Answer:
k ≈ - 0.069
Step-by-step explanation:
Given
A = 800 [tex]e^{kt}[/tex]
Substitute A = 400 and t = 10 into the equation
400 = 800 [tex]e^{10k}[/tex] ( divide both sides by 800 )
0.5 = [tex]e^{10k}[/tex] ( take the ln of both sides )
ln [tex]e^{10k}[/tex] = ln0.5
10k lne = ln0.5 [ lne = 1 ]
10k = ln 0.5 ( divide both sides by 10 )
k = [tex]\frac{ln0.5}{10}[/tex] ≈ 0.069 ( to the nearest thousandth )
Answer:
Step-by-step explanation:
400 = 800 * e^(k*t)
What are the units of t? I'm taking it as years.
Divide by 800
400/800 = e^(k*10)
1/2 = e^(k*10)
ln(1/2) = ln(e)^(k*10)
ln(1/2) = k*10 * ln(e)
ln(e) = 1
-0.69314 = k*10
-0.069314 = k
Check
A = 800 e^(-0.069314*10)
A = 800 e^(-0.69314)
A = 800 * 0.50000359
A = 400.0028722
Which is close enough to 400
help me plz god bless
Answer:
d.
Step-by-step explanation:
The gradient is -5 meaning that it's going downwards as x increases
The y-intercept is 3
Feel free to mark as brainliest :D
Write an equation of a line with slope -4 and y- intercept of 0
Answer:
y=-4x
Step-by-step explanation:
Take a look at the photo and please right an explanation for your answer
how do you change a fraction to a unit rate
Answer:
A unit rate is a rate with 1 in the denominator. If you have a rate, such as price per some number of items, and the quantity in the denominator is not 1, you can calculate unit rate or price per unit by completing the division operation: numerator divided by denominator.
Step-by-step explanation:
In a survey of 554 U.S. adults, it is found that 360 favor a ban on stem cell research. Set up the null and the alternative hypotheses to test whether there is sufficient evidence that over 61% favor a ban on stem cell research. If alpha is set to 3.0%, should the null hypothesis be rejected
Answer:
The null hypothesis will be rejected
Step-by-step explanation:
The null hypothesis is that people who favour ban on stem cell research is less than or equal to 0.61
The alternate hypothesis is that people who favour ban on stem cell research is greater than 0.61
Proportion of population = 0.61
Total events = 360
Sample size = 554
Sample proportion = 360/554 = 0.649
As per test statistics –
Z = (p-p0)/sqrt {(p0 (1-p0))/n} = (0.649 -0.61)/ {(0.61 (1-0.61))/554}
= 0.039/0.021
= 1.857
P (Z<1.857) = 1- P (Z<1.857) = 1-0.9664 = 0.0336
So alpha value is 0.064.
Thus, we will reject the null hypothesis
5/7 ÷ 2/3=?
Is it A?
Is it B?
Is it C?
Or is it D?
Answer:
[tex]C.[/tex] 5/7 × 2/3
Step-by-step explanation:
I will give Brainliest
Please help me find the answer
Answer:
in the first traingle
sinC = 36/39 = 12/13
CosC= 15/39 = 5/13
TanA= 15/36=5/12
this is the values i didnt understand the question so i just find the values
in the second Triangle
SinA=2√5/5
CosA=√5/5
TanB= √5/2√5=1/2
cos 30 = √3/2
sin45=√2/2
tan60= √3
hopefully its helpful iam sorry i didnt understand what they mean in the question my engilish is bad
Sin of c. Sin'-1(36/39)=90
Cos of c cos'-1(15/39)=67.38
Tan of a tan'-1(15/36)=22.62
Sin of a sin'-1(2squarroot5/5)=63.43
Cos od a cos'-1(squareroot5/5)=63.43
Tan of b tan'-1(2squareroot5/squareroot5)=63.43
Cos30 is pie/6 or squareroot of 3 /2
Sin of 45 is pie/4 or squareroot2/2
Tan60 is pie/3 or squareroot3
Degree and Radian Measures
Convert the given radian measure to a degree measure.
1.2 /pi (π)
a. -216°
b. 108°
c. 216°
d. -108°
Please select from the best choices provided
Answer:
C. 216°
Step-by-step explanation:
I calculated it logically
A right-angled triangle, with two sides adjacent to the right angle labeled 7 and 11 respectively, and the hypotenuse is labeled x.
Find the exact value of $x$ .
Answer:
170
c=a^2+b^2=7^2+11^2≈13.0384 or 170
Step-by-step explanation:
mrk me brainliest please
Which of the following is most likely the next step in the series
Answer:
A
Step-by-step explanation:
The pattern is blue red blue red
+
The pattern is vertical horizontal vertical horizontal
Answer:
A.
The second figure adds another red horizontal line to the first. The third adds a vertical blue line to the second. The fourth must add a red horizontal line to the third.
the perimeter of a square field is 880m. Find it's area in hectares
This is the answer hope it helps
The area of the square field is 4840 hectares.
What is perimeter of square?Perimeter of the square is defined as addition the lengths of the square's four sides.
Perimeter of the square equation is 4a
Where, a is length of the square
Given data as :
Perimeter of the square field = 880 m
Side of the square = Perimeter/4
Side of the square = 880/4
Side of the square = 220 m
So, length of each side of the square is 220 m
Area of square = Side × Side
Area of square = 220 m × 220 m
Area of square = 48400 square meters
Area of square = 48.4 square kilometers
As we know that 1 sq km = 100 hectares
So, 48.4 km = 48.4 × 100 = 4840 hectares
Hence, the area of the square field is 4840 hectares.
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The Ballantyne area has 200 people over the age of eighty-five living in it of these people, 56 of them have a dog, 24 of them have a cat, and 16 of them have both of a person
is chosen at random, find the probability that they have a cat, if it is known they have a dog.
a. 1/2
b.3/7
c.2/7
d.2/25
The product of two positive integer numbers is 40 and the sum of the same two numbers is 13.
9514 1404 393
Answer:
5 and 8
Step-by-step explanation:
Factor pairs that make 40 are ...
40 = 1×40 = 2×20 = 4×10 = 5×8
The pair that has a sum of 13 is 5 and 8.
An important problem in industry is shipment damage. A electronics distribution company ships its product by truck and determines that it cannot meet its profit expectations if, on average, the number of damaged items per truckload is greater than 12. A random sample of 12 departing truckloads is selected at the delivery point and the average number of damaged items per truckload is calculated to be 9.4 with a calculated sample of variance of 0.64. Select a 99% confidence interval for the true mean of damaged items.
a) [48.26, -30.02]
b) [10.67, 11.93]
c) [-0.6285, 0.6285]
d) [10.69, 11.91]
e) [11.37, 12.63]
f) none of the above
Answer:
the answer is b) (10.67,11.93)
Step-by-step explanation:
hope this helps
Here are some clues about my age. • Both my father’s age and mine are 2-digit numbers. • If you reverse the order of the digits of my father’s age, you get my age. • My father is 27 years older than I am. How old am I? Show your work and justify your thinking.
For the given condition the age of the son will be 69 years.
What is the equation?A mathematical equation asserts the equality of two expressions, which may or may not contain variables or integers. Equations are fundamental concerns, and efforts to rationally address them have served as the primary driving forces behind the creation of mathematics.
Suppose the two-digit number is x,
The father's and son's ages are 10x+y and 10y+x respectively.According to the given condition,
(10x+y) -(10y+x)=27
9x-9y=27
x-y=27/9
x-y=3
The value of x and y will be 4 and 1.
At x=9 and y=6, the age of the son is obtained as,
=10×6+9
=69 years
Thus, the age of the son will be 69 years.
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The sidewalk is 5 feet wide and the garden measures 20 feet across. Which measurement is closest to the area of the outer edge of the sidewalk?
A.
200 ft2
B.
400 ft2
C.
700 ft2
D.
1,000 ft2
Answer:
A (obviously)
Step-by-step explanation:
Info Given
Sidewalk is 5 ft. wideGarden is 20 ft. acrossIt has been observed that some persons who suffer acute heartburn, again suffer acute heartburn within one year of the first episode. This is due, in part, to damage from the first episode. The performance of a new drug designed to prevent a second episode is to be tested for its effectiveness in preventing a second episode. In order to do this two groups of people suffering a first episode are selected. There are 45 people in the first group and this group will be administered the new drug. There are 75 people in the second group and this group will be administered a placebo. After one year, 12% of the first group has a second episode and 14% of the second group has a second episode. Conduct a hypothesis test to determine, at the significance level 0.1, whether there is reason to believe that the true percentage of those in the first group who suffer a second episode is less than the true percentage of those in the second group who suffer a second episode.
A. [ z < -1.65, RHo].
B. [ z < -1.65 and z > 1.65, FRHo].
C. [z > 1.65, FRHo].
D. [z < -1.65 and z > 1.65, FRHo].
E. [z > -1.65 and z < 1.65, RHo].
F. None of the above.
Answer:
F. None of the above.
Step-by-step explanation:
Let the null and alternate hypothesis be
H0: p1 ≥ p2 against the claim Ha: p1 < p2
the significance level is 0.1
The critical region is z < z∝= 1.28
The test statistic is
Z= ( p^1-p^2)- (p1-p2)/√p1^q1^/n1 + p2^q2^/n2
Here n1= 45 , n2= 75
p1= 0.12 p2= 0.14
q1= 0.88 q2= 0.86
z= 0.12- 0.14/√0.12*0.88/45 +0.14*0.86/75
Z= 0.02/ √0.00235 + 0.00161
Z= 0.02/0.062891
z= 0.318
The calculated value of z= 0.318 lies in the critical region z < 1.28
therefore accept Ha.
All of the options are incorrect as the critical value for one tailed test for 0.1 is 1.28 .
Find the surface area of the composite figure.
6 cm
5 cm
4 cm
6 cm
15 cm
3 cm
The surface area of the given composite figure will be 384 square cm.
What is surface area?The space occupied by any two-dimensional figure in a plane is called the area. The area of the outer surface of any body is called the surface area.
In the given image we have a composite figure one is a rectangular cuboid and the other is a triangular prism. The surface area will be equal to the sum of all the outer sides of the figure.
The surface area of the triangular shape will be calculated as:-
SA = 2( Area of triangle ) + Area of rectangular surfaces
SA = 2 ( (1/2) B x H ) + (5 x 6 ) + ( 6 x 3 )
SA = ( 3 x 4 ) + ( 30 ) + ( 18 )
SA = 12 + 30 + 18
SA = 60 square cm
The surface area of the rectangular cuboid will be calculated as:-
SA = ( 4 x 6 ) + 2 ( 158 x 4 ) + 2 ( 15 X 6 )
SA = 24 + 120 + 180
SA = 324 square cm
Total surface area will be = 324 + 60 = 384 square cm.
Therefore the surface area of the given composite figure will be 384 square cm.
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2.247 divided into 7 equals what
Suppose that two investors A and B have exhibited the indifference probabilities as shown in table below. Indifference probability Investor A Investor B Net return (RM) -2000 0 0 - 1000 0.70 0.10 0 0.80 0.20 1000 0.85 0.30 2000 0.90 0.50 3000 0.95 0.60 4000 1.00 1.00 a) Determine the utility value (for each monetary value) for each investor and fill it in table above. b) Graph the utility functions for both investors and categorize each investor as either a risk- averse person or a risk seeker. c) Suppose that investor A has the chance to invest in one of two ventures. Venture I can produce a net return of RM3000 with probability 0.40 or a net loss of RM1000 with probability 0.60. Venture II can produce a net return of RM2000 with probability 0.60 and no return with probability 0.40. Based on utility function in (b), use the expected utility criterion to determine the venture investor A should select. What is the expected monetary value associated with the selected venture?
Answer:
Da Answer is Suppose that two investors A and B have exhibited the indifference probabilities as shown in table below. Indifference probability Investor A Investor B Net return (RM) -2000 0 0 - 1000 0.70 0.10 0 0.80 0.20 1000 0.85 0.30 2000 0.90 0.50 3000 0.95 0.60 4000 1.00 1.00 a) Determine the utility value (for each monetary value) for each investor and fill it in table above. b) Graph the utility functions for both investors and categorize each investor as either a risk- averse person or a risk seeker. c) Suppose that investor A has the chance to invest in one of two ventures. Venture I can produce a net return of RM3000 with probability 0.40 or a net loss of RM1000 with probability 0.60. Venture II can produce a net return of RM2000 with probability 0.60 and no return with probability 0.40. Based on utility function in (b), use the expected utility criterion to determine the venture investor A should select. What is the expected monetary value associated with the selected venture?
Step-by-step explanation:
LESSSSSSS GOOOOOOOOOO
Help please!!!! will Brainly!!!
Answer:
true
Step-by-step explanation:
.................
When factoring the difference of two squares, what will the signs in the parenthesis be
Answer:
The signs will be + and -
Step-by-step explanation:
Required
The signs in the parenthesis of difference of two squares
Let the expression be:
[tex](x^2 - a^2)[/tex]
Expand
[tex]x^2 - a^2 = x^2 -ax + ax - a^2[/tex]
Factorize
[tex]x^2 - a^2 = x(x -a) + a(x - a)[/tex]
Factor out x - a
[tex]x^2 - a^2 = (x +a)(x - a)[/tex]
See that the sign in front of a is + and - in the parentheses
When you roll two number cubes, what are the odds, in simplest form, in favor of getting two numbers less than 3?
Answer:
1/3
Step-by-step explanation:
there are 4 numbers total that are less than 3 and there are 12 sides total
so 4/12 would be the total and 1/3 would be simplified
Plz help find the rule 50 points
Answer:
1², 2²,3², 4², 5², 6², 7², 8², 9², 10², 11², 12², 13², 14², 15², 16², 17², 18², 19², 20²,........
Each number is multiplied by itself.
I do need to know NOTHING.
Answer:
Thats cool man.
Step-by-step explanation:
Pleaseeee helppppp!!
Answer:
60.4
Step-by-step explanation:
90-29.6= 60.4
complimentary means either of two angles whose sum is 90°.
The City of Irvine upgraded a bicycle lane in a section of road to have a physical barrier between the cyclists as opposed to just a painted white line on the road. They now want to do a study to see if the bicycle lane upgrades have encouraged more people to utilize the bike lane. Before the upgrade, on any given day, it was known that the section of road saw an average of 350 unique cyclists. After the upgrade, they took a random sample of 35 days in the year and counted the number of unique cyclists each day. The average was 405 cyclists with a standard deviation of 25. Test the hypothesis at the 0.05 significance level.
Answer:
The p-value of the test is 0 < 0.05, which means that there is significant evidence to conclude that more people utilize the bike lane after the change.
Step-by-step explanation:
Before the upgrade, on any given day, it was known that the section of road saw an average of 350 unique cyclists. Test if more people are using now.
At the null hypothesis, we test if the same number of people is still using, that is, the mean is 350. So
[tex]H_0: \mu = 350[/tex]
At the alternate hypothesis, we test if this mean increased, that is:
[tex]H_1: \mu > 350[/tex]
The test statistic is:
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, s is the standard deviation of the sample and n is the size of the sample.
350 is tested at the null hypothesis:
This means that [tex]\mu = 350[/tex]
After the upgrade, they took a random sample of 35 days in the year and counted the number of unique cyclists each day. The average was 405 cyclists with a standard deviation of 25.
This means that [tex]n = 35, X = 405, s = 25[/tex].
Test statistic:
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{405 - 350}{\frac{25}{\sqrt{35}}}[/tex]
[tex]t = 13.02[/tex]
P-value of the test and decision:
The p-value of the test is the probability of finding a sample mean above 405, which is a right-tailed test with t = 13.02 and 35 - 1 = 34 degrees of freedom.
Using a t-distribution calculator, this probability is of 0.
The p-value of the test is 0 < 0.05, which means that there is significant evidence to conclude that more people utilize the bike lane after the change.
Given the function f(x) = 4^x - 1, explain and show how to find the average rate of change between x = 1 and x = 4.
Answer:
84
Step-by-step explanation:
f(1)=4^1 - 1 = 3
f(4) = 4^4 - 1 = 255
rate of change = [tex]\frac{f(x_2)-f(x_1)}{x_2-x_1}[/tex]
(255 - 3) / (4 - 1) = 252 / 3 = 84
round 98,376 to the nearest thousand
Answer:
98000
Step-by-step explanation:
Somebody please help!
Answer:
57 7/9
Step-by-step explanation:
I used a fraction calculator.