To simplify an expression means to write it in the simplest way possible. Ideally, there would be no parentheses and everything has been 'expanded'.
Solving the QuestionWe're given:
[tex]5 (4x+3)-2[/tex][tex]5 (4x+3)-2[/tex]
Open up the parentheses by multiplying each term by 5:
[tex]=5*4x+5*3-2\\=20x+15-2\\=20x+13[/tex]
Answer[tex]20x+13[/tex]
The mean number of points in 1977 was 1189 points with standard deviation of 397 points. With a roughly normal distribution, what percent of performances would fall between 395 and 1983 points?
Your answer
A. 100%
B. 68%
C. 95%
D.99.7%
Answer:
C. 95%
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean.
Approximately 99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean of 1189 points, standard deviation of 397 points.
Percentage between 395 and 1983 points?
395 = 1189 - 2*397
1983 = 1189 + 2*397
So within 2 standard deviations of the mean, which by the Empirical Rule is approximately 95%, and the answer is option C.
When confronted with an in-flight medical emergency, pilots and crew can consult staff physicians at a global response center located in Arizona. If the global response center is called, there is a 4.8 percent chance that the flight will be diverted for an immediate landing. Suppose the response center is called 8,465 times in a given year.
This question is not complete, the complete question is;
When confronted with an in-flight medical emergency, pilots and crew can consult staff physicians at a global response center located in Arizona. If the global response center is called, there is a 4.8 percent chance that the flight will be diverted for an immediate landing. Suppose the response center is called 8,465 times in a given year.
a) What is the expected number of diversions
b) What is the probability of at least 400 diversions
c) What is the probability of fewer than 450 diversions?
Answer:
a) expected number of diversions μ is 406.32
b) the probability of at least 400 diversions is 0.6368
c) the probability of fewer than 450 diversions is 0.9861
Step-by-step explanation:
Given the data in the question;
n = 8465
π = 4.8% = 0.048
so expected number of diversions μ = nπ = 8465 × 0.048 = 406.32
and
σ = √(π(1 - π ) = √(8465 × 0.048(1 - 0.048 ) = √( 406.32 × 0.952 )
σ = √386.81664
σ = 19.6677
b) the probability of at least 400 diversions
P(at least 400 diversion ) = P( X ≥ 400 )
= P( X ≥ 399.5 )
so
z = (X - μ) / σ
we substitute
z = (399.5 - 406.32 ) / 19.6677
z = -6.82 / 19.6677
z = -0.35
so
P(Z > -0.35 ) = 0.500 + p( -0.35 ≤ z ≤ 0 )
= 0.5000 + p( 0 ≤ z ≤ 0.35 )
= 0.5000 + 0.1368
= 0.6368
Therefore, the probability of at least 400 diversions is 0.6368
c) the probability of fewer than 450 diversions
P(fewer than 450 diversion ) = P( X ≤ 450 )
= P( X ≤ 449.5 )
so
z = (X - μ) / σ
we substitute
z = (449.5 - 406.32 ) / 19.6677
z = 43.18 / 19.6677
z = 2.20
so
P(Z ≤ 2.20 ) = 0.500 + p( 0 ≤ z ≤ 2.20 )
= 0.5000 + 0.4861
= 0.9861
Therefore, the probability of fewer than 450 diversions is 0.9861
Please help!? Work out the size of angle x. 42 degrees and 123 degrees?
Answer:
x° = 99°
Step-by-step explanation:
Sum of angles on a straight line is 180°.
180° - 123° = 57° (sum of angles on a straight line)Sum of angles in a triangle is 180°. Let u be the value of the unknown angle in the triangle.
57° + 42° + u° = 180°u° = 180° - 57° - 42°
u° = 81°
Sum of angles on a straight line is 180°.
x° + 81° = 180°x° = 180° - 81°
x° = 99°
b→ = ⟨−1,3⟩ and c→ = ⟨−11,−2⟩.
What is c→ + b→ in component form?
Enter your answer by filling in the blanks.
c→+b→ = ⟨ __ , __ ⟩
Answer:
-12,1
(-12î, 1j)
is the ans
Answer:
The answer is, (-12î, 1j)
Step-by-step explanation:
Definition of component form:The ordered pair that describes the changes in the x- and y-values is the component form of a vector. the ordered pair that describes the changes is [tex](x_{2} -x_{1} ,y_{2} -y_{1} )[/tex].
According, to the question:
= (-11-1),(-2+3)
= -12,1
= (-12î, 1j)
The component form are (-12î, 1j)
To know more component form here, https://brainly.com/question/13450744
#SPJ2
It's free!
Enjoy! :)
A triangular pyramid is 30 meters tall and has a base area of 500 square meters. What is the volume of the pyramid?
A) 7,500
B) 5,000
C) 15,000
D) 6,200
Answer:
C
Step-by-step explanation:
if it has a base area that means 500/4 = 125 so each side is 125 on the base.
The formula for the volume of a triangular pyramid is 1/3lwh.
if L=125 and w=125 and H= 30
we multiply 125·125·30=468750
and 468750/3=156250
so rounding that, our base would be C)15,000
A side of 6 feet, and a 120° angle
A. One
B. None. C. Many
Answer:
C. Many ang sagot............
An army of clone warriors is quadrupling every year. If the army started with only one warrior
named Clone Alpha, how many clones will there be in a decade?
A) 262,144 clones
B) 4,194,304 clones
C) 1,048,576 clones
D 10,485,760 clones
Answer:
C) 1,048,576 clones
Step-by-step explanation:
An army of clone warriors is quadrupling every year.
This means that the amount of clone warriots after t years is given by:
[tex]A(t) = A(0)4^t[/tex]
Started with only one warrior:
This means that [tex]A(0) = 1[/tex], so:
[tex]A(t) = 4^t[/tex]
How many clones will there be in a decade?
A decade is 10 years, so this is A(10).
[tex]A(10) = 4^{10} = 1,048,576[/tex]
The correct answer is given by option C.
what is 13 more than 3 times a number is 34 and what is the solution
Answer:
13 + 3x = 34
Variables:
x = random number
The critic rating and audience score for 8 movies are shown in the table.
Critic Rating 72 80 65 23 28 60 41 35
Audience Score 64 92 90 48 55 70 44 80
An owner of a movie theater is investigating whether critic rating can be used to predict the mean audience score of movies. Assuming the conditions for inference have been met, which of the following inference procedures is the most appropriate to estimate the mean change in audience score for each 1 point increase in the critic rating?
A. A one-sample t-test for means
B. A linear regression t-interval for slope
C. A two-sample t-interval for a difference between means
D. A matched-pairs t-interval for a mean difference
E. A two-sample Z-interval for a difference between proportions
Answer:
B. A linear regression t-interval for slope
Step-by-step explanation:
Given the data for the critic rating and audience score, the relationship between this vmaues acb be modeled using regression, the slope value helps give the average change in the dependent variable (audience svi per unit change in the value of the independent variable (critic rating). The t distribution is employed due to the relatively small sample size which
does not form an approximately normal distribution according to the Central limit theorem.
Find the area of this circle.
6 in.
Use 3.14 for
pls help find area and perimeter
Answer:
A is 14 and P is 17
Step-by-step explanation:
working is above mentioned
Plsss help mark brain list
Answer:
105
Step-by-step explanation:
42 * 2 = 84
360 - ( 84+171 ) = 105
Answer:
arc RS = 105°
Step-by-step explanation:
arc RT = 2(42°) = 84°
arc RS = 360° - 84° - 171° = 105°
6 - 7x
a) constant binomial
b) linear binomial
c) quadratic binomial
d) cubic trinomial
Answer:linear binomial
Step-by-step explanation:
Answer:
B) Linear binomial.
Step-by-step explanation:
????
a2+9a+18
Can someone factor this for me
Answer:
(a+3)(a+6)
Step-by-step explanation:
a(a+6)+3(a+6)
(a+3)(a+6)
Researchers collected data from 100 randomly chosen counties in Texas on pollution levels and asthma rates. Pollution levels were measured by calculating the average number of air particulates (in mg/m3) and asthma rates were calculated as the percent of residents (0-100%) diagnosed with asthma. After confirming all relevant assumptions, they ran a linear model predicting asthma rates based on pollution level: Estimate Std. Error (Intercept) 3.61 2.05 pollution 0.78 0.29 Are pollution levels in Texas counties a significant linear predictor of asthma rates
Answer:
The answer is "3.14".
Step-by-step explanation:
The coefficient of pollution level is "b" and "a" intercept
[tex]\to y=a+bx\\\\[/tex]
We must verify it.
[tex]H_0 :\beta = 0\\\\H_a : \beta \neq 0\\\\[/tex]
[tex]Beta \to b=1.76, SE=0.56 \ Estimate[/tex]
The statistics on tets are now provided
[tex]\to t=\frac{b}{SE}=\frac{1.76}{0.56}=3.14[/tex]
Because statistics will be more than critical [tex](1.984)[/tex] values, we thus reject[tex]H_0[/tex]
40 pts please help (:
Find the geometric probability of throwing a dart and hitting the yellow ring. You may assume the dart will not miss the target entirely.
Answer:
c
Step-by-step explanation:
Answer:
i think it d
Step-by-step explanation:
sorry if it turn out wrong
State the null and alternative hypotheses for the situation described below for a statistical test. Testing to see if average sales are higher in stores where customers are approached by salespeople than in stores where they aren't. Let group be the group of stores where customers are approached by salespeople and let group be the group of stores where customers are not approached by salespeople.
Complete question is;
State the null and alternative hypotheses for the situation described below for a statistical test. Testing to see if average sales are higher in stores where customers are approached by salespeople than in stores where they aren't. Let group 1 be the group of stores where customers are approached by salespeople and let group 2 be the group of stores where customers are not approached by salespeople
Answer:
Null hypothesis; H0; μ1 = μ2
Alternative hypothesis; Ha; μ1 > μ2
Step-by-step explanation:
Group 1 = the group of stores where customers are approached by salespeople
Group 2 = the group of stores where customers are not approached by salespeople
Now, we want to test to check if average sales are higher in stores where customers are approached by salespeople than in stores where they aren't.
Thus, defining the hypotheses, we have;
Null hypothesis; H0; μ1 = μ2
Alternative hypothesis; Ha; μ1 > μ2
i need this fast thank you! :)
Answer:
C
Step-by-step explanation:
Hope this helps! Good Luck!
a
explanation
1/5280 = 5/x
the 1 and 5 represent the miles
5280 and x represent the total ft
so 5280 x 5 would be how to solve x because whatever you do the top you do the bottom which 1 x 5 being 5 so 5280 x 5 being 26400Write an equation in slope and intercept form of the line (0,4) and (2,0)
Answer:
y = -2x + 4
Step-by-step explanation:
1) First, find the slope of the line between the two points. Use the slope formula [tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex] and substitute the x and y values of (0,4) and (2,0) into it. Then, solve:
[tex]m = \frac{(0)-(4)}{(2)-(0)} \\m =\frac{0-4}{2-0} \\m = \frac{-4}{2} \\m = -2[/tex]
So, the slope is -2.
2) Now, identify the y-intercept of the line, or the point at which the line intersects the y-axis. All points on the y-axis have an x-value of 0. We're told that the line intersects (0,4), and that point has an x-value of 0. Thus, it must be the y-intercept.
3) With the found information, write the equation of the line in slope-intercept form, represented by the equation [tex]y = mx + b[/tex]. The [tex]m[/tex] , or the coefficient of the x-term, represents the slope. So, substitute -2 in its place. The [tex]b[/tex] represents the y-intercept of the line, so substitute 4 in its place. This gives the following answer:
[tex]y = -2x + 4[/tex]
Is 4/5 closer to 0,1/2, or 1?
Answer:
1
Step-by-step explanation:
4/5 is closer to 1
Find cot theta if 180° < theta < 270° and cos theta = - sqrt 3/2
Answer:
cot theta = -√3
Step-by-step explanation:
we are given that cos theta = - √3/2 within the range 180° < theta < 270° and
since cos theta = adj/hyp
adj = - √3
hyp = 2
Get the opposite using the pythagoras theorem
hyp^2 = opp^2 + adj^2
2² = opp² + (-√3)²
4 = opp² + 3
opp² = 4-3
opp² = 1
opp = 1
tan theta = opp/adj
tan theta = - 1/√3
Recall that cot theta = 1/tan theta
cot theta = 1/(-1/√3)
cot theta = -√3
х
Renaissance
Х
S M/JIB MYP MATH 1: Period 8-E X
B Post Attendee - Zo
ity-player/starcal/start
Jenna Hill
Ela is building a fence around her yard. She is
using boards that are 0.44 feet wide. She needs
enough boards to build 99 feet of fence. She will
place the boards side by side.
How many boards will Ela need?
Answer:
225 boards
Step-by-step explanation:
99 ft/0.44 ft = 225 ft
Erin competes in track meets. She has won blue ribbons and red ribbons. For every 3 blue ribbons she has won, she has won 2 red ribbons. At this rate, how many red ribbons will Erin have won after she has won 9 blue ribbons?
Question 9 options:
6 red
4 red
5 red
11 red
Answer:
the answer is A. 6 red
Step-by-step explanation:
3*3=9 3*2=6
Convert 42°F to degrees Celsius. If necessary, round your answer to the nearest tenth of a degree. Here are the formulas
c=5/9(F-32)
F=9/5 C+32
9514 1404 393
Answer:
5.6 °C
Step-by-step explanation:
Put the number in the formula and do the arithmetic.
C = 5/9(42 -32) = 5/9(10) = 50/9 = 5 5/9
42 °F ≈ 5.6 °C
Write 9/5 as a decimal number.
Answer:
1.8
Step-by-step explanation:
you have to divide 9 from 5 to get 1.8
Answer:
Decimal 1.8
Percentage 180%
Step-by-step explanation:
8. The difference between two numbers is 33 and the ratio
between them is 5:2. Find the numbers
Answer:
Step-by-step explanation:
x - y = 33
x/y = 5/2 Multiply both sides by y
y*x/y =5y/2
x = 5y/2 Multiply both sides by 2
2x = 5y Multiply the top equation by 2. Bring 5y to the left
2x - 2y = 66
====================
2x - 5y = 0
2x - 2y = 66 Subtract
-3y = - 66 Divide by - 3
y = 22
x - y = 33
x - 22 = 33 Add 22 to both sides
x = 22 + 33
x = 55
Multiplying Polynomials write in standard form
(x+3)(x+4)
Answer:
x² + 7x + 12
Step-by-step explanation:
1. (x +3)(x+4) - Distribute
2. x² + 4x +3x + 12 - Add like terms
3. x² +7x + 12
PLEASE HELP !! ILL GIVE BRAINLIEST !!
A certain store sells only T-shirts. Let the random variable X represent the number of T-shirts bought from the store on any day, with a mean of 75 and a standard deviation of 20. Let the random variable Y be the total revenue from this store on a randomly selected day. If the store charges $15 per T-shirt, what are the mean and standard deviation of Y
Answer:
[tex](a)\ \mu_y = 1125[/tex]
[tex](b)\ \sigma_y = 300[/tex]
Step-by-step explanation:
Given
[tex]\mu_x = 75[/tex] -- Mean of T-shirts
[tex]\sigma_x = 20[/tex] -- Standard deviation of T-shirts
[tex]Rate = \$ 15[/tex]
Solving (a): The mean of the revenue [tex](\mu_y)[/tex]
To solve this, we use:
[tex]\mu_y = Rate * \mu_x\\[/tex]
This gives:
[tex]\mu_y = 15 * 75[/tex]
[tex]\mu_y = 1125[/tex]
Solving (b): The standard deviation of the revenue [tex](\sigma_y)[/tex]
To solve this, we use:
[tex]\sigma_y = \sqrt{Rate^2 * \sigma_2^2}[/tex]
This gives:
[tex]\sigma_y = \sqrt{15^2 * 20^2}[/tex]
[tex]\sigma_y = \sqrt{90000}[/tex]
[tex]\sigma_y = 300[/tex]
Question 30
What was the median annual earnings for all U.S. civilian workers in 2016?
O $51,980
O $49,630
O $41,778
O $46,230