21 and 22 are complementary angles. The measure of Z1 is 60°. The
measure of 22 is 5(x - 1)º. Find the value of x.
Answers
Answer:
The value of x is 7
Step-by-step explanation:
Complementary angles have a sum of 90°, therefore the equation to solve for x is:
∠1+∠2=90°
60°+5(x-1)°=90°
5(x-1)=30°
x-1=6
x=7
So the value of x is 7
Related Questions
Animal populations are not capable of unrestricted growth because of limited habitat and food supplies. Under such conditions the population follows a logistic growth model: P(t) = d 1 + ke−ct where c, d, and k are positive constants. For a certain fish population in a small pond d = 1200, k = 11, c = 0.2, and t is measured in years. The fish were introduced into the pond at time t = 0. (a) How many fish were originally put in the pond? 100 Correct: Your answer is correct. fish (b) Find the population after 10, 20, and 30 years. (Round your answers to the nearest whole number.) 10 years 1 Changed: Your submitted answer was incorrect. Your current answer has not been submitted. fish 20 years fish 30 years fish (c) Evaluate P(t) for large values of t. What value does the population approach as t → [infinity]? P(t) =
Answers
Answer:
(a) 100 fishes
(b) t = 10: 483 fishes
t = 20: 999 fishes
t = 30: 1168 fishes
(c)
[tex]P(\infty) = 1200[/tex]
Step-by-step explanation:
Given
[tex]P(t) =\frac{d}{1+ke^-{ct}}[/tex]
[tex]d = 1200\\k = 11\\c=0.2[/tex]
Solving (a): Fishes at t = 0
This gives:
[tex]P(0) =\frac{1200}{1+11*e^-{0.2*0}}[/tex]
[tex]P(0) =\frac{1200}{1+11*e^-{0}}[/tex]
[tex]P(0) =\frac{1200}{1+11*1}[/tex]
[tex]P(0) =\frac{1200}{1+11}[/tex]
[tex]P(0) =\frac{1200}{12}[/tex]
[tex]P(0) = 100[/tex]
Solving (a): Fishes at t = 10, 20, 30
[tex]t = 10[/tex]
[tex]P(10) =\frac{1200}{1+11*e^-{0.2*10}} =\frac{1200}{1+11*e^-{2}}\\\\P(10) =\frac{1200}{1+11*0.135}=\frac{1200}{2.485}\\\\P(10) =483[/tex]
[tex]t = 20[/tex]
[tex]P(20) =\frac{1200}{1+11*e^-{0.2*20}} =\frac{1200}{1+11*e^-{4}}\\\\P(20) =\frac{1200}{1+11*0.0183}=\frac{1200}{1.2013}\\\\P(20) =999[/tex]
[tex]t = 30[/tex]
[tex]P(30) =\frac{1200}{1+11*e^-{0.2*30}} =\frac{1200}{1+11*e^-{6}}\\\\P(30) =\frac{1200}{1+11*0.00247}=\frac{1200}{1.0273}\\\\P(30) =1168[/tex]
Solving (c): [tex]\lim_{t \to \infty} P(t)[/tex]
In (b) above.
Notice that as t increases from 10 to 20 to 30, the values of [tex]e^{-ct}[/tex] decreases
This implies that:
[tex]{t \to \infty} = {e^{-ct} \to 0}[/tex]
So:
The value of P(t) for large values is:
[tex]P(\infty) = \frac{1200}{1 + 11 * 0}[/tex]
[tex]P(\infty) = \frac{1200}{1 + 0}[/tex]
[tex]P(\infty) = \frac{1200}{1}[/tex]
[tex]P(\infty) = 1200[/tex]
Please help very urgent
Answers
Answer:
it depends how many weeks look below
Step-by-step explanation:
1 week=$100.00
2 weeks=$115.00
3 weeks=$130.00
4 weeks=$145.00
and so on
pretty much every week you go up, she earns 15 bucks
hope this helps! have a good day :)
30 POINTS!!!!! I WILL GIVE BRAINLIEST!!!!!!
What is the measure of angle PQR?
Answers
Answer:
40
Step-by-step explanation:
It tells you what Q, R is for the opening. That means that it is 40
The measure of angle PQR is 70 degrees
We have a right triangle - r is 90 degrees
based on geometric rules: angle RPQ = 20
40 : 2
90 + 20 = 110
110 + x = 180
What is the perimeter of the triangle?
The perimeter of the triangle is 180 degrees
The triangle has 180 degrees.
This means that 180 - 110 =70 degrees.
The measure of angle PQR is 70 degrees.
Given m= <3,7> and n=<1,5> what is m+3n?
Answers
Answer:
i thought it was one number
Step-by-step explanation:
how many oz do you think this cup is
Answers
Answer:
I'm gonna say 12??
Step-by-step explanation:
Am I close?
Have a nice day! <3
Please hurry and help me
Answers
Answer:
The last option is your answer
Step-by-step explanation:
I keep looking and I can’t find the answer
Answers
Answer:
B
Step-by-step explanation:
sInce his average is equal or greater than league's average
PLEASE HELPPO?!!!! Look at the attachment below
Answers
Answer:
157
Step-by-step explanation:
just trust me bro
Coach Elyson claims that 90% of her volleyball serves are good serves. The captain of the team thinks Coach Elyson has a lower rate of good serves. To test this, 50 of the coach's serves are randomly selected and 41 of them are good. To determine if these data provide convincing evidence that the proportion of Coach Elyson's serves that are good is less than 90%, 100 trials of a simulation are conducted. The team captain's hypotheses are: H o: p = 90% and H a: p < 90%, where p = the true proportion of Coach Elyson's serves that are good. Based on the results of the simulation, what is an estimate of the P-value of the test?
Answers
Answer:
The correct answer is: 2%
Step-by-step explanation:
Took the quiz
In this experiment researchers randomly assigned smokers to treatments. Of the 193 smokers taking a placebo, 29 stopped smoking by the 8th day. Of the 266 smokers taking only the antidepressant buproprion, 82 stopped smoking by the 8th day. Calculate the estimated standard error for the sampling distribution of differences in sample proportions.
Answers
Answer:
The estimated standard error for the sampling distribution of differences in sample proportions is 0.0382.
Step-by-step explanation:
To solve this question, we need to understand the Central Limit Theorem and subtraction of normal variables.
Central Limit Theorem
The Central Limit Theorem estabilishes 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.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Subtraction of normal variables:
When we subtract normal variables, the mean is the subtraction of the means, while the standard error is the square root of the sum of the variances:
Of the 193 smokers taking a placebo, 29 stopped smoking by the 8th day.
This means that:
[tex]p_S = \frac{29}{193} = 0.1503[/tex]
[tex]s_S = \sqrt{\frac{0.1503*0.8497}{193}} = 0.0257[/tex]
Of the 266 smokers taking only the antidepressant buproprion, 82 stopped smoking by the 8th day.
This means that:
[tex]p_A = \frac{82}{266} = 0.3083[/tex]
[tex]s_A = \sqrt{\frac{0.3083*0.6917}{266}} = 0.0283[/tex]
Calculate the estimated standard error for the sampling distribution of differences in sample proportions.
[tex]s = \sqrt{s_S^2 + s_A^2} = \sqrt{0.0257^2 + 0.0283^2} = 0.0382[/tex]
The estimated standard error for the sampling distribution of differences in sample proportions is 0.0382.
9 decreased by 4 times a number
Answers
Answer:
4x - 9
Step-by-step explanation:
4 times a number means 4x
9 decreased by means -9
Combined:
4x - 9
Answer:
9 - 4x
Step-by-step explanation:
this is so easy
Find 0% of 44:
Find 100% of 44:
Find 50% of 44:
Find 25% of 44:
Find 75% of 44:
Answers
Answer:
0% of 44=0
100% if 44=44
50% of 44=22
25% of 44=11
75% of 44=33
Find the equation of circle passing through points (5 7) and (2 -2 ) whose center lies on the 2x-y=1
Answers
Answer:
(x-2)²+(y-3)²=5².
Step-by-step explanation:
1. the equation of line through points (5;7) and (2;-2) is:
[tex]\frac{x-5}{3} =\frac{y-7}{9}; \ => \ 3x-y-8=0.[/tex]
2. to find the equation of the line, which is perpendicular to the line 3x-y-8=0:
the vector (3;-1) is perpendicular to the line 3x-y-8=0 and it is the vector-pointer for the requred line, and if |n₁|*|n₂|=0 (where n₁ is normal vector to the line 3x-y-8=0 and n₂ is normal vector to the required line), then 3*x-1*y=0 (where 'x' and 'y' any numbers). x=1; y=3, then n₂(1;3), then the required line is x+3y+C=0, where C - is unknown number.
3. to find the equation of the line, which is perpendicular to the line 3x-y-8=0 and passes through the middle point of (5;7) and (2;-2):
middle point is (7/2;5/2), then after substitution of coordinates of the middle point into the equation x+3y+C=0 it will be 3.5+3*2.5+C=0, ⇒ C= -11.
the required equation is x+3y-11=0
4. to calculate the intersection point of x+3y-11=0 and 2x-y=1:
[tex]\left \{ {{2x-y=1} \atop {x+3y=11}} \right. \ => \ (2;3)[/tex]
the point (2;3) is the centre of the required circle.
5. to calculate the radius² of the required circle:
r²=(5-2)²+(7-3)² or r²=(2-2)²+(2+3)², then r²=5².
6. if the centre of the required circle is (2;3) and its r²=25, then it is possible to make up the equiation of the circle:
(x-2)²+(y-3)²=5².
A tree grows at a rate of 1.2 centimeters per day. How many meters will it grow in 80 days?
Answers
Answer:
0.96meters
Step-by-step explanation:
1.2*80 = 96
96cm = 0.96meters
A family spends 1/10 of it's annual income for housing 1/4 for food and clothing 1/5 for general expenses and 2/15 for entertainment what fractional part of their income is spent on these items altogether.
Answers
Answer:
The family spends 41/60 of its income on these items altogether.
Step-by-step explanation:
Given that a family spends 1/10 of it's annual income for housing, 1/4 for food and clothing, 1/5 for general expenses and 2/15 for entertainment, to determine what fractional part of their income is spent on these items altogether the following calculation must be performed:
10, 4, 5, and 15 have a common least multiple at 60.
1/10 = 6/60
1/4 = 15/60
1/5 = 12/60
2/15 = 8/60
6 + 15 + 12 + 8 = 41
Therefore, the family spends 41/60 of its income on these items altogether.
A picture is to be printed onto a sheet of paper with dimensions of 81/2 x 11 inches, A margin of 1 1/2 inches is to be left on all sides of the picture. What is the area of the printed picture?
Answers
Answer:
The area of the printed picture is 172.5 square inches.
Step-by-step explanation:
Since a picture is to be printed onto a sheet of paper with dimensions of 81/2 x 11 inches, and a margin of 1 1/2 inches is to be left on all sides of the picture, to determine what is the area of the printed picture the following calculation must be carried out, knowing that the area of a rectangle is equal to the base multiplied by the height:
81/2 = 40.5
1/2 = 0.5
40.5 - 1.5 x 4 = 34.5
11 - 1.5 x 4 = 5
34.5 x 5 = 172.5
Therefore, the area of the printed picture is 172.5 square inches.
What is the equation of the line shown in the graph at the right?
Answers
$102 headphones, 7.5% tax
Answers
Answer:
You are correct the tax would be that
Step-by-step explanation:
Selena is a freelance graphic artist who charges $65 per hour for her services. A client paid her $195 for her last project. The equation below represents this situation.
65h = 195
For how many hours did Selena work on that project?
Answers
Answer: 3 hours
Step-by-step explanation:
195/65=3
Answer:
3
Step-by-step explanation:
$195 divided by $65 is 3 hours of work
A group of 15 people were surveyed about the month they were
born. How many of the students were born in March?
.
3/5 born in September
1/3 born in December
Answers
3/5 is 9/15
1/3 is 5/15
This gives us 14/15 so 1/15 we’re born in March. Only 1 person.
Jesse has already daved $276 for a trip to Florida. This is 75% of his goal. How much money does he want to save?
Answers
Answer:
Total savings= $368
Step-by-step explanation:
Giving the following formula:
Jesse has already saved $276 for a trip to Florida. This is 75% of his goal.
To calculate the total amount to be saved, we need to use the following formula:
Total savings= amount saved / saving percentage
Total savings= 276 / 0.75
Total savings= $368
I have to go to a few places but my friend needs help with this specific equation!
Thank you!
~Hocus Pocus
Answers
Answer:
Hello, this would be a vertical angle graph. Since this graph is a supplementary graph since it stretches about 180 degrees, you would take both 7x and x+20 and set it equal to 180 like this:
7x+x+20=180
Then, you combine the xs and you would get this:
8x+20=180
Then, subtract 20 from both sides like this:
8x=160
Lastly, you would divide 8 by both sides and get x which is:
x=20
Step-by-step explanation:
I hope this helped you!
Can u guys help me pls ill give u 20 points
Answers
Answer:
Its either L or N im not sure but if i had to guess out of the two i think its L.
Step-by-step explanation:
divide 12 unto two parts such that
their product is 35
Answers
What is the equation of the graph below?
y = sec(x) + 2
y = csc(x) + 2
y = csc(x + 2)
y = sec(x + 2)
Answers
Answer:
y = csc(x) + 2
Step-by-step explanation:
The equation for the given graph is y = csc(x) + 2
What is an equation of a graph?'In graph theory, Graph equations are equations in which the unknowns are graphs. One of the central questions of graph theory concerns the notion of isomorphism. The graphs are expressed differently in terms of graph equations.'
According to the given problem,
We know, periodicity of a.csc( bx + c ) + d = [tex]\frac{periodicity of cscx}{[b]}[/tex]
The periodicity of csc(x) is 2π,
⇒ [tex]\frac{2\pi }{1}[/tex]
= 2π
Hence, we can conclude, the equation y = csc(x) + 2 represents the given graph.
Learn more about equations of graphs here: https://brainly.com/question/24866278
#SPJ2
My cousin needs help with this question.
Answers
Answer:
3 feet per minute
Step-by-step explanation:
Look at an easy to read point on a grid line intersection.
Then find the slope. Slope = constant of proportionality.
For example, look at point (2, 6) which means that when time = 2 minutes, distance = 6 feet.
(6 ft)/(2 sec) = 3 feet per minute
Answer: 3 feet per minute
It takes Andre 4 minutes to swim five laps, if Andre swims 22 laps, at the same rate as she swam 5 laps, how long does it take him?
Answers
Answer:
17.6
Step-by-step explanation:
But im not sure if u can use decimals
A company that manufactures electronic components wants to know the mean discharge time of one particular type of capacitor that it makes. In order to estimate this value, they randomly select 100 capacitors and measure how long they take to discharge. The mean of this sample was 7.25 seconds with a standard deviation of 0.15 seconds. Assuming that this distribution is normal, construct a 99% confidence interval to estimate the mean discharge time for all capacitors of this type. Is this question asking for a confidence interval or hypothesis test
Answers
Answer:
99% confidence interval to estimate the mean discharge time for all capacitors of this type
(7.2146, 7.2854)
Step-by-step explanation:
Step(i):-
Given that the sample size 'n' = 100
Given that the mean of sample x⁻ = 7.25 seconds
Given that the standard deviation of the sample (S) = 0.15 seconds
Level of significance = 0.01
Degrees of freedom = n-1 =100-1 =99
t₀.₀₁ , ₉₉ = 2.3646
We have to find that the 99% of the confidence interval of the mean
Step(ii):-
99% confidence interval to estimate the mean discharge time for all capacitors
[tex](x^{-} - t_{0.01 , 99} \frac{S}{\sqrt{n} } , x^{-} + t_{0.01 , 99} \frac{S}{\sqrt{n} } )[/tex]
[tex](7.25 - 2.3646 \frac{0.15}{\sqrt{100} } , 7.25 + 2.3646 \frac{0.15}{\sqrt{100} } )[/tex]
(7.25 - 0.0354 , 7.25 + 0.0354)
(7.2146, 7.2854)
Final answer:-
99% confidence interval to estimate the mean discharge time for all capacitors of this type
(7.2146, 7.2854)
The dot plots show the time it takes to get to school for ten sixth graders
Answers
Answer:
Im confused it is not the full information for the question
Step-by-step explanation:
Answer:
it the Ine that you add 3+ 7+2 so it make 9 but it is 10 be cus it 6th so that make 60 so it Canada
Step-by-step explanation:
Data set: 47, 45, 44, 41, 48
1. Find the mean.
Mean = 47 + 45 + 44 + 41 + 48
5
= 225
5
= 45
2. Find each absolute deviation.
Absolute deviations: 2, 0, 1, 4, 3
What is the mean absolute deviation (MAD) for the data set?
Answers
Answer:
2
Step-by-step explanation:
Answer:
The answer is 2, i did the instruction on edge already.
Step-by-step explanation: