9514 1404 393
Answer:
J. 2085
Step-by-step explanation:
Fill in the desired value for y and solve for x.
1500 = 50(1.05^x)
30 = 1.05^x . . . . . . . divide by 50
log(30) = x·log(1.05) . . . . . take logarithms
x = log(30)/log(1.05) ≈ 69.71
Since x represents years after December 2015, x = 69.7 will be some time in mid 2085.
By how much is the sum of 3 2/3 and 2 1/5 less than 7
Step-by-step explanation:
32/3+21/5÷7
14.87÷7
2.124
The formula for the surface area of a cylinder is:
SA = 2π r 2 + 2πrh note: that π= 3.14
a. Solve for h showing all work.
b. If the height of a can of soup is 5 inches and the radius is 1.5 inches, what is the surface area?
Answer:
Below in bold.
Step-by-step explanation:
a. SA = 2π r^2 + 2πrh
2πrh = SA - 2π r^2
h = (SA - 2πr^2)/2πr
When π = 3.14 we have
h = (SA - 6.28r^2)/ 6.28r
b. SA = 6.28*1.5^2 + 6.28*1.5* 5
= 61.23 in^2
The population of a certain town was 10,000 in 1990. The rate of change of the population, measured in people per year, is modeled by , where t is measured in years since 1990. Discuss the meaning of . Calculate the change in population between 1995 and 2000. Do we have enough information to calculate the population in 2020
The question is incomplete. The complete question is :
The population of a certain town was 10,000 in 1990. The rate of change of a population, measured in hundreds of people per year, is modeled by P prime of t equals two-hundred times e to the 0.02t power, where t is measured in years since 1990. Discuss the meaning of the integral from zero to twenty of P prime of t, d t. Calculate the change in population between 1995 and 2000. Do we have enough information to calculate the population in 2020? If so, what is the population in 2020?
Solution :
According to the question,
The rate of change of population is given as :
[tex]$\frac{dP(t)}{dt}=200e^{0.02t}$[/tex] in 1990.
Now integrating,
[tex]$\int_0^{20}\frac{dP(t)}{dt}dt=\int_0^{20}200e^{0.02t} \ dt$[/tex]
[tex]$=\frac{200}{0.02}\left[e^{0.02(20)}-1\right]$[/tex]
[tex]$=10,000[e^{0.4}-1]$[/tex]
[tex]$=10,000[0.49]$[/tex]
=4900
[tex]$\frac{dP(t)}{dt}=200e^{0.02t}$[/tex]
[tex]$\int1.dP(t)=200e^{0.02t}dt$[/tex]
[tex]$P=\frac{200}{0.02}e^{0.02t}$[/tex]
[tex]$P=10,000e^{0.02t}$[/tex]
[tex]$P=P_0e^{kt}$[/tex]
This is initial population.
k is change in population.
So in 1995,
[tex]$P=P_0e^{kt}$[/tex]
[tex]$=10,000e^{0.02(5)}$[/tex]
[tex]$=11051$[/tex]
In 2000,
[tex]$P=10,000e^{0.02(10)}$[/tex]
[tex]=12,214[/tex]
Therefore, the change in the population between 1995 and 2000 = 1,163.
Consider the following system of equations:
y = −2x + 3
y = x − 5
Which description best describes the solution to the system of equations?
Lines y = −2x + 3 and y = 3x – 5 intersect the x-axis.
Line y = −2x + 3 intersects line y = x − 5.
Lines y = −2x + 3 and y = 3x − 5 intersect the y-axis.
Line y = −2x + 3 intersects the origin.
Hi there!
»»————- ★ ————-««
I believe your answer is:
"Line y = −2x + 3 intersects line y = x − 5."
»»————- ★ ————-««
Here’s why:
When the system of equations are graphed, they would intersect at a point. This means that there is a solution to the system. The solution is [tex](\frac{8}{3} ,-\frac{7}{3} )[/tex].While the statement that the lines intersect the x-axis is true, the question asks the statement that describes the solution. The solution is the point of intersection between the two lines.⸻⸻⸻⸻
See the Graph Attached
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
Help!!
f is a quadratic function where f(2) = 0, f(-2) = 0, and f(0) = -0.12. Find an algebraic equation for
f(u).
Answer:
bad gvkvkgcnhvvjzadhljang
v
gjddkfzutwdjtabkf
What is cos 0 when sin 0= 2/3
Answer:
your answer is √7/3
Step-by-step explanation:
your answer is √7/3
Find the measure of the are or central angle indicated. Assume that lines which appear to be
diameters are actual diameters.
2) m SPU
Answer:
120°
Step-by-step explanation:
m L SPU = 180° - 60° = 120°
Choose the system for the graph.
========================================================
Explanation:
The darkest shaded region is in the northern most region. This region is above both blue boundary lines.
A sample point from this region is (5,2)
We'll plug these coordinates into the first inequality of choice A
[tex]3x+4y \le 12\\\\3(5)+4(2) \le 12\\\\23 \le 12\\\\[/tex]
which is false. So we can rule out choice A.
We can rule out choice B for the exact same reason.
The answer is between C and D
---------------------------
Let's plug those x,y coordinates into the first inequality of choice C
[tex]3x+4y \ge 12\\\\3(5)+4(2) \ge 12\\\\23 \ge 12\\\\[/tex]
which is true. So far, so good.
Now repeat for the second inequality of choice C
[tex]2x-5y \ge 10\\\\2(5)-5(2) \ge 10\\\\0 \ge 10\\\\[/tex]
which is false. We rule out choice C. Choice D is the only thing left, so it must be the answer.
---------------------------
Let's check the second inequality of choice D just for the sake of completeness
[tex]2x-5y \le 10\\\\2(5)-5(2) \le 10\\\\0 \le 10\\\\[/tex]
which is true.
We can see that (x,y) = (5,2) makes both inequalities of choice D to be true, and therefore we have found the final answer.
Answer: TRUST ITS THE CHOICE D
Step-by-step explanation:
4(x+9)=2x-6
Solve for x
Answer:
-21
Step-by-step explanation:
4(x+9) = 4x+36
4x+36 = 2x-6
-36 -36
minus 36 from both sides
4x = 2x-42
2x = -42
-42/2 = -21
x = -21
Hi there!
We are given the equation below:
[tex] \large \boxed{4(x + 9) = 2x - 6}[/tex]
1. Expand 4 in the expression.
When expand in the expression, it is like multiply everything in the expression. So when we expand 4 in x+9, it becomes 4(x)+9(4).[tex] \large{(4 \times x) + (9 \times 4) = 2x - 6} \\ \large{(4x) + (36) = 2x - 6}[/tex]
Cancel the brackets.
[tex] \large{4x + 36 = 2x - 6}[/tex]
2. Isolate x-term and solve for the variable.
Think it easy. If you want to isolate x-term then what should you do? Well simply swap sides, and change the operator/sign.[tex] \large{4x - 2x = - 6 - 36}[/tex]
Finally, combine like terms.
[tex] \large{2x = - 42}[/tex]
Then divide both sides by 2 so we can finally leave only x-term.
[tex] \large{ \frac{2x}{2} = \frac{ - 42}{2} } \\ \large \boxed{x = - 21}[/tex]
3. Check the solution if it is right or wrong.
This step is optional but if you are not confident on your answer, this step is recommended.To check the answer, we simply substitute the value of x which is -21 in the equation and see if both sides are equal or not. If both sides are equal then the answer is correct, if not then the answer is wrong. Therefore,
[tex] \large{4(x + 9) = 2x - 6 \longrightarrow 4( - 21 + 9) = 2 ( - 21) - 6} \\ \large{4( - 12) = - 42 - 6} \\ \large{ - 48 = - 48}[/tex]
Since both sides are equal when substitute in x = -21.
4. Answer
Hence, the answer for this equation is x = -21.I hope this helps and let me know if you have any doubts!
Which type of parent function is f(x) =1/2
Answer:
I think you are missing something unless the answer is a horizontal line.
Step-by-step explanation:
Answer:
square root
Step-by-step explanation:
just took the test :)
los tornillos vienen en bolsa de 100. cada 10 bolsas se empaqueta una caja. las cajas se embalan de a 10 en cajones y los cajones se guardan de a 10 en un contenedor para ser transportados. ¿ cuantos tornillos lleva un contenedor?
Answer:
lleva 10 000 tornillos un contenedor
Step-by-step explanation:
Please help ASAP ASAP
Step-by-step explanation:
[tex] \sqrt{53} [/tex]
Determine which data are qualitative and which data are quantitative. Explain your reasoning
a. The yearly salaries of the employees at a school district. (9)
b. The employee numbers of the employees at an accounting firm.
c. The area codes of a sample of 350 residents of nursing homes. (2)
d. The ages of a sample of 350 residents of nursing home. (eta)
e. The answers to a survey of 5000 people about how likely is it that the US will enter a 1930s-like depression. The answers are: Very likely, somewhat likely, not very likely, not at all likely. (20)
f. The IQ index of the students in a statistics class.
What are the levels of measurement of data in question 4? Justify
a. Yearly salaries: (20)
b. Employee numbers: (ca)
c. Area codes: (eca)
d. The ages:
e. Survey answers: (ca)
f. IQ index: (en)
Answer:
1. A. Quantitative data
B. Quantitative data
C. Qualitative data
D. Quantitative data
E. Qualitative data
F. Quantitative data
2.a. Yearly salaries: interval or ratio data
b. Employee numbers: interval or ratio data
c. Area codes : nominal data
d. The ages: interval or ratio data
e. Survey answers: ordinal data
f. IQ index: interval or ratio data
Explanation:
Qualitative data is data in the form of a quality such as a characteristic. It is usually a noun, such as whether a person is fair or dark in complexion. Quantitative data is data in form of quantity such as the amount in dollars of one's salary.
There are four levels of data measurement. They are: nominal data, ordinal data, interval data, and ratio data. Nominal and ordinal data are qualitative data while interval and ratio data are quantitative data.
Suppose your marketing colleague used a known population mean and standard deviation to compute the standard error as 67.5 for samples of a particular size. You don't know the particular sample size but your colleague told you that the sample size is greater than 70. Your boss asks what the standard error would be if you quadruple (4x) the sample size. What is the standard error for the new sample size
Answer:
The standard error for the new sample size will be of 33.75.
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Standard error as 67.5 for samples of a particular size.
We have that [tex]s = \frac{\sigma}{\sqrt{n}}[/tex], that is, the standard error is inversely proportional to the square root of the sample size, so if you quadruple (4x) the sample size, the standard error will be divided by half. So
67.5/2 = 33.75
The standard error for the new sample size will be of 33.75.
the radius of a circle in cm ,with area 77 over 2 cm square is
Answer:
7/√2 cm
Step-by-step explanation:
Area of circle = 77 cm^2
=> π(r)^2 = 77
=> (22/7) x (r)^2 = 77
=> (r)^2 = (77 x 7) / 22
=> (r)^2 = 49/2
=> (r) = 7/√2 cm
Represent the following sentence as an algebraic expression, where "a number" is the letter x.
\text{7 is added to a number.}
7 is added to a number.
Answer:
7+x
Step-by-step explanation:
X will be the unknown
Ahmed packs 8 text books each of mass x grams. And two dictionaries each mass y grams into a box of mass 250 grams. What is total mass of the box now?
Answer:
8x + 2y + 250 grams
Step-by-step explanation:
The box contains
8 text books each with a mass of x grams = 8x
2 dictionaries each with a mass of y grams = 2y
1 box = 250 grams
Total = 8x + 2y + 250
The ratio of girls to boys in a particular classroom is 4: 3. What fraction of the total number of students are boys?
The ratio of boys to the total number of students in a particular classroom is
Answer:
3 : 7
Step-by-step explanation:
The ratio of girls to boys = 4 : 3
Since there are only two possible genders :
Then the total fraction of student is the sum of the ratio = (4 + 3)
Since,
Boys = 3
The ratio of boys to the total number of student in the class will be :
Boys : Total
3 : 7
Assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. Find the probability that a given score is less than and draw a sketch of the region.
Answer:
0.5000
Step-by-step explanation:
According To The Question,
The Area under the Standard Normal Curve, We Can Use the Statistical Tables , That Reported Area As P(z < a) .
Thus, We need to use the following Relationship.
P(z > a) = 1 - P(z < a)Now solve, P(z > 0) = 1 - P(z < 0) ⇔ 1 - 0.5000 ⇔ 0.5000
(Diagram, Please Find in Attachment)
No step by steps or links please
Answer:
Six at top, ten at second, twenty-seven at third, and four at bottom.
Consider the following conditional statement. Determine the contrapositive
of the statement and then determine if the contrapositive is true or false.
If two angles are not complements, then their measures do not add up to 180°.
The contrapositive of the statement is true.
The contrapositve of the statement is false.
Answer:
The contrapositive of the statement is true.
Step-by-step explanation:
For a general statement:
p ⇒ q
The contrapositive statement is:
¬q ⇒ ¬p
where:
¬q is the negation of the proposition q.
Here we have the statement:
If two angles are not complements, then their measures do not add up to 180°
So we have:
p = two angles are not complements
q = their measures do not add up to 180°
Then the negations are:
¬p = two angles are complements
¬q = their measures do add up to 180°
The contrapositive statement is:
"if for two angles their measures do add up to 180°, then the two angles are complements"
This is true, if for two angles the sum of their measures is equal to 180°, then these angles are complementary.
Then: The contrapositive of the statement is true.
Find the following list of data calculate a demean be the maid and see mode or mothers for the following numbers listed in the picture above above
Answer:
Mean = 4.8875
Median = 4.6
Mode = 4.5 and 7.7
Step-by-step explanation:
Mean is the sum of total of data divided by the sample size
Sum total = 1.5 + 4.7 + 6 + 7.7 + 7.7 + 4.5 + 2.5 + 4.5
Sum total = 39.1
Sample size = 8
Mean = 39.1/8
Mean = 4.8875
To get the median we need to first rearrange
1.5, 2.5, 4.5, 4.5, 4.7, 6, 7.7, 7.7
Median = 4.5 + 4.7/2
Median = 4.6
Hence the median is 4.6
Mode is the value occuring the most. Since 4.5 and 7.7 both occurs twice, hence the mode of the data is 4.5 and 7.7
3
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1
As
→
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-3
-2
-1
1
2
3
4
-1-
MY
-2
Col
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SA
MY
What is the slope of the line?
Pro
Answer:
1/2
Step-by-step explanation:
choose 2 points, I chose (-3,2) (1,4)
[tex]m = \frac{4 - 2}{1 - ( - 3)} = \frac{2}{4} = \frac{1}{2} [/tex]
what is the average rate of change from 0 to 2 of the function represented by the graph? Enter your answer, as a simplified fraction, in the box
Answer:
=>The graph of an exponential relation is also non-linear.
=>The graph of an exponential relation becomes nearly parallel to x-axis on one and then curves upward and becomes nearly parallel to the y-axis on the other sid.
The average rate of change from 0 to 2 of the function represented by the graph is [tex]\frac{3}{2}[/tex].
What is average rate of change?It is a measure of how much the function changed per unit, on average, over that interval. It is derived from the slope of the straight line connecting the interval's endpoints on the function's graph.
According to the question
[tex]x_{1} =0[/tex], [tex]x_{2} =2[/tex]
f(0) = 1, f(2) = 4
The average rate of change = [tex]\frac{f(x_{2})-f(x_{1}) }{x_{2}-x_{1} }[/tex]
= [tex]\frac{f(2)-f(0) }{2-0 }[/tex]
= [tex]\frac{4-1}{2}[/tex]
= [tex]\frac{3}{2}[/tex]
Hence, the average rate of change from 0 to 2 of the function represented by the graph is [tex]\frac{3}{2}[/tex].
Find out more information about average rate of change here
https://brainly.com/question/13235160
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sammy is on level 40 , which is five times as much as rocky.what islevel rocky on
Answer:
8
Step-by-step explanation:
40÷5=8
Hope this helps! :)
11 Roger has m toy cars. Don has twice as many cars as Roger. Larry has five more cars than Roger. Write down an expression, in terms of m, to complete each statement. Don has cars H Larry has cars
Step-by-step explanation:
Roger has m toy cars.→ Number of cars Roger has = m
Don has twice as many cars as Roger.→ Number of cars Don has = 2(Cars Roger has)
→ Number of cars Don has = 2m
Larry has five more cars than Roger.→ Number of cars Larry has = 5 + (Cars Roger has)
→ Number of cars Larry has = 5 + m
In a mathematics each correct answer gains 5 marks - However, 1 mark is deducted for each incorrect answer. Mary answered 30 questions for a total of 78 marks Determine the number of correct and incorrect questions Mary answered.
Answer:
Correct answers= 18
Incorrect answers=30-18= 12 answers
Step-by-step explanation:
total questions=30
correct answers= x
incorrect answers= 30-x
given: 5 marks for each correct answer
therefore, marks for correct answers = 5*x = 5x
Given: 1 mark deducted for every incorrect answer
therefore, marks deducted = 1(30-x) = 30-x
Total marks scored= 78
★ The Difference of Marks scored for Correct Answers and Marks deducted for Incorrect Answers should be equal to 78
5x- (30-x) =78
5x-30+x=78
5x+x=78+30
6x= 108
x=108/6 = 18
Correct answers= 18
Incorrect answers=30-18= 12 answers
16. Using divisibility tests, check whether the number 240720 is divisible by
2, 3, 4, 5, 6, 8, 9, 10 and 11. (Give reason)
In a bag of mini candy bars, 40% of the candy bars are Snickers. There are 120 Snickers in the bag. How many total mini candy bars are in the bag?
Answer:
The amswer is 48.
Step-by-step explanation:
120×0.40=48
In communicating with an orbiting satellite, suppose that a 30-bit message is sent to thesatellite. Transmission of messages can sometimes be distorted. If the probability of eachbit being received incorrectly is 0.001, where each bit is received independently of the others,what is the probability that at least one bit is received incorrectly?
Answer:
0.0296 = 2.96% probability that at least one bit is received incorrectly.
Step-by-step explanation:
For each bit, there are only two possible outcomes. Either it is received correctly, or it its not. Each bit is received independently of the others, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
The probability of each bit being received incorrectly is 0.001
This means that [tex]p = 0.001[/tex]
30-bit message
This means that [tex]n = 30[/tex]
What is the probability that at least one bit is received incorrectly?
This is:
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{30,0}.(0.001)^{0}.(0.999)^{30} = 0.9704[/tex]
Then
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.9704 = 0.0296[/tex]
0.0296 = 2.96% probability that at least one bit is received incorrectly.