If the number on the other side of the inequality sign is negative, your equation either has no solution or all real numbers as solutions. Use the sign of each side of your inequality to decide which of these cases holds. If the number on the other side of the inequality sign is positive, proceed to step 3.
Sean and Evan are college roommates who have part-time jobs as servers in restaurants. The distribution of Sean’s weekly income is approximately normal with mean $225 and standard deviation $25. The distribution of Evan’s weekly income is approximately normal with mean $240 and standard deviation $15. Assuming their weekly incomes are independent of each other, which of the following is closest to the probability that Sean will have a greater income than Evan in a randomly selected week?
a. 0.67
b. 0.700
c. 0.227
d. 0.303
e. 0.354
Answer:
d. 0.303
Step-by-step explanation:
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.
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
In this question:
We want the probability of Sean having a greater income than Evan, which is the probability of the subtraction of Sean's income by Evan's income is greater than 0.
Distribution of the difference between Sean's and Evan's income:
Sean has mean 225, Evan 240. So
[tex]\mu = 225 - 240 = -15[/tex]
Sean's standard deviation is of 25, Evan's of 15. So
[tex]\sigma = \sqrt{25^2+15^2} = 29.15[/tex]
Probability that Sean will have a greater income than Evan in a randomly selected week:
Probability of the subtraction being greater than 0, which is 1 subtracted by the pvalue of Z when X = 0. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{0 - (-15)}{29.15}[/tex]
[tex]Z = 0.51[/tex]
[tex]Z = 0.51[/tex] has a pvalue of 0.695
1 - 0.695 = 0.305.
Closest to 0.303, option d.
find mHK please help
Answer:
66°
Step-by-step explanation:
When a radius(diameter in this case) is perpendicular to a chord, it bisects the chord and the arc formed by the chord. Because of this, we can say mHJ is equal to mKJ. We can write an equation:
mHJ = mKJ
and substitute:
x + 20 = 6x - 45
20 = 5x - 45
65 = 5x
x = 13
mHK is the sum of mHJ and mKJ, we can write mHK as the expression:
x + 20 + 6x - 45
7x - 25
We can substitute x:
7(13) - 25
91 - 25
66°
I need help to find m
Answer:
∠MNO = 75°
Step-by-step explanation:
∠mno = 1/2 ( arc MLP - arc MOP )
arc MLP = 241 and arc MOP = 91
so ∠MNO = 1/2 ( 241 - 91 )
241 - 91 = 150
150/2 = 75
Hence, ∠MNO = 75°
Need help solving this problem.
-30x+147=-171-24x
Answer:
-30x+147= -171-24x
+24x +24x
-6x+147= -171
-147 -147
-6x= -318
x=53
Hope this helps!
Can u help me please I will mark u brilliant
Answer:
c
Step-by-step explanation:
Answer:
the answer is 5
Step-by-step explanation:
I need the answer pls answer fast
Answer:
A = 846 in²
Step-by-step explanation:
The area (A) of a rhombus is calculated as
A = [tex]\frac{1}{2}[/tex] × d₁ × d₂ ( d₁ and d₂ are the diagonals ) , then
A = [tex]\frac{1}{2}[/tex] × 36 × 47 = 18 × 47 = 846 in²
Answer:
846
Step-by-step explanation:
area of a rhombus is [tex]\frac{pq}{2}[/tex] where p and q are the two diagonals ..
so [tex]A=\frac{36*47}{2}[/tex]
A=846
Factor the following the expression,
-15m -25
Answer:
[tex]-5(3m+5)[/tex]
Step-by-step explanation:
Factor by grouping:
'-5' is a common factor.
Factoring out '-5'....
[tex]-15m-25\\\\\boxed{-5(3m+5)}[/tex]
Hope this helps.
Calculator
A normal distribution has a mean of 102 and a standard deviation of 2.9.
What is the z-score of 105?
Enter your answer, rounded to the nearest hundredth, in the box.
Answer:
the z score of 105 is 1.03
Step-by-step explanation:
Given that
the mean is 102
And, the standard deviation is 2.9
We need to find the z score of 105
As we know that
Z score = (Observed value - mean) ÷ standard deviation
= (105 - 102) ÷ 2.9
= 1.03
Hence, the z score of 105 is 1.03
The same would be considered and relevant
3a+5b-9: a=2, b=3 that is my question I need help
Answer:
12
Step-by-step explanation:
Find the value of x, if angle X measures 102°.
х
to
w7x+4yº(5x - 4yº
w
Z
Answer:
A. 13
Step-by-step explanation:
The non-vertex angles of a kite are always congruent. Therefore,
m<X = m<Z = 102°
Sum of all angels of a kite = 360°
Thus:
m<X + m<Y + m<Z + m<W = 360°
Substitute
102 + (5x - 4) + 102 + (7x + 4) = 360
102 + 5x - 4 + 102 + 7x + 4 = 360
Add like terms
204 + 12x = 360
12x = 360 - 204
12x = 156
x = 156/12
x = 13
There are two tables shown below. Which table shows a constant rate?
Answer:
Option B
Step-by-step explanation:
To calculate the rate of the table is given by the expression,
Rate = [tex]\frac{\triangle y}{\triangle x}[/tex]
For table A,
x y [tex]\triangle y[/tex] [tex]\triangle x[/tex] [tex]\frac{\triangle y}{\triangle x}[/tex]
2 10 - - -
3 15 15 - 10 = 5 3 - 2 = 1 [tex]\frac{5}{1}=5[/tex]
5 20 20 - 15 = 5 5 - 3 = 2 [tex]\frac{5}{2}=2.5[/tex]
8 25 25 - 20 = 5 8 - 5 = 3 [tex]\frac{5}{3}=1.67[/tex]
Therefore, rate is not constant in this table.
For table B
x y [tex]\triangle y[/tex] [tex]\triangle x[/tex] [tex]\frac{\triangle y}{\triangle x}[/tex]
3 9 - - -
5 15 15 - 9 = 6 3 - 5 = 2 [tex]\frac{6}{2}=3[/tex]
8 24 24 - 15 = 9 8 - 5 = 3 [tex]\frac{9}{3}=3[/tex]
10 30 30 - 24 = 6 10 - 8 = 2 [tex]\frac{6}{2}=3[/tex]
Therefore, table B shows a constant rate of 3.
Option B is the correct option.
Can someone please help me I will mark u brilliant
Answer:
the first one
Step-by-step explanation:
The problem says that the plot must have a maximum of 44, which means the most right dot must be on the 44 mark. All the graphs fit this requirement (the dashes are in increments of 2) The problem says that it must have an upper quartile of 39, which means the line closest to the maximum dot must be on the 39 mark. Graphs 2 and 3 do not meet this requirement, so they are eliminated. The last requirement is the median of 25. The median is represented by the middle line in the middle of the boxes. Graph 4 does not fit this requirement, so it is eliminated. Thus, only the first graph follows all 3 requirements.
helppppp! how do I find this?
Answer:
y=3x-6
Step-by-step explanation:
(2,0). y=mx+b or 0=3 × 2+b, or solving for b: b=0-(3)(2). b=-6.
(3,3). y=mx+b or 3=3 × 3+b, or solving for b: b=3-(3)(3). b=-6.
Plugging in the two points from the graph.
Hence, y=3x-6
A right triangle has one angle that measures 36°. What is the measure of the other acute angle?
Answer:
54 degrees
Step-by-step explanation:
The total degree of a triangle is 180. Since it is a right angle, one of the angles is 90 degrees. The equation is, 36+90+x=180. You should then get 54 degrees.
Find the lie 3 of the 4 statements are true find the false one statement
Answer:
Step-by-step explanation:
If those choices given (there is one missing) the false statement is the constant term is 3. It's not. -3 is the constant term.
Answer:
Step-by-step explanation:
C. the constant term is not 3
Robert must read a few books from his home library. He read any 4 out of 6 books from the top shelf, and then any 2 out of 3 books from the middle shelf and then any 3 out of 6 books from the bottom shelf. In how many ways can Robert read the books, if different orders in which the books will be read count as different ways
Answer:
Robert can read the books in 129,600 different ways.
Step-by-step explanation:
The order in which the book are read is important, which means that the permutations formula is used to solve this question.
Permutations formula:
The number of possible permutations of x elements from a set of n elements is given by the following formula:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
Top shelf:
4 books from a set of 6. So
[tex]P_{(6,4)} = \frac{6!}{2!} = 360[/tex]
Middle shelf:
2 books from a set of 3. So
[tex]P_{(3,2)} = \frac{3!}{2!} = 3[/tex]
Bottom shelf:
3 books from a set of 6. So
[tex]P_{(6,3)} = \frac{6!}{3!} = 120[/tex]
Total:
360*3*120 = 129,600
Robert can read the books in 129,600 different ways.
A package of colored paper contains 20 pieces of yellow paper. This represents 25% of the total pieces of colored paper in the package. 6.RP.3c Part A. Write 25% as a rate per 100 in simplest form. How many total pieces of colored paper are in the package?
Answer:
There were 80 pieces of colored paper in the package.
Step-by-step explanation:
Given that a package of colored paper contains 20 pieces of yellow paper, and this represents 25% of the total pieces of colored paper in the package, to determine how many total pieces of colored paper are in the package, the following calculation must be performed:
25 = 20
100 = X
100 x 20/25 = X
2,000 / 25 = X
80 = X
Therefore, there were 80 pieces of colored paper in the package.
Sally has 3 yards of yarn. She will use 6 inches per bracelet. How many bracelets can she make?
3 feet in a yard... 12x3 = 36...... 36+36+36 =108 inches
108 divided by 6 is 18 bracelets
I which of the following is the correct measure of angle ACD?
Answer:
And the reasoning behind this calculation is because they're alternate angles on parallel lines. So, therefore, we can say, using the information that we've been given, we can say that the measure of angle is equal to 127 degrees
A windshield wiper turns through an angle of 150°. The top of the blade traces the are with a 20-inch radius. How long is the
arc?
A. 52.36 inches
B. 75.4 inches
C. 0.1308 inches
D. 3000 inches
Answer:
A
Step-by-step explanation:
Arc length is given by the formula:
[tex]\displaystyle s=2\pi r\frac{\theta}{360^\circ}[/tex]
Where r is the radius and θ is the central angle, in degrees.
The windshield wiper has a radius of 20 inches and a central angle of 150°. Hence:
[tex]\displaystyle s=2\pi (20)\left(\frac{150}{360}\right)[/tex]
Use a calculator:
[tex]\displaystyle s=\frac{50}{3}\pi \approx52.36\text{ inches}[/tex]
Our answer is A.
which is greater? 0.04 or 0.39
Answer:
0.39
Step-by-step explanation:
think about it this way, if you take away the decimal it would be 39 and 04. 04 is another way to write 4 and 4 is less than 39. so 0.04 is less than 0.39
Answer:
0.04 > - 0.39
Step-by-step explanation:
0.04 > - 0.39
Rewrite the function f(x)=-4(x+3)2 – 2 in the form f(x) = ax²+bx+c.
음
Х
?
Recheck
Try again
Answer:
f(x) = -4x² - 24x - 38
Step-by-step explanation:
f(x )= -4(x + 3)² – 2
Expand the squared term
f(x) = -4 (x² + 6x + 9) - 2
Distribute the -4
f(x) = (-4x² - 24x - 36) - 2
Combine like terms
f(x) = -4x² - 24x - 38
Find the indicated limit, if it exists.
The limit is approaching 5.
Possible Options:
a) 0
b) 8
c) 3
d) The limit does not exist
Answer:
d) The limit does not exist
General Formulas and Concepts:
Calculus
Limits
Right-Side Limit: [tex]\displaystyle \lim_{x \to c^+} f(x)[/tex]Left-Side Limit: [tex]\displaystyle \lim_{x \to c^-} f(x)[/tex]Limit Rule [Variable Direct Substitution]: [tex]\displaystyle \lim_{x \to c} x = c[/tex]
Limit Property [Addition/Subtraction]: [tex]\displaystyle \lim_{x \to c} [f(x) \pm g(x)] = \lim_{x \to c} f(x) \pm \lim_{x \to c} g(x)[/tex]
Step-by-step explanation:
*Note:
In order for a limit to exist, the right-side and left-side limits must equal each other.
Step 1: Define
Identify
[tex]\displaystyle f(x) = \left\{\begin{array}{ccc}5 - x,\ x < 5\\8,\ x = 5\\x + 3,\ x > 5\end{array}[/tex]
Step 2: Find Right-Side Limit
Substitute in function [Limit]: [tex]\displaystyle \lim_{x \to 5^+} 5 - x[/tex]Evaluate limit [Limit Rule - Variable Direct Substitution]: [tex]\displaystyle \lim_{x \to 5^+} 5 - x = 5 - 5 = 0[/tex]Step 3: Find Left-Side Limit
Substitute in function [Limit]: [tex]\displaystyle \lim_{x \to 5^-} x + 3[/tex]Evaluate limit [Limit Rule - Variable Direct Substitution]: [tex]\displaystyle \lim_{x \to 5^+} x + 3 = 5 + 3 = 8[/tex]∴ Since [tex]\displaystyle \lim_{x \to 5^+} f(x) \neq \lim_{x \to 5^-} f(x)[/tex] , then [tex]\displaystyle \lim_{x \to 5} f(x) = DNE[/tex]
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Limits
Select the correct answer. Consider the function f(x) = 10x and the function g(x), which is shown below. How will the graph of g(x) differ from the graph of f(x)? A. The graph of g(x) is the graph of f(x) shifted 6 units up. B. The graph of g(x) is the graph of f(x) shifted to the left 6 units. C. The graph of g(x) is the graph of f(x) shifted 6 units down. D. The graph of g(x) is the graph of f(x) shifted to the right 6 units.
Answer:B
Step-by-step explanation:
The graph of g(x) is the graph of f(x) shifted to the left 6 units. Then the correct option is B.
What is a function?A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.
Consider the function f(x)= 10ˣ and the function g(x), which is shown below.
g(x)= f(x - 6) = 10⁽ˣ⁻⁶⁾
If we subtract any constant from the variable then the function gets shifted toward the left by constant units.
Similarly, 6 is subtracted from the variable then the function gets shifted toward the left by 6 units.
More about the function link is given below.
https://brainly.com/question/5245372
#SPJ2
1/8 times 5/8 in simplest form
Answer:
5/64
Step-by-step explanation:
numerators 1 time 5 is 5 and denominators 8 times 8 is 64; 5/64
The circumference of a circular painting is 40.82 feet. What is the radius of the painting? Use 3.14 for pie and do not round your answer.
Answer:
The radius is equal to 6.5 feet.
Step-by-step explanation:
To solve this we need to know that circumference equals 2πr (where "r" is the radius). Therefore, we can make the following equation...
2πr = 40.82
πr = 20.41
3.14r = 20.41
r = 6.5
Now we know that the radius is equal to 6.5 feet.
Ten years ago, Scott bought a board game for $30. That board game has now increased it's value by 83%
Answer:
the awnser is 54.9 ( mark as best awnser )
A quarter has a diameter of 2.4 centimeters. What is the area of the coin (round answer to nearest tenth)?
Answer:
4.5
Step-by-step explanation:
The equation of an area of a circle is A=πr² where r is the radius.
The radius is also half the diameter. So the radius of the quarter is 1.2
A=π(1.2)²
A=π(1.44)
A=4.52389
Answer:
4.5 answer is on the picture below. :) Thank you!
Step-by-step explanation:
Proof...
Factor the following expression 8x^2+2x-158x2+2x−15
Answer:
(9-x)
Step-by-step explanation:
In the figure, lines ℓ and m are parallel. Describe ∠1 and ∠2.
∠1 and ∠2 are equal angles as the lie on same side of transversal, are on parallel lines and are corresponding to each other
thank you