Answer:
b = 50°
c = 130°
Step-by-step explanation:
Two angles A and B are complementary if:
A + B = 90°
And two angles are supplementary if:
A + B = 180°
Then, we know that:
a = 40°
b is a complement of a (this means that a and b are complementary angles)
c is a supplement of b (this means that b and c are supplementary angles).
From the first statement, we have that:
b + a = 90°
Replacing the value of a we get
b + 40° = 90°
b = 90° - 40° = 50°
b = 50°
And now we can use that b and c are supplementary, then:
b + c = 180°
replacing the value of b we get:
50° + c = 180°
c = 180° - 50° = 130°
c = 130°
Then the values we wanted are:
b = 50°
c = 130°
To find the equation of a line, we need the slope of the line and a point on the line. Since we are requested to find the equation of the tangent line at the point (36, 6), we know that (36, 6) is a point on the line. So we just need to find its slope. The slope of a tangent line to f(x) at x
Answer:
[tex]m = \frac{1}{12}[/tex]
Step-by-step explanation:
Given
[tex](x,y) = (36,6)[/tex]
[tex]f(x) = \sqrt x[/tex] ----- the equation of the curve
Required
The slope of f(x)
The slope (m) is calculated using:
[tex]m = \lim_{h \to 0} \frac{f(a + h) - f(a)}{h}[/tex]
[tex](x,y) = (36,6)[/tex] implies that:
[tex]a = 36; f(a) = 6[/tex]
So, we have:
[tex]m = \lim_{h \to 0} \frac{f(a + h) - f(a)}{h}[/tex]
[tex]m = \lim_{h \to 0} \frac{f(36 + h) - 6}{h}[/tex]
If [tex]f(x) = \sqrt x[/tex]; then:
[tex]f(36 + h) = \sqrt{36 + h}[/tex]
So, we have:
[tex]m = \lim_{h \to 0} \frac{\sqrt{36 + h} - 6}{h}[/tex]
Multiply by: [tex]\sqrt{36 + h} + 6[/tex]
[tex]m = \lim_{h \to 0} \frac{(\sqrt{36 + h} - 6)(\sqrt{36 + h} + 6)}{h(\sqrt{36 + h} + 6)}[/tex]
Expand the numerator
[tex]m = \lim_{h \to 0} \frac{36 + h - 36}{h(\sqrt{36 + h} + 6)}[/tex]
Collect like terms
[tex]m = \lim_{h \to 0} \frac{36 - 36+ h }{h(\sqrt{36 + h} + 6)}[/tex]
[tex]m = \lim_{h \to 0} \frac{h }{h(\sqrt{36 + h} + 6)}[/tex]
Cancel out h
[tex]m = \lim_{h \to 0} \frac{1}{\sqrt{36 + h} + 6}[/tex]
[tex]h \to 0[/tex] implies that we substitute 0 for h;
So, we have:
[tex]m = \frac{1}{\sqrt{36 + 0} + 6}[/tex]
[tex]m = \frac{1}{\sqrt{36} + 6}[/tex]
[tex]m = \frac{1}{6 + 6}[/tex]
[tex]m = \frac{1}{12}[/tex]
Hence, the slope is 1/12
16.7.1
One-fifth of the length of a foot-race is 7 miles. Find the length of the race.
Answer:
35 miles
Step-by-step explanation:
1/5 = 7
so each part is 7, which means that 5 parts would be 7*5.
7*5 = 35
cross check:
35/5 = 7
hope this helps :)
If f(x) is a linear function, what is the value of n?
х
_4
f(x)
---25
-10
-1
n
20
2
оооо
9
Step-by-step explanation:
You can simply plot these points on a graph and see where the line goes. It go
Myrtle Air Express decided to offer direct service from Cleveland to Myrtle Beach. Management must decide between a full-price service using the company’s new fleet of jet aircraft and a discount service using smaller capacity commuter planes. It is clear that the best choice depends on the market reaction to the service Myrtle Air offers. Management developed estimates of the contribution to profit for each type of service based upon two possible levels of demand for service to Myrtle Beach: strong and weak. The following table shows the estimated quarterly profits (in thousands of dollars):
Demand for Service
Service Strong Weak
Full price $960 -$490
Discount $670 $320
1. What is the decision to be made, what is the chance event, and what is the consequence for this problem?
2. How many decision alternatives are there?
Number of decision alternatives =
3. How many outcomes are there for the chance event?
Number of outcomes =
4. If nothing is known about the probabilities of the chance outcomes, what is the recommended decision using the optimistic, conservative, and minimax regret approaches?
a. Optimistic approach
b. Conservative approach
c. Minimax regret approach
here i attached the answer
The decision to be made is the type of service to be provided. The chance event is the level of demand for the air service.
What is Air Service?The services performed by an airline, as flights between various destinations to transport passengers, freight, and mail.
The decision to be made is the type of service to be provided. The chance event is the level of demand for the air service. The consequence can be considered as the amount of quarterly profit. Full price and discount price services are two decision alternatives. The number of outcomes for chance event is two, which are strong demand and weak demand.
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The radioactive isotope carbon-14 is present in small quantities in all life forms, and it is constantly replenished until the organism dies, after which it decays to stable carbon-12 at a rate proportional to the amount of carbon-14 present, with a half-life of 5549 years. Let C(t) be the amount of carbon-14 present at time t.
(a) Find the value of the constant k in the differential equation C' = -kC.
(b) In 1988 three teams of scientists found that the Shroud of Turin, which was reputed to be the burial cloth of Jesus, contained 91% of the amount of carbon-14 contained in freshly made cloth of the same material. How old was the Shroud of Turin at the time of this data?
Answer:
a) k = 0.00012491389
b) The Shroud of Turin was 755 years old at the time of this data.
Step-by-step explanation:
(a) Find the value of the constant k in the differential equation C' = -kC.
First we find the differential equation, by separation of variables. So
[tex]\int \frac{C^{\prime}}{C} dt = -\int k dt[/tex]
So
[tex]\ln{C} = -kt + K[/tex]
In which K is the constant of integration, representing the initial amount of substance. So
[tex]C(t) = C(0)e^{-kt}[/tex]
Half-life of 5549 years.
This means that [tex]C(5549) = 0.5C(0)[/tex]. We use this to find k. So
[tex]C(t) = C(0)e^{-kt}[/tex]
[tex]0.5C(0) = C(0)e^{-5549k}[/tex]
[tex]e^{-5549k} = 0.5[/tex]
[tex]\ln{e^{-5549k}} = \ln{0.5}[/tex]
[tex]-5549k = \ln{0.5}[/tex]
[tex]k = -\frac{\ln{0.5}}{5549}[/tex]
[tex]k = 0.00012491389[/tex]
So
[tex]C(t) = C(0)e^{-0.00012491389t}[/tex]
(b) In 1988 three teams of scientists found that the Shroud of Turin, which was reputed to be the burial cloth of Jesus, contained 91% of the amount of carbon-14 contained in freshly made cloth of the same material. How old was the Shroud of Turin at the time of this data?
This is t for which [tex]C(t) = 0.91C(0)[/tex]
So
[tex]C(t) = C(0)e^{-0.00012491389t}[/tex]
[tex]0.91C(0) = C(0)e^{-0.00012491389t}[/tex]
[tex]e^{-0.00012491389t} = 0.91[/tex]
[tex]\ln{e^{-0.00012491389t}} = \ln{0.91}[/tex]
[tex]-0.00012491389t = \ln{0.91}[/tex]
[tex]t = -\frac{\ln{0.91}}{0.00012491389}[/tex]
[tex]t = 755[/tex]
The Shroud of Turin was 755 years old at the time of this data.
2. Find the Perimeter AND Area of the
figure below.
5 in.
6 in.
8 in.
9 in.
53:28
Nathan and Jordan design surveys to determine the average amount of time bicyclists in a race spend training each
week. Nathan surveys every fifth bicyclist crossing the finish line after a race. Jordan surveys the first five bicyclists to
finish the race. Which best explains which sample is likely to be the most valid?
Nathan's because his sample was more random
Jordan's because his sample was more random
Nathan's because his sample contained elements of the population
Jordan's because his sample contained elements of the population
Answer:
Nathan's because his sample was more random
Step-by-step explanation:
Nathan's survey could be described as a Systematic random sampling technique whereby every 5th observation taken as a sample from the population. With these technique we have a more random observation than with.
Answer:
C
Step-by-step explanation:
Tim did a survey at a large shopping centre. He asked 400 visitors to the centre to choose the main reason for their visit. The reasons were shops, free parking, food court and location.
From the people taking part in the survey, one person is chosen at random to get a prize. Find the probability a female who chose location gets the prize.
shops free park. food location total
male 88 24 40 21 173
female 110 38 56 23 227
total 198 62 96 44 400
Answer:
23 / 400 = 0.0575
Step-by-step explanation:
Given the distribution :
_____shops__ free park. food _: location total
male 88 24 40 21 173
female 110 38 56 23 227
total 198 62 96 44 400
From the table of the distribution Given, we obtain :
n(Female n location) = 23
n(Total) = 400
Hence, the probability that a female who chose location gets the prize will be ;
n(Female n location) / n(Total) = 23 / 400 = 0.0575
PLEASE I NEED HELP!!!!!
Find the volume of this sphere.
Use 3 for TT.
L-r=3ft
V [?]ft3
V = Tr3
Answer:
113.1 =VOLUME , 4/3 X 3.14 (3) ^3 = 113.1
During a recent election, 54 of every 100 registered voters in a certain city voted. If there were 157,400 registered voters in that city, how many people voted?
expand and simplify (x-2)(x+5)(2x-1)
Answer:
simplified: 2x^3+5x^2-23x+10
Step-by-step explanation:
find a number such that when it is multiplied by 7 and 17 is subtracted from the product the result is the same as when it is multiplied by 3 and 19 added to the product .
Answer:
9
Step-by-step explanation:
Let the number be X
From the problem we have the following equation:
7x - 17 = 3x + 19
-> 4x = 36
-> x = 9
Answer:
9
Step-by-step explanation:
that is the procedure above
The office needs 6 new devices worth $7200. The order consists of new computers (C) which cost $1425 each and printers (P) which cost $750 each. How many of the new devices are computers and how many are printers?
A manufacturer of nails claims that only 4% of its nails are defective. A random sample of 20 nails is selected, and it is found that two of them, 10%, are defective. Is it fair to reject the manufacturer's claim based on this observation?
Answer:
The p-value of the test is 0.0853 > 0.05, which means that there is not enough evidence to reject the manufacturer's claim based on this observation.
Step-by-step explanation:
A manufacturer of nails claims that only 4% of its nails are defective.
At the null hypothesis, we test if the proportion is of 4%, that is:
[tex]H_0: p = 0.04[/tex]
At the alternative hypothesis, we test if the proportion is more than 4%, that is:
[tex]H_a: p > 0.04[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
4% is tested at the null hypothesis
This means that [tex]\mu = 0.04, \sigma = \sqrt{0.04*0.96}[/tex]
A random sample of 20 nails is selected, and it is found that two of them, 10%, are defective.
This means that [tex]n = 20, X = 0.1[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.1 - 0.04}{\frac{\sqrt{0.04*0.96}}{\sqrt{20}}}[/tex]
[tex]z = 1.37[/tex]
P-value of the test and decision:
Considering an standard significance level of 0.05.
The p-value of the test is the probability of finding a sample proportion above 0.1, which is 1 subtracted by the p-value of z = 1.37.
Looking at the z-table, z = 1.37 has a p-value of 0.9147
1 - 0.9147 = 0.0853
The p-value of the test is 0.0853 > 0.05, which means that there is not enough evidence to reject the manufacturer's claim based on this observation.
Answer:
Considering an standard significance level of 0.05.
The p-value of the test is the probability of finding a sample proportion above 0.1, which is 1 subtracted by the p-value of z = 1.37.
Looking at the z-table, z = 1.37 has a p-value of 0.9147
1 - 0.9147 = 0.0853
The p-value of the test is 0.0853 > 0.05, which means that there is not enough evidence to reject the manufacturer's claim based on this observation.
Step-by-step explanation:
Write two pairs of integers (a, b) such that a / b = -4.
One such pair is (8, -2) because 8/ -2 = (-4).
Answer: a= 16 a=8
b=4 b=2
because, 2 when multiplied by 4 gives 8
4 when multiplied gives 16
The perimeter of an equilateral triangle is 126mm.
State the length of one of its sides.
Explanation:
Divide 126 over 3. This is because any equilateral triangle has all three sides the same length
126/3 = 42
Each side is 42 mm long
So its perimeter is 3*42 = 126 mm
Side note: if your teacher says a triangle is equiangular, then it's automatically equilateral as well (and vice versa).
The length of one of its sides of an equilateral triangle is 42 mm.
What is equilateral triangle?In geometry, an equilateral triangle exists as a triangle that contains all its sides equivalent in length. Since the three sides stand equivalent therefore the three angles, opposite to the equivalent sides, stand equivalent in measure. Thus, it stands also named an equiangular triangle, where each angle measure 60 degrees.
The perimeter of an equilateral triangle exists 126 mm.
The equilateral triangle contains all three sides of the same length
126/3 = 42
Each side stands 42 mm long
So its perimeter stands 3 [tex]*[/tex] 42 = 126 mm
Therefore, the length of one of its sides = 42 mm.
To learn more about equilateral triangle
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On a map of a town, 3 cm represents 150 m. Two points in the town are 1 km apart. How far apart are the two points on the map?
Answer:
5000 km
Step-by-step explanation:
We are given that
3 cm represents on a map of a town=150 m
Distance between two points=1 km
We have to find the distance between two points on the map.
3 cm represents on a map of a town=150 m
1 cm represents on a map of a town=150/3 m
1 km=1000 m
1 m=100 cm
[tex]1km=1000\times 100=100000 cm[/tex]
100000 cm represents on a map of a town
=[tex]\frac{150}{3}\times 100000[/tex] m
100000 cm represents on a map of a town=5000000 m
100000 cm represents on a map of a town
=[tex]\frac{5000000}{1000} km[/tex]
100000 cm represents on a map of a town=5000 km
Hence, two points are separated by 5000 km on the map.
Yalll ya gurl is struggling I need help SOS
Answer:
22 mi
Step-by-step explanation:
From the question given above, the distance from E to F is 6 in.
Thus, we can obtain the distance from E to F (i.e mi) by using the scale provided in the question. This is illustrated below:
3 in = 11 mi
Therefore,
6 in = 6 in × 11 mi / 3 in
6 in = 22 mi
Therefore, the distance from E to F is 22 mi
20. In the image, ABC has measure 58°. What is the measure of ABD?
A. 116°
OB. 29°
O C. 58
OD. There is not enough information to determine LABD.
Answer:
Option B, 29°
Step-by-step explanation:
The diagram is a angle bisecting diagram which divides the 58° angle into two 29° angles.
Answered by GAUTHMATH
Help please!!!!!!!!!!!
Answer:
y = 14
Step-by-step explanation:
[tex] \frac{15}{21} = \frac{5}{7} [/tex]
[tex] \frac{10}{x} = \frac{5}{7} [/tex]
[tex]x = 14[/tex]
Now,
10/15 = y/21
15y = 10*21
y = 210/15
y = 14
This is a Right answer...
I hope you understand..
Mark me as brainliest...
tan sin^-1(-1/2)+tan^-1(3/4)
exact value!
Answer:
m
Step-by-step explanation:
vfmjj vdzaazb knkuvggb
What is the volume of the composite figure if both the height and the diameter of the cylinder are 3.5 feet? Give the exact answer and approximate to two decimal places.
Answer:
Volume of composite figure = 44.9 feet³
Step-by-step explanation:
Given:
Height of cylinder = 3.5 feet
Diameter of cylinder = 3.5 feet
Diameter of hemisphere = 3.5 feet
Find:
Volume of composite figure
Computation:
Radius of cylinder and sphere = 3.5/2 = 1.75 feet
Volume of composite figure = Volume of cylinder + Volume of hemisphere
Volume of composite figure = πr²h + (2/3)πr³
Volume of composite figure = (3.14)(1.75)²(3.5) + (2/3)(3.14)(1.75)³
Volume of composite figure = (3.14)(3.0625)(3.5) + (2/3)(3.14)(5.359375)
Volume of composite figure = 33.656875 + 11.2189583
Volume of composite figure = 44.8758
Volume of composite figure = 44.9 feet³
HELP
-5(2m-3)-4<81
I need the steps also well
Answer:
m>-7
Step-by-step explanation:
expand
-10m+15-4<81
-10m+11<81
collect like terms
-10m<81-11
-10m<70
m>-7
An experiment consists of tossing a coin and rolling a six-sided die simultaneously. Step 1 of 2 : What is the probability of getting a head on the coin and the number 2 on the die
Answer:
[tex]\frac{1}{12}[/tex] probability of getting a head on the coin and the number 2 on the die
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
Independent events:
If two events, A and B are independent, the probability of both events happening is the multiplication of the probabilities of each event happening, that is:
[tex]P(A \cap B) = P(A)P(B)[/tex]
Probability of getting a head on the coin:
Head or tails, fair coin, so:
[tex]P(A) = \frac{1}{2}[/tex]
Probability of getting the number 2 on the die:
6 numbers, one of which is 2, so:
[tex]P(B) = \frac{1}{6}[/tex]
What is the probability of getting a head on the coin and the number 2 on the die?
[tex]P(A \cap B) = P(A)P(B) = \frac{1}{2} \times \frac{1}{6} = \frac{1}{12}[/tex]
[tex]\frac{1}{12}[/tex] probability of getting a head on the coin and the number 2 on the die
Which of the following indicates that Triangle ABC and Triangle DEF are similar?
Answer:
D
Step-by-step explanation:
The symbol ~ means similarity (same shapes, not same size)
Determine if each proportion on the left is true or false
9514 1404 393
Answer:
FalseTrueTrueTrueStep-by-step explanation:
An easy way to tell if the equation is true is to multiply it by the product of the denominators (cross multiply).
7×7 ≠ 12×4 . . . . proportion is False
9×8 = 36×2 . . . . proportion is True
8×9 = 24×3 . . . . proportion is True
5×104 = 8×65 . . . . proportion is True
PLEASE BE RIGHT AND SOLVE
Answer:
Option B: Rotation
Step-by-step explanation:
The shape appears to have the same size, but it has been moved in a way that is not reflection. Through the process of elimination, the answer is rotation.
solve for x. 4^(×-1)=1
Answer:
[tex]4^{\left(x-1\right)}=1[/tex]
[tex]\Rightarrow\left(x-1\right)\ln \left(4\right)=\ln \left(1\right)[/tex]
[tex]\hookrightarrow x=1[/tex]
❅❅❅❅❅❅❅❅❅❅
OAmalOHopeO
❅❅❅❅❅❅❅❅❅❅
What is the midpoint of the segment shown below?
10
A. (5,-4)
(16,5)
B. (10,-4)
C. (10,-2)
10
15
(-6.-9)
D. (5,-2)
Answer:
D
Step-by-step explanation:
Use the midpoint formula to find the midpoint of the line segment.
data in the bar graph to solve the following problems. Choose the letter of the correl answer.
Distance from Churh (meters)
250
210
190
200
175
150
150
100
50
C. 25m
1. How much farther does Paolo walk thạnIgpher? Joshua
Topher
A. 20m
B. 15 m
C. 10m
D. 5m
2. How much farther does Joshua walk than Lucas?
A. 15m
B. 20m
D. 30m
3. How much farther does Topher than Lucas?
A. 50m
B. 40m
C. 30m
D. 20m
4. If you combine Paolo's and Lucas' distance from the church and compare it against the combined
distance walked by Joshua and Topher, which combined distance is farther
from the church?
A. Joshua and Topher
C. Joshua and Paolo
B. Paolo and Lucas
D. Topher and Lucas
5. Find the average distance of the houses of the 4 friends from the church?
A. 181
B. 191
C. 180
Answer:
The answer is below
Step-by-step explanation:
The bar chart to the question is attached below.
The distance traveled by Paolo = 210 m, The distance traveled by Lucas = 150 m, The distance traveled by Jashua = 175 m, The distance traveled by Topher = 190 m
1) The farther distance walk by Paolo = The distance traveled by Paolo - The distance traveled by Topher = 210 m - 190 m = 20 m
2) The farther distance walk by Jasha = The distance traveled by Jashua - The distance traveled by Lucas = 175 m - 150 m = 25 m
3) The farther distance walk by Topher = The distance traveled by Topher - The distance traveled by Lucas = 190 m - 150 m = 40 m
4) Combined distance of Paolo's and Lucas = 210 m + 150 m = 360 m
Combined distance of Jashua and Topher = 175 m + 190 m = 365 m
Therefore the Combined distance of Jashua and Topher is more
5) Average distance = (210 + 150 + 175 + 190)/4 = 181.25 m
