Step-by-step explanation:
Let's say the position of the fire is point C.
Bearings are measured from the north-south line. So ∠BAC = 55°, and ∠ABC = 60°.
Since angles of a triangle add up to 180°, ∠ACB = 65°.
Using law of sine:
190 / sin 65° = a / sin 60° = b / sin 55°
Solving:
a = 181.6
b = 171.7
Station A is 181.6 miles from the fire and station B is 171.7 miles from the fire.
It took 2 men 5 hours to build an airstrip. Working at the same rate, how many additional men could have been hired in order for the job to have taken 1/hour less? (A) Two (B) Three (C) Four (D) Six
The problem is to calculate the number of additional men needed to build an airstrip in less time given two men already took five hours. The additional man required is one after solving the equation, but this is not an option provided, indicating a potential error in the question.
Explanation:The question involves calculating the number of additional men required to build an airstrip in less time. If it took 2 men 5 hours to build an airstrip, we can say they have a combined work rate of 1 airstrip per 5 hours, or (1/5) airstrip per hour. To finish the job in 4 hours, which is 1 hour less than the original time, we would need a work rate of 1 airstrip per 4 hours.
So, if we let the number of additional men be X, we can set up the equation as follows:
(2 + X) men × 4 hours = 2 men × 5 hours(2 + X) × 4 = 102 + X = 10 / 4X = 2.5 - 2X = 0.5Since we cannot hire half a person, we round up to the nearest whole number. Hence, one additional man would be sufficient to complete the work in 1 hour less time. However, none of the options given (A) Two, (B) Three, (C) Four, or (D) Six, are correct. Therefore, the answer is not provided in the given options and this represents a possible error in the question itself.
Stephanie cuts a five-meter-long piece of rope into five equal parts. What is the length of each piece of rope?
Final answer:
Stephanie cuts the rope into five 1-meter-long pieces by dividing the total length (5 meters) by the number of pieces (5).
Explanation:
If Stephanie cuts a five-meter-long piece of rope into five equal parts, we would divide the total length of the rope by the number of parts to find the length of each piece. In this case, the calculation would be:
Total length of rope = 5 metersNumber of parts = 5Length of each part = Total length of rope ÷ Number of partsSo, the length of each part would be 5 meters ÷ 5, which equals 1 meter. Therefore, each piece of rope would be 1 meter long.
Can I get these solved so I will have the points to mark them on a graph?
Y = -2X + 2
X + 3Y = -4
Answer:
points on the first line: (0, 2), (1, 0)points on the second line: (-4, 0), (-7, 1)Step-by-step explanation:
For equations like these, where the coefficient of one of the variables is 1, it is convenient to choose values for the other variable. Values of 0 and 1 are usually easy to work with.
In the first equation, ...
for x=0, y = 2 . . . . . . . . . point (0, 2)
for x=1, y = -2+2 = 0 . . . point (1, 0)
In the second equation, ...
for y=0, x = -4 . . . . . . . . . point (-4, 0)
for y=1, x +3 = -4, so x = -7 . . . . point (-7, 1)
According to the research, 43% of homes sold in a certain month and year were purchased by first-time buyers. A random sample of 165 people who just purchased homes is selected. Complete parts a through e below. what is the probabilty that less than 75 of them are first time buyers
Answer Do it
Step-by-step explanation 165 divided by 100 =x times 43
How many collections of six positive, odd integers have a sum of 18? Note that 1 + 1 + 1 + 3 + 3 + 9 and 9 + 1 + 3 + 1 + 3 + 1 are considered to be the same collection.
Answer:
11
Step-by-step explanation:
Suitable software can generate these collections. They are ...
{13,1,1,1,1,1}, {11,3,1,1,1,1}, {9,5,1,1,1,1}, {9,3,3,1,1,1},
{7,7,1,1,1,1}, {7,5,3,1,1,1}, {7,3,3,3,1,1}, {5,5,5,1,1,1},
{5,5,3,3,1,1}, {5,3,3,3,3,1}, {3,3,3,3,3,3}}
The number of distinct collections of six positive odd integers that sum to 18 is indeed:[tex]\[\boxed{11}\][/tex]
[tex]\[2(k_1 + k_2 + k_3 + k_4 + k_5 + k_6) + 6 = 18\]\[k_1 + k_2 + k_3 + k_4 + k_5 + k_6 = 6\][/tex]
Here are the possible combinations of non-negative integers (up to permutations) that sum to 6:
[tex]1. \( (6, 0, 0, 0, 0, 0) \)2. \( (5, 1, 0, 0, 0, 0) \)3. \( (4, 2, 0, 0, 0, 0) \)4. \( (4, 1, 1, 0, 0, 0) \)5. \( (3, 3, 0, 0, 0, 0) \)6. \( (3, 2, 1, 0, 0, 0) \)7. \( (3, 1, 1, 1, 0, 0) \)8. \( (2, 2, 2, 0, 0, 0) \)9. \( (2, 2, 1, 1, 0, 0) \)10. \( (2, 1, 1, 1, 1, 0) \)11. \( (1, 1, 1, 1, 1, 1) \)[/tex]
Now let's map these back to the odd integers using [tex]\(a_i = 2k_i + 1\):[/tex]
[tex]1. \( (13, 1, 1, 1, 1, 1) \)2. \( (11, 3, 1, 1, 1, 1) \)3. \( (9, 5, 1, 1, 1, 1) \)4. \( (9, 3, 3, 1, 1, 1) \)5. \( (7, 7, 1, 1, 1, 1) \)6. \( (7, 5, 3, 1, 1, 1) \)7. \( (7, 3, 3, 3, 1, 1) \)8. \( (5, 5, 5, 1, 1, 1) \)9. \( (5, 5, 3, 3, 1, 1) \)10. \( (5, 3, 3, 3, 3, 1) \)11. \( (3, 3, 3, 3, 3, 3) \)[/tex]
These are all distinct collections (up to permutations) of positive odd integers that sum to 18.
Thus, the number of distinct collections of six positive odd integers that sum to 18 is indeed:[tex]\[\boxed{11}\][/tex]
Consider the following equation. f(x, y) = sin(2x + 5y), P(−5, 2), u = 1 2 3 i − j (a) Find the gradient of f. ∇f(x, y) = (b) Evaluate the gradient at the point P. ∇f(−5, 2) = (c) Find the rate of change of f at P in the direction of the vector u. Duf(−5, 2) =
The gradient of function f is (∂f/∂x, ∂f/∂y) = (2cos(2x + 5y), 5cos(2x + 5y)). The gradient at the point P(-5, 2), is ∇f(-5, 2) = (2cos(-20), 5cos(-20)). Rate of change of f at P in the direction of the vector u is (-1/2, 3). Duf(-5, 2) = ∇f(-5, 2) · (-1/2, 3).
(a) To find the gradient of the function f(x, y) = sin(2x + 5y), we need to compute the partial derivatives with respect to x and y:
Gradient of f(x, y) = (∂f/∂x, ∂f/∂y).
Taking the partial derivative with respect to x:
∂f/∂x = ∂/∂x(sin(2x + 5y)) = 2cos(2x + 5y).
Taking the partial derivative with respect to y:
∂f/∂y = ∂/∂y(sin(2x + 5y)) = 5cos(2x + 5y).
So, the gradient of f is (∂f/∂x, ∂f/∂y) = (2cos(2x + 5y), 5cos(2x + 5y)).
(b) To evaluate the gradient at point P(-5, 2), we substitute these values into the gradient expression:
∇f(-5, 2) = (2cos(2(-5) + 5(2)), 5cos(2(-5) + 5(2))).
Calculating these values gives the gradient at P.
The gradient at point P is ∇f(-5, 2) = (2cos(-20), 5cos(-20)).
(c) To find the rate of change of f at point P(-5, 2) in the direction of the vector u = (1/2, 3) - (1, 0) = (-1/2, 3), we use the dot product:
Duf(-5, 2) = ∇f(-5, 2) · (-1/2, 3).
Calculate this dot product to find the rate of change of f in the direction of u at point P.
Learn more about Gradients of function here:
https://brainly.com/question/34538521
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#5 Points possible: 3. Total attempts: 5
Using your calculator, find the range and standard deviation, round to two decimals places:
The table below gives the number of hours spent watching TV last week by a sample of 24 children.
76
57
89
73
88
42
31
46
80
42
38
57
49
50
89
36
69
82
27
88
39
89
95
18
Range =
Standard Deviation =
Answer:
honesty you cant realy use a calculator because you need to meadian mode and range them first
Step-by-step explanation:
Find the following standard normal probability: p(-1.23 szs +1.23) OA..7814 B. .8907 O C..1093 D. .2186
In the formula used to convert "real-world" data values into z numbers, the standard deviation of the data is never considered. O True O False
Answer: a) 0.7814
b) False
Step-by-step explanation:
To find : The p-value of z , where
[tex]-1.23<z< +1.23[/tex]
[tex]P(-1.23<z< +1.23)=1-P(z<-1.23)\\\\=1-0.1093=0.7814[/tex]
Hence, the standard normal probability [tex]P(-1.23<z< +1.23)=0.7814[/tex]
In the formula used to convert "real-world" data values into z numbers, the standard deviation of the data is considered.
The formula to calculate the z score is [tex]z=\dfrac{x-\mu}{\sigma}[/tex].
If sample size (n) is given then , the [tex]z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
Hence, the statement is false.
If a dart was thrown randomly at the dart board shown below, what is the probability that it would land between the outer circle and the middle circle? The radius of the bulls eye is 2 cm, the radius of the middle circle is 8 cm, and the radius of the outer circle is 14 cm
A.68%
B.67%
C.14%
D.75%
Answer: B) 67%
Step-by-step explanation:
Find the Area of the Bullseye and Middle ring
A = π r²
A (inside) = π(8)² = 64π
Find the Area of the entire Target
A (target) = π (14)² = 196π
Find the Area of the Outer ring
A (outer ring) = A (target) - A(inside)
= 196 π - 64π
= 132 π
The last step is to find the probability of landing on the outer ring:
[tex]P=\dfrac{success (area\ of\ outer\ ring)}{total\ possible\ outcomes(area\ of\ target)}=\dfrac{132\pi}{196\pi}=0.673=\large\boxed{67\%}[/tex]
Answer:
67%
Step-by-step explanation:
Suppose a variable has a normal distribution with mean 67 and standard deviation 4. What percentage of the distribution is less than 75? (Use z-score.)
Answer:
The percentage of the distribution is less than 75 is 97.72%.
Step-by-step explanation:
Given,
Mean of the distribution,
[tex]\mu=67[/tex]
Standard deviation,
[tex]\sigma = 4[/tex]
Thus, the z-score of the score 75,
[tex]z=\frac{x-\mu}{\sigma}[/tex]
[tex]=\frac{75-67}{4}[/tex]
[tex]=\frac{8}{4}[/tex]
[tex]=2[/tex]
With the help of z-score table,
[tex]P(x<75)=0.9772=97.72\%[/tex]
Hence, the percentage of the distribution is less than 75 is 97.72%.
Suppose the lengths of the pregnancies of a certain animal are approximately normally distributed with mean mu equals 192 daysμ=192 days and standard deviation sigma equals 12 daysσ=12 days.What is the probability that a randomly selected pregnancy lasts less than 188188 days? The probability that a randomly selected pregnancy lasts less than 188188 days is approximately
Answer: 0.5237
Step-by-step explanation:
Mean : [tex]\mu=192\text{ days}[/tex]
Standard deviation : [tex]\sigma = 12\text{ days}[/tex]
The formula to calculate the z-score is given by :-
[tex]z=\dfrac{x-\mu}{\sigma}[/tex]
For x = 188 days ,
[tex]z=\dfrac{188-192}{12}\approx-0.33[/tex]
For x = 107 miles per day ,
[tex]z=\dfrac{107-92}{12}=1.25[/tex]
The P-value =[tex]P(-0.33<z<1.25)=P(z<1.25)-P(z<-0.33)[/tex]
[tex]0.8943502-0.3707=0.5236502\approx0.5237[/tex]
Hence, The probability that a randomly selected pregnancy lasts less than 188 days is approximately 0.5237.
What is the domain of the function y = ^3 sqrt x ??
Answer:
-∞ < x < ∞
Explanation:
x³ is the inverse of ∛x and x³ has range of all real numbers and is one to one function, so its inverse will have domain of all real numbers.
Answer:
Option 1 negative (-) infinity < X < infinity
Step-by-step explanation:
what is 6% sales tax on $4929.00
Answer: $5,224.74
Step-by-step explanation:
You need to calculate the 6% of $4,929.00.
Convert the percentage to decimal form:
[tex]\frac{6}{100}=0.06[/tex]
Now multiply $4,929.00 by 0.06:
[tex](\$4,929.00)(0.06)=\$295.74[/tex] (This is the 6% of $4,929.00)
Finally, you need to add $295.74 to $4,929.00. Then you get:
[tex]\$4,929.00+\$295.74=\$5,224.74[/tex]
Therefore, the 6% sales tax on $4,929.00 is: $5,224.74
Papa John wants to know if he should rename an old favorite pizza for his restaurant. He gives 60 patrons a pepperoni pizza and asks them to rate both the names ‘pepperoni deluxe’ and ‘venti extra cheesy pepperoni on toasted pan bread with tomato zest pesto’. He takes the ratings and wants to perform a statistical test. What would be the best statistical test to be used?
Answer:
gragh
Step-by-step explanation:
its one of the few ways to analyze data and compare it to find the best choice
Prove that for all integers n, if n^(2)-6n is odd then n is odd.
Step-by-step explanation:
o - odd number
e - even number
n × e = e, n is either odd or even...rule 1
n - e = o, n must be odd...rule 2
n - e = e, n must be even...rule 3
n^2 = o, n must be odd...rule 4
n^2 = e, n must be even...rule 5
6n is even, no matter if n is odd or even following rule 1
if n^2 - 6n = o, n must be odd following rule 2
if n^2 = o, n must be odd following rule 4
Line m is parallel to line n. The measure of angle 3 is 86. What is the
measure of angle 5?
OA) 86
OB) 104°
OC) 94°
OD) 75
(Kinda hard to read sorry)
Answer:
C.94
Step-by-step explanation:
The alternate interior angle of angle c is angle 6. So from there you just subtract the 84 from the 180 to get the 94 degrees.
In a clinical trial of a cholesterol drug, 374 subjects were given a placebo, and 21% of them developed headaches. For such randomly selected groups of 374 subjects given a placebo, identify the values of n, p, and q that would be used for finding the mean and standard deviation for the number of subjects who develop headaches. The value of n is __________. (Do not round.) The value of p is __________. (Type an integer or a decimal. Do not round.) The value of q is __________. (Type an integer or a decimal. Do not round.)
Answer: The value of n is 374. The value of p is 0.21. The value of q is 0.79.
Step-by-step explanation:
Given : In a clinical trial of a cholesterol drug, 374 subjects were given a placebo, and 21% of them developed headaches.
∴ Sample size : [tex]n=374[/tex]
The probability that cholesterol drug developed headaches :[tex]p=0.21[/tex]
Then , the probability that cholesterol drug did not develop headaches :[tex]q=1-p=1-0.21=0.79[/tex]
Hence, The value of n is 374.
The value of p is 0.21.
The value of q is 0.79.
Part A: Solve −np − 80 < 60 for n. Show your work. (4 points)
Part B: Solve 2a − 5d = 30 for d. Show your work. (6 points)
Answer:
Part A ⇒ n>-140/p and p≠0
Part B. ⇒ d=-30-2a/5
Step-by-step explanation:
Part A. -np-80<60
First, add by 80 both sides of equation.
-np-80+80<60+80
Simplify.
60+80=140
-np<140
Then, multiply by -1 both sides of equation.
(-np)(-1)>140(-1)
Simplify.
np>-140
Divide by p both sides of equation.
np/p>-140/p; p≠0
Simplify to find the answer.
n>-140/p; p≠0 is the correct answer from part a.
___________________________________
Part B. 2a-5d=30
First add by 2a from both sides of equation.
2a-5d+2a=30+2a
Then, simplify.
-5d=30-2a
Divide by -5 from both sides of equation.
-5d/-5=30/-5-2a/5
Simplify, to find the answer.
d=-30-2a/5 is the correct answer from part b.
Part A:
For this case we have the following inequality:
[tex]-np-80 <60[/tex]
We add 80 to both sides of the inequality:
[tex]-np <60+80\\-np <140[/tex]
Dividing between -p on both sides, having to change the inequality sign:
[tex]n> - \frac {140} {p}[/tex]
Part B:
For this case we have the following equation:
[tex]2a-5d = 30[/tex]
Subtracting 2a on both sides:
[tex]-5d = 30-2a[/tex]
Dividing between -5 on both sides:
[tex]d = \frac {30-2a} {- 5}\\d = \frac {-30+2a} {5}\\d = - \frac {30} {5} +\frac {2a} {5}\\d = -6+ \frac {2a} {5}[/tex]
Answer:
[tex]n> - \frac {140} {p}\\d = -6+\frac {2a} {5}[/tex]
How do you simplify this sum?
Answer:
Step-by-step explanation:
You can't simplify the sum, but you can factor it.
t^2 + 2t - 3
(t + 3)(t - 1 )
That's about all you can do.
Answer:
It is already in simplest form.
Step-by-step explanation:
It cannot be further simplified because it does not have any like terms.
The Cooper family, consisting of 6 children and 2 adults, goes to the movies and pays a total of $86. The Griffen birthday party, consisting of 10 children and 3 adults, pays a total of $139 for tickets. Let x = the cost of a child ticket and y = the cost of an adult ticket. How much does a child's ticket cost and how much does an adult ticket cost?
Answer: The cost of child's ticket = $10
The cost of adult ticket = $ 13
Step-by-step explanation:
Let x be the cost of a child ticket and y be the cost of an adult ticket.
Then According to the question, we have
[tex]6x+2y=86..........................(1)\\\\10x+3y=139.......................(2)[/tex]
Multiply equation (1) by 3 and equation (2) by 2, then we have
[tex]18x+6y=258.......................(1)\\\\20x+6y=278...........................(2)[/tex]
Subtract equation (1) from equation (2), we have
[tex]2x=20\\\\\Rightarrow\ x=10[/tex]
Substitute the value of x in equation (1), we get
[tex]60+2y=86\\\\\Rightarrow\ 2y=26\\\\\Rightarrow\ y=13[/tex]
Hence, the cost of child's ticket = $10
The cost of adult ticket = $ 13
Use induction to prove: For every integer n > 1, the number n5 - n is a multiple of 5.
Answer:
we need to prove : for every integer n>1, the number [tex]n^{5}-n[/tex] is a multiple of 5.
1) check divisibility for n=1, [tex]f(1)=(1)^{5}-1=0[/tex] (divisible)
2) Assume that [tex]f(k)[/tex] is divisible by 5, [tex]f(k)=(k)^{5}-k[/tex]
3) Induction,
[tex]f(k+1)=(k+1)^{5}-(k+1)[/tex]
[tex]=(k^{5}+5k^{4}+10k^{3}+10k^{2}+5k+1)-k-1[/tex]
[tex]=k^{5}+5k^{4}+10k^{3}+10k^{2}+4k[/tex]
Now, [tex]f(k+1)-f(k)[/tex]
[tex]f(k+1)-f(k)=k^{5}+5k^{4}+10k^{3}+10k^{2}+4k-(k^{5}-k)[/tex]
[tex]f(k+1)-f(k)=k^{5}+5k^{4}+10k^{3}+10k^{2}+4k-k^{5}+k[/tex]
[tex]f(k+1)-f(k)=5k^{4}+10k^{3}+10k^{2}+5k[/tex]
Take out the common factor,
[tex]f(k+1)-f(k)=5(k^{4}+2k^{3}+2k^{2}+k)[/tex] (divisible by 5)
add both the sides by f(k)
[tex]f(k+1)=f(k)+5(k^{4}+2k^{3}+2k^{2}+k)[/tex]
We have proved that difference between [tex]f(k+1)[/tex] and [tex]f(k)[/tex] is divisible by 5.
so, our assumption in step 2 is correct.
Since [tex]f(k)[/tex] is divisible by 5, then [tex]f(k+1)[/tex] must be divisible by 5 since we are taking the sum of 2 terms that are divisible by 5.
Therefore, for every integer n>1, the number [tex]n^{5}-n[/tex] is a multiple of 5.
Final answer:
The statement is true for all integers greater than 1.
Explanation:
The n5 - n is a multiple of 5 for every integer n > 1, we will use proof by induction.
Base Case: For n = 2,
n5 - n = 25 - 2 = 32 - 2 = 30,
which is clearly a multiple of 5. Hence, our base case holds true.
Inductive Step: Assume that for some integer k > 1, the statement holds true, i.e.,
k5 - k is a multiple of 5. We need to show that k5 - k + 5(k4 + k3 + k2 + k + 1) is also a multiple of 5.
If k5 - k is a multiple of 5, then adding a number which is a multiple of 5 (5 times a sum of powers of k) to it will also result in a multiple of 5. This means that (k + 1)5 - (k + 1) will be a multiple of 5, hence the statement holds for k + 1. By the principle of mathematical induction, the statement holds true for all integers n > 1.
A box contains 1 plain pencil and 4 pens. A second box contains 5 color pencils and 5 crayons. One item from each box is chosen at random. What is the probability that a plain pencil from the first box and a color pencil from the second box are selected?
Write your answer as a fraction in simplest form.
1 pencil and 4 pens = 5 total
Picking the pencil would be 1/5 ( 1 pencil out of 5 total items)
5 color pencils + 5 crayons = 10 total items.
Picking a color pencil would be 5/10 which reduces to 1/2
To find the probability of both happening, multiply them together:
1/5 x 1/2 = 1/10
The probability is 1/10
force of 400 N stretches a spring 2 m. A mass of 50 kg is attached to the end of the spring and is initially released from the equilibrium position with an upward velocity of 10 m/s. Find the equation of motion?
Answer:
x = -5 sin (2t)
Step-by-step explanation:
k is the spring stiffness. The unstretched length of the spring is L.
When the mass is added, the spring stretches to an equilibrium position of L+s, where mg = ks. When the mass is displaced a distance x (where x is positive if the displacement is down and negative if it's up), the spring is stretched a total distance s + x.
There are two forces on the mass: weight and force from the spring. Sum of the forces in the downward direction:
∑F = ma
mg − k(s + x) = ma
mg − ks − kx = ma
Since mg = ks:
-kx = ma
Acceleration is second derivative of position, so:
-kx = m d²x/dt²
Let's find k:
F = kx
400 = 2k
k = 200
We know that m = 50. Substituting:
-200x = 50 d²x/dt²
-4x = d²x/dt²
d²x/dt² + 4x = 0
This is a linear second order differential equation of the form:
x" + ω² x = 0
The solution to this is:
x = A cos (ωt) + B sin (ωt)
Here, ω² = 4, so ω = 2.
x = A cos (2t) + B sin (2t)
We're given initial conditions that x(0) = 0 and x'(0) = -10 (remember that down is positive and up is negative).
Finding x'(t):
x' = -2A sin (2t) + 2B cos (2t)
Plugging in the initial conditions:
0 = A
-10 = 2B
Therefore:
x = -5 sin (2t)
(CO 3) A survey indicates that shoppers spend an average of 22 minutes with a standard deviation of 8 minutes in your store and that these times are normally distributed. Find the probability that a randomly selected shopper will spend less than 20 minutes in the store. 0.40 0.50 0.60 0.22
Final answer:
To calculate the probability of a shopper spending less than 20 minutes in the store, the Z-score is found using the formula Z = (X - μ) / σ, resulting in a Z-score of -0.25, which corresponds to a probability of approximately 0.40.
Explanation:
The question asks for the probability that a randomly selected shopper will spend less than 20 minutes in a store, given that the average time spent is 22 minutes with a standard deviation of 8 minutes, and that these times are normally distributed. To find this probability, we use the Z-score formula:
Z = (X - μ) / σ
Where X is the value we are checking (20 minutes), μ is the mean (22 minutes), and σ is the standard deviation (8 minutes). Plugging in the numbers, we get:
Z = (20 - 22) / 8 = -0.25
Next, we look up the Z-score in a standard normal distribution table, or use a calculator with normal distribution functions, to find the probability that a Z-score is less than -0.25. This probability is approximately 0.40.
evaluate the logarithmic expression.
Answer:
Step-by-step explanation:
I'm making the assumption you are looking for a graph of y=log_3(x)
So 3^0=1 which means log_3(1)=0 graph (1,0)
3^1=3 which means log_3(3)=1 graph (3,1)
3^2=9 which means log_3(9)=2 graph (9,2)
3^3=27 which means log_3(27)=3 graph (27,3)
Can you find a graph that fits these points?
A furniture manufacturer sells three types of products: chairs, tables, and beds. Chairs constitute 35% of the company's sales, tables constitute 55% of the sales, and beds constitute the rest. Of the company's chairs, 5% are defective and have to be returned to the shop for minor repairs, whereas the percentage of such defective items for tables and beds are 12% and 8% respectively. A quality control manager just inspected an item and the item was not defective. What is the probability that this item was a table? Round your result to 2 significant places after the decimal (For example, 0.86732 should be entered as 0.87).
Answer:
53.27
Step-by-step explanation:
To begin, we want to figure out what percent of products are defective and non defective, and of which type, so we can figure out probabilities. So, we start with that 5% of chairs are defective. We know that 35% of product sales are chairs, so 5% of 35% is 35%*0.05 (a percent can be divided by 100 to convert to decimals)= 1.75%. For tables, 12% of 55 is 55*0.12=6.6 percent. For beds, we first must figure out what percent of sales are beds. For this, we must take our total (100%) and subtract everything that is not beds, which is tables and chairs. This, 100-35-55=10, which is our percent of beds. Then, 8% of that is 0.8%. So, we know that the probability that an item is defective is 0.8+6.6+1.75=9.15%. The item pulled was not defective, so we want to figure out the probability of that, which would be the total-defective=100-9.15=90.85%. We then need to figure out which of that 90.85 is divided by tables, as we want to figure out what the probability of a table is. We know that 12% of tables are defective, so 100-12=88% are not. 88% of 55% is 55*0.88=48.4, so there is a 48.4% chance that if you picked out anything, it would be a non defective table. However, we are only picking things out from nondefective items, or the 90.85%. We know that 48.4 is 48.4% of 100, but we want to figure out what percent 48.4 is of 90.85. To find this, we do (48.4/90.85) * 100, which is 53.27 rounded. Feel free to ask further questions!
Find Each Measure.
m1, m2, m3
Answer:
The second choice is correct.
Step-by-step explanation:
These are triangles, so the interior angles have to add up to 180 degrees. Since 45 degrees and m<1 are vertical angles, they will have the same measure. So right off the back we know that m<1 =45. To find the measure<2 all you need to do is add 45 and 59, then subtract that answer from 180. M<2= 76. That leaves only one option. The second one.
The measurements of the angles are Angle 1 = 45 degrees, Angle 2 = 76 degrees, Angle 3 = 80 degrees. The correct option is b) 1 = 45, 2 = 76, 3 = 80.
Let's solve this step by step to find the measurements of angles 1, 2, and 3.
We named the two triangles as OAB and OCD, with a common vertex O. angle O makes vertically opposite angle 45 degree in triangle OAB and angle 1 in OCD, angle A makes angle 2, angle B makes angle 59 degree, angle C makes 55 degree and angle D makes angle 3.Given the information:
In triangle OAB:
Angle OAB (angle 2) = 59 degrees
Angle O = 45 degrees (vertically opposite to angle 1)
In triangle OCD:
Angle O = 45 degrees (again, vertically opposite to angle 1)
Angle OCD (angle 3) = ?
First, let's find angle 2 in triangle OAB:
In triangle OAB, the sum of angles in a triangle is 180 degrees.
So, angle 2 + angle O + angle OAB = 180 degrees.
59 + 45 + angle OAB = 180 degrees.
Now, solve for angle OAB:
angle OAB = 180 degrees - 59 degrees - 45 degrees
angle OAB = 76 degrees
Now, let's find angle 3 in triangle OCD:
In triangle OCD, the sum of angles in a triangle is also 180 degrees.
So, angle O + angle OCD + angle C = 180 degrees.
45 + angle 3 + 55 = 180 degrees.
Now, solve for angle 3:
angle 3 = 180 degrees - 45 degrees - 55 degrees
angle 3 = 80 degrees
So, the measurements of angles 1, 2, and 3 are as follows:
Angle 1 = 45 degrees
Angle 2 = 76 degrees
Angle 3 = 80 degrees
The correct option is:
b) 1 = 45, 2 = 76, 3 = 80
To know more about angle:
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using induction, verify the inequality. (1 + x)" ? 1 + nx, for x ?-1 and ? 1
Answer with explanation:
The Inequality should be:
[tex](1+x)^n\geq 1+n x[/tex]
Where, n and x are any integers.
⇒For, x= -1
L HS
[tex]=[1+(-1)]^n\\\\=(0)^n\\\\=0[/tex]
R HS
→1+n × (-1)
=1-n
If, n is any Integer, then for, n=1
1-1=0
For, n=2
1-2= -1
....
So, [tex](1+x)^n\geq 1+n x[/tex]
for, x=-1.
⇒For, x=1
L HS
[tex]=[1+(1)]^n\\\\=(2)^n[/tex]
For, n=1
L H S=1
For, =2
L H S=4
R HS
→1+n × (1)
=1+n
If, n is any Integer, then for, n=1
1+1=2
For, n=2
1+2= 3
....
So, [tex](1+x)^n\geq 1+n x[/tex]
for, x=1.
What Number is 5% of 220 ???
Answer: 11
Step-by-step explanation:
5% × 220 =
(5 ÷ 100) × 220 =
(5 × 220) ÷ 100 =
1,100 ÷ 100 =
11;
5% of 220 = 11
Answer:
44% is your answer.
Step-by-step explanation:
So, 220/5= 44/1= 44%
Because if you divide 220 by 5 you'll get 44 and 5 divided by 5 ofcourse is 1.
(I'm doing these also in my class, so hopefully i helped you.)
Graph the solution set of the system of inequalities or indicate that the system has no solution.
y ≥ 2x – 4
x + 2y ≤ 7
y ≥ -2
x ≤ 1
Answer:
the graph is shown below
Step-by-step explanation:
The solution region is that quadruply-shaded area above the line y=-2 and to the left of the line x=1. It is further bounded above by the line y = -1/2x +3.5.