Answer:
(a) No solution
(b) Infinitely many solution
(c) No solution
(d) Infinitely many solution
Step-by-step explanation:
Solving (a):
[tex]2x + 10y = 9[/tex] --- (1)
[tex]3x + 15y = 13[/tex] --- (2)
Multiply (1) by 1.5
1.5 * [[tex]2x + 10y = 9[/tex]]
[tex]3x + 15y = 13.5[/tex] --- (3)
Subtract 2 and 3
[tex]3x - 3x + 15y - 15y = 13.5 - 13[/tex]
[tex]0 = 0.5[/tex]
The above is false; Hence, the system has no solution
Solving (b):
[tex]2x + 8y = 5[/tex] --- (1)
[tex]3x + 12y = 7.5[/tex] -- (2)
Multiply 1 by 1.5
1.5 * [[tex]2x + 8y = 5[/tex]]
[tex]3x + 12y = 7.5[/tex]
Subtract 2 and 3
[tex]3x - 3x + 12y - 12y = 7.5 - 7.5[/tex]
[tex]0 = 0[/tex]
The above implies that the system has infinitely many solutions
Solving (c):
[tex]y = 3 - x[/tex]
A second equation is required to solve for (c)
Solving (d):
[tex]5x - 8y = -1[/tex] --- (1)
[tex]-\frac{5}{2}x+ 4y = \frac{1}{2}[/tex] --- (2)
Multiply (2) by 2
[tex]-5x + 8y = 1[/tex] --- (3)
Add 1 and 3
[tex]5x - 5x -8y + 8y = -1 + 1[/tex]
[tex]0 = 0[/tex]
The above implies that the system has infinitely many solutions
Find the missing length indicated
Please help, no links
Answer:
x = 135
Step-by-step explanation:
m = length of perpendicular line to hypotenuse
81/m = m/144
m² = 81 x 144 = 11664
m =√11664 = 108
Using the Pythagorean theorem:
x² = 81² + 108² = 6561 + 11664 = 18225
x = √18225 = 135
9514 1404 393
Answer:
x = 135
Step-by-step explanation:
Side x is the geometric mean of the hypotenuse segments it touches.
x = √(81×(81+144)) = √81×√225 = 9×15
x = 135
An elevator has a placard stating that the maximum capacity is 1600 lb�10 passengers. So, 10 adult male passengers can have a mean weight of up to 1600/10=160 pounds. If the elevator is loaded with 10 adult male passengers, find the probability that it is overloaded because they have a mean weight greater than 160 lb. (Assume that weights of males are normally distributed with a mean of 166 lb and a standard deviation of 29 lb.)
1.The probability the elevator is overloaded is?
*-Please show work to help me understand-*
2. Does this elevator appear to be safe?
A.Yes, there is a good chance that 10 randomly selected people will not exceed the elevator capacity.
B. No, 10 randomly selected people will never be under the weight limit.
C.Yes, 10 randomly selected people will always be under the weight limit.
D.No, there is a good chance that 10 randomly selected people will exceed the elevator capacity.
Answer:
1. 0.7421 = 74.21% probability the elevator is overloaded.
2. D.No, there is a good chance that 10 randomly selected people will exceed the elevator capacity.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
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.
Assume that weights of males are normally distributed with a mean of 166 lb and a standard deviation of 29 lb.
This means that [tex]\mu = 166, \sigma = 29[/tex]
Sample of 10.
This means that [tex]n = 10, s = \frac{29}{\sqrt{10}}[/tex]
1.The probability the elevator is overloaded is?
Probability that the sample mean is above 160 pounds, which is 1 subtracted by the p-value of Z when X = 160. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{160 - 166}{\frac{29}{\sqrt{10}}}[/tex]
[tex]Z = -0.65[/tex]
[tex]Z = -0.65[/tex] has a p-value of 0.2579.
1 - 0.2579 = 0.7421
0.7421 = 74.21% probability the elevator is overloaded.
2. Does this elevator appear to be safe?
High probability of the elevator being overloaded, so not safe. Correct answer is given by option D.
Right Triangles
Evaluate the function requested. Write your answer as a fraction in lowest terms.
Find cos B.
a. cos B = 41/40
b. cos B - 9/41
c. cos B = 40/41
d. cos B = 9/40
Please select the best answer from the choices provided
Answer:
B. cos B = 9/41
Step-by-step explanation:
I calculated it logically
Answer:
b
Step-by-step explanation:
cos B = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{BC}{AB}[/tex] = [tex]\frac{9}{41}[/tex] → b
I need help on this please!
No links
Study guide for exam.
∠AGB and ∠EGD are □ angles.
What is the simplified expression for -3(2x-7)+2y+ 2(x+y)?
Answer:
-4x+42+4yStep-by-step explanation:
-3(2x-7) + 2y + 2 (x+y)
-6x+42 + 2y + 2x + 2y
Take the same coefficents and subtract or add
-6x + 2x= -4x
2y + 2y= 4y
Help pls will give BRAINLIST
Please help
Find the Arc Length of arc b, given the radius is 5 cm.
Answer:
Arc length= 180/360 ( 2 pi × 5cm)180/360 (2 ×22/7×5cm)
18/36=1/2× 2×22/ 7 ×5cm
1×22/7×5cm
22/7×5cm
110/7
=15.715cm
8x²y²-18
factorise in process
Answer:
u
Step-by-step explanation:
8x²y²-182(4x²y²-9)2((2xy)²-3²)2(2xy-3)(2xy+3)stay safe healthy and happy. PLSSS HElpppp!! DUE TODAYYY⛔️
Some children measured the lengths of their feet. The lengths are given in the line plot. What is the difference in length between the shortest and longest foot?
Answer:
Step-by-step explanation:
I need help graphing the right points so please send a picture of the graph also
In the xy-coordinate plane, the graph of the equation y = 3x2 - 12x – 36 has zeros
at x = a and x = b, where a
Part A: Graph the function.
Answer:
you cant send pictures unless created on a graphing website but ill try to help. you first have to simplify y, and if you could comment a clearer equation that would be nice because your equation is confusing(cant tell if its all together
Convert x^2+ (y + 8)^2= 64 to a polar equation that
expresses r in terms of theta.
Answer:
their graphed
Step-by-step explanation:
HELP PLEASE!!!!!! ILL MARK U BRAINLESS!!!!! FOR THE FIRST PERSON!!!
Answer:
54,000 teenagers
Step-by-step explanation:
72/100* 75,000/1=54,000
Write the slope intercept form of this equation 7x-5y=35
Solve the equation for exact solutions over the interval [0, 2π).
Answer:
[tex]\displaystyle x=\left\{0, \frac{2\pi}{3}, \frac{4\pi}{3}\right\}[/tex]
Step-by-step explanation:
We want to solve the equation:
[tex]-2\cos^2(x)=-\cos(x)-1[/tex]
Over the interval [0, 2π).
First, notice that this is in quadratic form. So, to make things simpler, we can let u = cos(x). Substitute:
[tex]-2u^2=-u-1[/tex]
Rearrange:
[tex]2u^2-u-1=0[/tex]
Factor:
[tex](2u+1)(u-1)=0[/tex]
Zero Product Property:
[tex]2u+1=0\text{ or } u-1=0[/tex]
Solve for each case:
[tex]\displaystyle u=-\frac{1}{2}\text{ or } u=1[/tex]
Back-substitute:
[tex]\displaystyle \cos(x)=-\frac{1}{2}\text{ or } \cos(x)=1[/tex]
Using the unit circle:
[tex]\displaystyle x=\left\{0, \frac{2\pi}{3}, \frac{4\pi}{3}\right\}[/tex]
whats 2 plus 7 plus 3
Answer:
Hi, there your answer will 12
2+7+3=12
Have a nice day
Step-by-step explanation:
Answer:
12Step-by-step explanation:
I added it up XD Thanks for the points.
The graph below has:
Answer:
One repetad linear
Step-by-step explanation:
Line m contains the points G(-2,3) and H (5,1).
What is the slope of a line perpendicular to line m?
Answer:
3.5
Step-by-step explanation:
Given points are ,
G(-2,3) H (5,1)Firstly find the slope of the line passing through these two points . Therefore ,
=> m = y₁ - y₂ / x₁ - x ₂
=> m = ( 3 - 1)/(-2-5)
=> m = -2/7
The slope of line perpendicular to it will be negative of reciprocal of the slope . Let m' be the slope of perpendicular line .=> m' = -1/m
=> m' = -1 ÷ -2/7
=> m' = -1 × -7/2
=> m' = 7/2 = 3.5
Hence the slope of the line perpendicular to the given line is 3.5 .8 times the sum of a number and 5 is 3 years the variable Y for the unknown number
Answer:
8(y+ 5) =3
Step-by-step explanation:
i don’t know if it’s A or B
Answer:
A
Step-by-step explanation:
this is true due to the ratio of a 30-60-90 triangle, which is 1-2-sqrt(3). The 12 corresponds to the sqrt(3), which means that the 1 corresponds to 4sqrt3 and the 2 to 8sqrt3.
:)
write the coefficient of a in 7 a
Given:
The term is 7a.
To find:
The coefficient of "a" in the given term "7a".
Solution:
In the product of a number and a variable, the number is called the coefficient of that variable.
In the expression "7a", the number is "7" and the variable is "a". It means the number 7 is the coefficient of "a".
Therefore, the coefficient of "a" in the given term "7a" is 7.
Angle x and 56 are complementary. What is the value of x?
149
34
56
90
Answer:
34°
Step-by-step explanation:
90-56=34°
__________
Lee's goal is to log more
than 10,000 steps each day. If
she is awake 16 hours a day,
how many steps does she need
Ito take each hour?
Answer: 625 steps per hour
Step-by-step explanation:
10,000/16=625
How many different 10-letter arrangements are possible using the letters in the word AUTOMOBILE?
Answer:
1,814,400
Step-by-step explanation:
the formula would be: nPr / x_1 ! x_2!....
since there are 2 O's and it is a 10-LETTER ARRANGEMENT, the equation would now be:
10P10 / 2!
10P10 would simplify down to 10! so you would have :
10! / 2!
if you simplify this above: you would get 1,814,400
3. Find the value of x.
(2x-71
Answer:
33
Step-by-step explanation:
2x-7 = 73
2x = 73-7
2x = 66
x = 66÷2
x = 33
Therefore, the value of x is 33
Two angles in a triangle have measures of 62° and 15º.What is the measure of the third angle?
Answer:
103 degrees
Step-by-step explanation:
The angles in a triangle always add up to 180 degrees
so 62+15=77
180-77=103
hope it helps :)
Answer:
103º
Step-by-step explanation:
All angles of a triangle add up to 180º
This means:
62º + 15º + the third angle = 180º
Then you just solve:
180º - 77º = 103º
Hope this helps :)
A pharmaceutical sale representative gets paid $50,000 annually plus 3.5% commissions on total sales. This year he sold $420,000 in pharmaceuticals. What are his annual total earnings? someone help pls
Answer:
[tex] \frac{3.5}{100} \times 420000 = 14700commission \\ total \: earnings = 50000 + 14700 \\ = 64700[/tex]
Rick, Diane, and Lu are selling cookies, fruit cakes, and chocolate bars in a neighborhood snack sale. The number of cookie packs,
cakes, and chocolate bars sold by each person is given in the table.
A what prices did Rick, Diane, and Lu sell the eatables?
A)
$1.00 for a cookie pack, $2.50 for a fruit cake, and $1.50 for a chocolate bar
B)
$1.50 for a cookie pack, $2.50 for a fruit cake, and $1.00 for a chocolate bar
9
$1.00 for a cookie pack, $1.50 for a fruit cake, and $2.50 for a chocolate bar
D)
$1.50 for a cookie pack, $2.50 for a fruit cake, and $1.00 for a chocolate bar
Answer:
I think it's A
Step-by-step explanation:
but I do not know this clearly
Answer: The Answer is A.
I plugged the numbers into Excel.
Step-by-step explanation:
What is the surface area of the triangular prism? 1 5ft 3 ft 5 ft 4 ft
Answer:
134
Step-by-step explanation:
Find an explicit formula for the geometric sequence -9\,,-18\,,-36\,,-72,...
Answer:
[tex]f(x)=-9(2)^(^x^-^1^)[/tex]
Explanation:
First, we find the common ratio by dividing any term by its previous term. We should do this a couple of times to make sure it's consistent. In this case, our common ratio is 2. Our first (or 1th) term of the sequence is -9, so our formula becomes
[tex]f(x)=-9(2)^(^x^-^1^)[/tex].