Answer:
0.074
Step-by-step explanation:
convert 7.4% to a decimal.
Many utility companies promote energy conservation by offering discount rates to consumers who keep their energy usage below certain established subsidy standards. A recent EPA report notes that 70% of the island residents of Puerto Rico hae reduced their electricity usage sufficiently to qualify for discounted rates. If five residential subscribers are randomly selected from San Juan, Puerto Rico, find the probability of each of the following events.a. All five qualify for the favorable rateb. At least four qualify for the favorable rates
Answer:
a. 0.1681 = 16.81% probability that all five qualify for the favorable rate.
b. 0.5283 = 52.83% probability that at least four qualify for the favorable rates
Step-by-step explanation:
For each Puerto Rico resident, there are only two possible outcomes. Either they qualify for discounted rates, or they do not. The probability of a person in the sample qualifying for discounted rates is independent of any other person in the sample. This means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
70% of the island residents of Puerto Rico have reduced their electricity usage sufficiently to qualify for discounted rates.
This means that [tex]p = 0.7[/tex]
Five residential subscribers are randomly selected from San Juan, Puerto Rico
This means that [tex]n = 5[/tex]
a. All five qualify for the favorable rate
This is P(X = 5). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 5) = C_{5,5}.(0.7)^{5}.(0.3)^{0} = 0.1681[/tex]
0.1681 = 16.81% probability that all five qualify for the favorable rate.
b. At least four qualify for the favorable rates
This is
[tex]P(X \geq 4) = P(X = 4) + P(X = 5)[/tex]
So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 4) = C_{5,4}.(0.7)^{4}.(0.3)^{1} = 0.3602[/tex]
[tex]P(X = 5) = C_{5,5}.(0.7)^{5}.(0.3)^{0} = 0.1681[/tex]
[tex]P(X \geq 4) = P(X = 4) + P(X = 5) = 0.3602 + 0.1681 = 0.5283[/tex]
0.5283 = 52.83% probability that at least four qualify for the favorable rates
If a class of 27 students had a mean of 72 on a test, interpret the mean of 72 in the sense of a fair share measure of the center of the test scores.
The fair share measure would mean that the score of 72 would be the score all 27 students got on the test if they all had the same score.
A fair share measure of the center of the test scores is 72 be the score all 27 students got on the test.
We have given that
a class of 27 students had a mean of 72 on a test,
What is the fair share?An equitable or reasonable portion or share of something
The fair share measure would mean that a score of
72 be the score all 27 students got on the test.
If they all had the same score.
Therefore 72 was the score all 27 students got on the test.
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can somebody help me with math TwT:
question one 1: Which number(s) are 6 units from zero on a number line?
1. 3
2. 6
3. -6
4. 12
----------------------------------------------------------------------------
Question 2 ^^: Which comparison is not correct?
1. -3 < 4
2. 3 < 6
3. 1 > -9
4. -8 > -6
tell me the answers also for question 1 its either one or more than one answer ^^ ty and please don’t steal my points :(
1. 12 (i think)
i don't know about question 2
Answer: -8 > -6
Step-by-step explanation:
What is the value of x?
Enter your answer in the box.
x =
$\text{Basic}$
$x$$y$$x^2$$\sqrt{ }$$\frac{x}{ }$
$x\frac{ }{ }$
$x^{ }$$x_{ }$$\degree$$\left(\right)$$\abs{ }$$\pi$$\infty$
The figure shows 2 right triangles, triangle K L J with right angle J and triangle L J M with right angle M. The measure of angle L K J is 30 degrees. The measure of angle L J M is 45 degrees. The length of side K L is 8 square root 2. The length of side L M is x.
Answer:
4
Step-by-step explanation:
I took the quiz, here's proof
can somebody help me with math I have 3 more questions OWO:
If Jeff drives 200 miles per hour in his race car, and this relationship is graphed, which ordered pair would not be on the graph?
1. (2, 400)
2. (0, 0)
3. (8, 1,600)
4. (5, 1,200)
please don’t steal all my points UwU :( :’)
The ordered pair would not be on the graph is (5, 1200)
The correct option is (4).
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
If Jeff drives 200 miles per hour in his race car.
So, if we denote the distance by y and time by x then relation is
y = 200x
For x = 0
y=0
and, x= 2
y= 400
and, x= 8
y= 1600
and, x= 5
y = 1000
Hence, the point not on the graph is (5, 1200)
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which value from the set makes 12n-15=42 true?
A.2.25
B.2.8
C.3.5
D.4.75
Which of the following best classifies a quadrilateral with coordinates A(7,0), B(3, 1), C(4,7), and D(8, 6)?
A.Rectangle
B.Parallelogram
C.Trapezoid
D.Square
Answer:
B. Parallelogram
Step-by-step explanation:
The opposite sides of the quadrilateral are equal and so the quadrilateral is a rectangle, the correct option is A.
What is a Quadrilateral?A quadrilateral is a polygon with four sides.
The coordinates of a quadrilateral are:
A(7,0), B(3, 1), C(4,7), and D(8, 6)
The distance between the coordinates has to be determined to identify the type of quadrilateral
The distance formula is
[tex]\rm D = \sqrt { ( x- x_1)^2 + (y-y_1)^2}[/tex]
[tex]\rm AB = \sqrt { (3-7)^2 + (1-0)^2}\\AB = \sqrt { 17}[/tex]
[tex]\rm BC = \sqrt { ( 1)^2 + (6)^2}\\BC = \sqrt {37}[/tex]
Similarly,
[tex]\rm CD= \sqrt { 17}\\\\AD = \sqrt{37}[/tex]
The opposite sides of the quadrilateral are equal and so it is a rectangle.
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What do u think 2+2 is can u tell me ?
Answer:
the answer is 4 your welcome
Answer: bro its 22. It's ez math. 2 + 2 = 22
Step-by-step explanation:
You just combine the numbers piece of ice cream It's actually peace of cake but I like ice cream more sooo yuh)
-3(4x - 2) = 42
A x=3
B x=-3
C x=3.67
D x=7
Answer:
B) x=-3
Step-by-step explanation:
-3(4x-2)=42
4x-2=42/-3
4x-2=-14
4x=-14+2
4x=-12
x=-12/4
x=-3
A small liberal arts college in the Northeast has 350freshmen. One hundred five of the freshmen are female. Suppose sixty freshmen are randomly selected (without replacement).Step 2 of 2:Find the standard deviation of the number of females in the sample. Round your answer to two decimal places, if necessary.
Answer:
The standard deviation of the number of females in the sample is 3.21.
Step-by-step explanation:
For each freshmen, there are only two possible outcomes. Either it is a female, or it is not. Sixty freshmen are randomly selected (without replacement). This means that the hypergeometric distribution is used to solve this question.
Standard deviation of the hypergeometric distribution:
We have that:
N is the population size.
n is the sample size.
s is the number of successes in the sample.
The standard deviation is given by:
[tex]\sigma = \sqrt{n(\frac{s}{N})(1 - \frac{s}{N})(\frac{N - n}{N-1})}[/tex]
A small liberal arts college in the Northeast has 350freshmen.
This means that [tex]N = 350[/tex]
One hundred five of the freshmen are female.
This means that [tex]s = 105[/tex]
Suppose sixty freshmen are randomly selected
This means that [tex]n = 60[/tex]
Find the standard deviation of the number of females in the sample.
[tex]\sigma = \sqrt{60(\frac{105}{350})(1 - \frac{105}{350})(\frac{350 - 60}{350 -1})} = 3.21[/tex]
The standard deviation of the number of females in the sample is 3.21.
Which of these is the algebraic expression for "5 less than 6 times some number"?
6t - 5
5t - 6
5 - 6t
6 - 5t
In 5 days, a scientist wrote 3 pages of a research paper, At that rate, how many days will it take the scientist to write a 30- page research paper?
A 18 days C 25 days
B 30 days D 50 days
Answer:
50 days
Step-by-step explanation:
5/3 = 50/30
pls brainliest
I would really appreciate it if someone could answer this I will give a brainlist:)
5.7
Pythagorean Theorem is a² + b² = c²
Answer:
x = 5.7
Step-by-step explanation:
Formula:
a² + b² = c²
4² + b² = 7²
16 + b² = 49
b² = 49 - 16
b² = 33
[tex]\sqrt{b^2} =\sqrt{33}[/tex]
b = 5.7
Find the area of each triangle o the nearest tenth.
Answer:
A is , 18.1058 B is , 24.91575
Step-by-step explanation:
Suppose that the Celsius temperature at the point (x, y) in the xy-plane is T(x, y) = x sin 2y and that distance in the xy-plane is measured in meters. A particle is moving clockwise around the circle of radius 1 m centered at the origin at the constant rate of 2 m/sec.How fast is the temperature experienced by the particle changing in degrees Celsius per meter at the point?
Missing information:
How fast is the temperature experienced by the particle changing in degrees Celsius per meter at the point
[tex]P = (\frac{1}{2}, \frac{\sqrt 3}{2})[/tex]
Answer:
[tex]Rate = 0.935042^\circ /cm[/tex]
Step-by-step explanation:
Given
[tex]P = (\frac{1}{2}, \frac{\sqrt 3}{2})[/tex]
[tex]T(x,y) =x\sin2y[/tex]
[tex]r = 1m[/tex]
[tex]v = 2m/s[/tex]
Express the given point P as a unit tangent vector:
[tex]P = (\frac{1}{2}, \frac{\sqrt 3}{2})[/tex]
[tex]u = \frac{\sqrt 3}{2}i - \frac{1}{2}j[/tex]
Next, find the gradient of P and T using: [tex]\triangle T = \nabla T * u[/tex]
Where
[tex]\nabla T|_{(\frac{1}{2}, \frac{\sqrt 3}{2})} = (sin \sqrt 3)i + (cos \sqrt 3)j[/tex]
So: the gradient becomes:
[tex]\triangle T = \nabla T * u[/tex]
[tex]\triangle T = [(sin \sqrt 3)i + (cos \sqrt 3)j] * [\frac{\sqrt 3}{2}i - \frac{1}{2}j][/tex]
By vector multiplication, we have:
[tex]\triangle T = (sin \sqrt 3)* \frac{\sqrt 3}{2} - (cos \sqrt 3) \frac{1}{2}[/tex]
[tex]\triangle T = 0.9870 * 0.8660 - (-0.1606 * 0.5)[/tex]
[tex]\triangle T = 0.9870 * 0.8660 +0.1606 * 0.5[/tex]
[tex]\triangle T = 0.935042[/tex]
Hence, the rate is:
[tex]Rate = \triangle T = 0.935042^\circ /cm[/tex]
f(x) = -x^2- 4x + 10
in the standard form
f(x) = a(x – h)^2 + k
Answer:
y = - ( x + 2 )² + 14
Step-by-step explanation:
f(x) = ax² + bx + c
f(x) = a(x - h)² + k (where (h, k) are coordinates of the vertex.
h = - [tex]\frac{b}{2a}[/tex]
~~~~~~~~~~~~
f(x) = - x² - 4x + 10
a = - 1, b = - 4, c = 10
h = - [tex]\frac{-4}{2(-1)}[/tex] = - 2
k = - ( - 2)² - 4( - 2) + 10 = 14
(h, k) = ( - 2, 14 )
y = - ( x + 2 )² + 14
a map has a scale of 1 cm :15.5 km two cities are 2.3 cm apart on the map. to the nearest tenth of a kilometer,whatis the actual distance corresponding to the map distance
Write the expanded form in the condensed form.
9z+9z
Answer:
nine z plus nine z.
lol tell me.if.its wrong
Sweet corn of a certain variety is known to produce individual ears of com with a mean weight of 8 ounces. A farmer is testing a new fertilizer designed to produce larger ears of com, as measured by their weight. He selects a random sample of 10 ents of com and determines their weight (in ounces). The data are as follows: 8.25 7359,05 8.00 8.25 8.75 9.00 7.60 8.45 8.55
Do the data provide convincing evidence at the a=0.05 level that the fertilizer had a positive impact on the weight of the com cars?
Answer:
We can conclude that there is significant evidence that dL fertilizer has a positive impact on larger weight of coms
Step-by-step explanation:
Given the data :
8.25 7.35 9.05 8.00 8.25 8.75 9.00 7.60 8.45 8.55
Using calculator :
Mean, x = 8.325
Standard deviation, s = 0.560
Null hypothesis :
H0: μ = 8
H1 : μ > 8
The test statistic,
(x - μ) / (s/sqrt(n))
(8.325 - 8) / (0.56 / sqrt(10))
0.325 / 0.177
= 1.835
The Pvalue ; using the Tstatistic calculator ;
α = 0.05 ; df = 10 - 1 = 9
Pvalue = 0.04985
Reject H0 ; if Pvalue is < α
Hence, since 0.04985 < 0.05 ; we reject H0
. We can conclude that there is significant evidence that dL fertilizer has a positive impact on larger weight of coms
Plz help me!! I’m having a bit of trouble
Answer:
x= 27
Step-by-step explanation:
Peter Company, a produce distributer, always tries to sell its oldest produce first.
Peter company
Answer:
what is this a maths problem
Can someone help me with this?
Find x. Round to the nearest tenth.
xº
13
15
Answer:
x= 49.1
Step-by-step explanation:
Please see the attached picture for the full solution.
What is the area of the figure?
O 11 square units
O 18 square units
24 square units
32 square units
Answer:
18
Step-by-step explanation:
Answer:
yes 18 is correct
Step-by-step explanation:
The point (-2, 4) is plotted on the coordinate plane.
The point is reflected across the y-axis. What are the coordinates of the reflected point
A (-2,-4)
B (-2,4)
C (2,-4)
D (2,4)
Answer:
I would say B
Step-by-step explanation:
The main office staff collected 55 cans, the counseling staff collected 89 cans, and the custodial staff collected 67 cans.
Which three steps are correct when solving this quadratic equation by completing the square? X^2-10x=39
Step-by-step explanation:
Any answer that involes,
Step 1: Complete the Square
[tex] {x}^{2} - 10x = 39[/tex]
[tex]( \frac{ - 10}{2} ) {}^{2} = 25[/tex]
[tex] {x}^{2} - 10x + 25 = 64[/tex]
Step 2: Turn the left side into a binomial
[tex](x - 5) {}^{2} = 64[/tex]
Step 3: Solve for x.
[tex]x - 5 = + - 8[/tex]
[tex]x - 5 = 8[/tex]
[tex]x = 13[/tex]
OR
[tex]x - 5 = - 8[/tex]
[tex]x = - 3[/tex]
X=-3 or X=13
3. What is the difference of a number and 10?
Answer:
the difference between a number and 10 simply means ,that number minus 10
hope it helps. please do me a favor and Mark me Brainleist please please please please please please please please please please please please please please please please please please please please.
7 (4 1/3) using distributive property
Answer:
so 7*4 is 28 and 7*1/3 is 2 an 1/3 so it would be 30 and 1/3
Step-by-step explanation:
find the time required for an investment of $3000 to grow to $8000 at an interest rate of 7.5% per year, compounded quarterly ( round the answer to two decimal places)
Answer:
13.20 yearsStep-by-step explanation:
Investment P = $3000Final amount F = $8000Interest rate r = 7.5% = 0.075Compound number n = 4Time t = ?Formula:
F = P(1 + r/4)^(4t)Solve for t:
8000 = 3000(1 + 0.075/4)^(4t)8/3 = 1.01875^(4t)4t log 1.01875 = log (8/3)4t = 0.42596 / 0.008067t = 1/4(52.80)t = 13.20For the following right triangle, find the side length x.