ x]^{\dfrac{\pi}{3}}_{\dfrac{-\pi}{3}} \\ \\ \\ V = \pi [4(\dfrac{\pi}{3}) - tan (\dfrac{\pi}{3}) - 4(-\dfrac{\pi}{3})+ tan (-\dfrac{\pi}{3})] \\ \\ \\ V = \pi [4(\dfrac{\pi}{3}) - tan (\dfrac{\pi}{3}) + 4(\dfrac{\pi}{3})- tan (\dfrac{\pi}{3})] \\ \\ \\ V = \pi [8(\dfrac{\pi}{3}) - 2 \ tan (\dfrac{\pi}{3}) ][/tex]
[tex]\mathbf{V = \pi [ \dfrac{8 \pi}{3} - 2\sqrt{3}]}[/tex]