Answer:
[tex]\huge\boxed{r<8}[/tex]
Step-by-step explanation:
[tex]5 > r - 3[/tex]
Adding 3 to both sides
[tex]5 + 3 > r[/tex]
[tex]8 > r\\OR \\r < 8[/tex]
Answer: D. r<8
Step-by-step explanation:
[tex]5>r-3[/tex]
add 3 to both sides
[tex]r-3+3<5+3[/tex]
[tex]5+3=8[/tex]
simplify
[tex]r<8[/tex]
Among a simple random sample of 331 American adults who do not have a four-year college degree and are not currently enrolled in school, 48% said they decided not to go to college because they could not afford school.
Part II: Exercise 6.16 presents the results of a poll where 48% of 331 Americans who decide to not go to college do so because they cannot afford it.
#1: Calculate a 90% confidence interval for the proportion of Americans who decide to not go to college because they cannot afford it, and interpret the interval in context.
(a) lower bound: ______ (please round to four decimal places)
(b) upper bound: _____ (please round to four decimal places)
#2: Interpret the confidence interval in context:
(A) We can be 90% confident that our confidence interval contains the sample proportion of Americans who choose not to go to college because they cannot afford it
(B) 90% of Americans choose not to go to college because they cannot afford it
(C) We can be 90% confident that the proportion of Americans who choose not to go to college because they cannot afford it is contained within our confidence interval
#3: Suppose we wanted the margin of error for the 90% confidence level to be about 1.5%. How large of a survey would you recommend?
(a) A survey should include at least ________ people.
Answer:
(1) Therefore, a 90% confidence interval for the proportion of Americans who decide to not go to college because they cannot afford it is [0.4348, 0.5252].
(2) We can be 90% confident that the proportion of Americans who choose not to go to college because they cannot afford it is contained within our confidence interval
(3) A survey should include at least 3002 people if we wanted the margin of error for the 90% confidence level to be about 1.5%.
Step-by-step explanation:
We are given that a simple random sample of 331 American adults who do not have a four-year college degree and are not currently enrolled in school, 48% said they decided not to go to college because they could not afford school.
Firstly, the pivotal quantity for finding the confidence interval for the population proportion is given by;
P.Q. = [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = sample proportion of Americans who decide to not go to college = 48%
n = sample of American adults = 331
p = population proportion of Americans who decide to not go to
college because they cannot afford it
Here for constructing a 90% confidence interval we have used a One-sample z-test for proportions.
So, 90% confidence interval for the population proportion, p is ;
P(-1.645 < N(0,1) < 1.645) = 0.90 {As the critical value of z at 5% level
of significance are -1.645 & 1.645}
P(-1.645 < [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < 1.645) = 0.90
P( [tex]-1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < [tex]\hat p-p[/tex] < [tex]1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.90
P( [tex]\hat p-1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < p < [tex]\hat p+1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.90
90% confidence interval for p = [ [tex]\hat p-1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] , [tex]\hat p+1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ]
= [ [tex]0.48 -1.96 \times {\sqrt{\frac{0.48(1-0.48)}{331} } }[/tex] , [tex]0.48 +1.96 \times {\sqrt{\frac{0.48(1-0.48)}{331} } }[/tex] ]
= [0.4348, 0.5252]
(1) Therefore, a 90% confidence interval for the proportion of Americans who decide to not go to college because they cannot afford it is [0.4348, 0.5252].
(2) The interpretation of the above confidence interval is that we can be 90% confident that the proportion of Americans who choose not to go to college because they cannot afford it is contained within our confidence interval.
3) Now, it is given that we wanted the margin of error for the 90% confidence level to be about 1.5%.
So, the margin of error = [tex]Z_(_\frac{\alpha}{2}_) \times \sqrt{\frac{\hat p(1-\hat p)}{n} }[/tex]
[tex]0.015 = 1.645 \times \sqrt{\frac{0.48(1-0.48)}{n} }[/tex]
[tex]\sqrt{n} = \frac{1.645 \times \sqrt{0.48 \times 0.52} }{0.015}[/tex]
[tex]\sqrt{n}[/tex] = 54.79
n = [tex]54.79^{2}[/tex]
n = 3001.88 ≈ 3002
Hence, a survey should include at least 3002 people if we wanted the margin of error for the 90% confidence level to be about 1.5%.
From a group of 11 people, 4 are randomly selected. What is the probability the 4 oldest people in the group were selected
The probability that the 4 oldest people in the group were selected is based on combinatorics is 0.00303 or 0.303%.
Given that:
Find how many ways the 4 oldest people can be selected from the group.
Since the 4 oldest people are already determined, there is only 1 way to select them.
n = 11 (total number of people in the group) and k = 4 (number of people to be selected).To calculate the probability, to determine the total number of ways to select 4 people from the group of 11. This can be found using the combination formula:
Number of ways to choose k items from n items :
C(n,k) = n! / (k!(n-k)!)
Calculate the total number of ways to select 4 people from the group:
Plugging n and k value from given data:
C(11,4 )= 11! / (4!(11-4)!)
On simplifications gives:
C(11, 4) = 330.
Calculate the probability:
Probability = Number of ways 4 oldest people selected / Total number of ways to select 4 people
Plugging the given data:
Probability = 1 / 330
Probability ≈ 0.00303 or 0.303%.
Therefore, the probability that the 4 oldest people in the group were selected is based on combinatorics is 0.00303 or 0.303%.
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The function g is defined as follows for the domain given.
g(x) = 2x+1,
domain = (-5, -1, 2, 3)
Write the range of g using set notation. Then graph g
Answer:
g(x): 2(-5)+1= -10+1=-9
2(-1)+1= -2+1=-1
2(2)+1= 4+1=5
2(3)+1=6+1= 7
Hence, the range of [tex]g[/tex] using the set notation is [tex](-9,-1,5,7)[/tex].
What is the function?
Functions are often defined by a formula that describes a combination of arithmetic operations and previously defined functions; such a formula allows computing the value of the function from the value of any element of the domain.
Here given that,
The function g is defined as follows for the domain given.
[tex]g(x) = 2x+1,[/tex] and domain [tex]= (-5, -1, 2, 3)[/tex]
So,
[tex]x=-5\\2(-5)+1\\= -10+1\\=-9\\\\x=-1\\2(-1)+1\\= -2+1\\=-1\\\\x=2\\2(2)+1\\= 4+1\\=5\\\\x=3\\2(3)+1\\=6+1\\= 7[/tex]
Hence, the range of [tex]g[/tex] using the set notation is [tex](-9,-1,5,7)[/tex].
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Sarah needs to go to five different stores. How many ways can she go to two of them before lunch?
Answer:
10
Step-by-step explanation:
Solution 1: At first, you might think that because there are 5 ways to choose the first store and 4 ways to choose the second store, the answer is 5 * 4 = 20 but this is over-counting by a factor of 2. Say that two of the stores are A and B. If she went to A then B, that's the same as going to B then A since you still go to the same stores, therefore, the answer is 20 / 2 = 10.
Solution 2: We need to find the number of ways to choose 2 stores from 5, we can do this by calculating ₅C₂ which equals:
5! / 2! * 3!
= 5 * 4 * 3 * 2 * 1 / 2 * 1 * 3 * 2 * 1
= 5 * 4 / 2 * 1
= 10
Factor by grouping cd-9d-4c+36
Answer:
(d-4)(c-9)
Step-by-step explanation:
cd-9d-4c+36
d(c-9)-4(c-9)
pull out the (c-9),
(d-4)(c-9)
1 A. All master photographers are artists.
2. Ansel Adams is a master photographer.
Therefore, Ansel Adams is an artist.
B. 1. All master photographers are artists.
2. Ansel Adams is an artist.
Therefore, Ansel Adams is a master photographer.
Answer:
A is the appropriate option.
Step-by-step explanation:
The question given is a conditional statement.
With the condition that all master photographers are artist. This implies that any person who is a master photographer is automatically an artist.
A. Comparing the statement here, since Ansel Adam's is a master photographer, he is an artist.
B. Ansel Adams is an artist, but it is possible that not all artists are master photographer.
A is the correct option.
1. All master photographers are artists.
2. Ansel Adams is a master photographer.
Therefore, Ansel Adams is an artist.
Answer:
The correct answer is A.
Step-by-step explanation:
HELP ASAP ROCKY!!! will get branliest.
Answer:
work pictured and shown
Answer:
Last one
Step-by-step explanation:
● [ ( 3^2 × 5^0) / 4 ]^2
5^0 is 1 since any number that has a null power is equal to 1.
●[ (3^2 ×1 ) / 4 ]^2
● (9/4)^2
● 81 / 16
In your own words, define Quadratic Equation. How many solutions does a Quadratic Equation have?
Answer: an equation that has one term which is nameless and squared also no term which gets raised to higher power.
Step-by-step explanation:
A passenger train traveled 180 miles in the same amount of time it took a freight train to travel 120 miles. The rate of the freight train was 15 miles per hour slower than the rate of the passenger train. Find the rate of the passenger train.
Answer:
The passenger train is moving at 45 miles per hour
Step-by-step explanation:
Let the amount of time it took the two trains to travel the distance = t.
Since the two trains traveled the distance at the same time,
Rate of the passenger train =[tex]\frac{180}{t}[/tex]
Rate of the freight train = [tex]\frac{120}{t}[/tex]
Where t is in hours.
From the problem, we can see that the rate of the freight train was 15 miles per hour slower than the rate of the passenger train. Mathematically, we can represent this as
[tex]\frac{120}{t}= \frac{180}{t}-15[/tex]
from the above equation, we can now get our value for t as
[tex]\frac{120-180}{t}=-15\\\frac{-60}{t}=-15\\t=4 hours[/tex]
We have our time of travel for the two trains as 4 hours.
The rate of the passenger train can now be calculated by 180/4 = 45 miles per hour
Multiply: (x−5)(x−7) A x2−12x+35 B x2+2x+35 C x2+35 D x2+35x−12
Answer:
x^2 -12x+35
Step-by-step explanation:
(x−5)(x−7)
FOIL
first x*x = x^2
outer -7x
inner -5x
last -7*-5 = 35
Add them together
x^2 -7x-5x +35
x^2 -12x+35
Answer:
Step-by-step explanation:
x*x=2x
x*-7=-7x
-5*x=-5x
-5*-7=+35
2x-12x+35
A
Kent Co. manufactures a product that sells for $60.00. Fixed costs are $285,000 and variable costs are $35.00 per unit. Kent can buy a new production machine that will increase fixed costs by $15,900 per year, but will decrease variable costs by $4.50 per unit. What effect would the purchase of the new machine have on Kent's break-even point in units?
0riginal break even point:
285000/ 60/35 = $166,250
New break even point = new fixed costs / ( selling price - variable cost/ selling price)
New break even point = 285,000 + 15,900. / ( 60-( 35-4.50)/60
300,900 / 60-30.50/60 = $612,000
The new break even point increases.
10. (01.02)
Given the function f(x)
3x - 4
5
which of the below expressions is correct? (1 point)
5x+4
f-1(x) =
3
f-1(x)
5x - 4
3
O f-'(x)
-344
-3x – 4
5
4–3x
f-1(x) =
5
Answer:
5x+4f-1(x)=3 this is short answer
Multiple Choice The opposite of –4 is A. 4. B. –4. C. –(–(–4)). D. –|4|.
Answer:
a. 4
Step-by-step explanation:
-1(-4) = 4
Answer:
A 4
Step-by-step explanation:
opposite of –4 = 4
If h(x)=-2x-10 ,find h(-4)
Answer:
h(-4) = -2
Step-by-step explanation:
h(x)=-2x-10
Let x = -4
h(-4)=-2*-4-10
=8-10
= -2
Answer:
[tex]\huge \boxed{{-2}}[/tex]
Step-by-step explanation:
[tex]\sf The \ function \ is \ given:[/tex]
[tex]h(x)=-2x-10[/tex]
[tex]\sf To \ find \ h(-4), \ put \ x=-4.[/tex]
[tex]h(-4)=-2(-4)-10[/tex]
[tex]h(-4)=8-10[/tex]
[tex]h(-4)=-2[/tex]
Consider the polynomial 2x5 + 4x3 - 3x8
Part A The polynomial in standard form is:
Part B: The degree of the polynomial is:
Part C: The number of terms in the polynomial is:
Part D: The leading term of the polynomials:
Part E: The leading coefficient of the polynomial is:
Answer:
Step-by-step explanation:
Considering the polynomial 2x⁵ + 4x³ - 3x⁸. The polynomial is not yet in standard form. For a polynomial to be in standard form, the power of the variables must decrease as we progress to the right of the expression.
A) The polynomial in standard form is therefore - 3x⁸ + 2x⁵ + 4x³. We can see that the power are reducing as we move through each terms i.e from 8 to 5 then to 3.
B) The degree of a polynomial is the maximum degree among all the terms of the polynomial. The term that has the maximum degree is -3x⁸. Hence, the degree of the polynomial is 8
C) There are only 3 terms in the polynomial given. The terms are separated by mathematical signs. The terms if the polynomial are 2x⁵, 4x³ and - 3x⁸.
D) The leading term of the polynomial is the term that comes first after rewriting the polynomial in standard format. Given the standard from of the polynomial given as -3x⁸ + 2x⁵ + 4x³, the leading term will be - 3x⁸
E) Given the leading term to be - 3x⁸, the leading coefficient of the polynomial will be the coefficient of the leading term. The coefficient of -3x⁸ is -3
for the first one the answer are
add 5 to both sides
subtract 5 from both sides
add 1/2x to both sides
subtract 1/2 from both sides
the second one is
multiply both sides by 1/5
dived both sides by 1/5
multiply both sides by 6/7
dived both sides by 6/7
Answer:
1. add 1/2x to both sides
a. you want to combine the like terms. in this case, it is the x variable.
you are left with 7/6x = 5
2. multiply by 6/7
a. the reciprocal of 7/6 will cancel out the values
Please help. I’ll mark you as brainliest if correct!
Answer:
9 3 -7 -13
4 -4 11 8
0 9 2 -4
Step-by-step explanation:
9 3 -7 -13
4 -4 11 8
0 9 2 -4
Answer: 9 3 -7 -13
4 -4 11 8
0 9 2 -4
Step-by-step explanation:
Will give brainliest. A farmer is painting a new barn. He will need to calculate the surface area of the barn to purchase the correct amount of paint. In which of the following units can the farmer expect to calculate the surface area? yd2 yd m3 m
Answer:
yd^2
Step-by-step explanation:
I took the test :)
The farmer calculate surface area in unit of [tex]yd^{2}[/tex]
Surface area :The surface area of any given object is the area or region occupied by the surface of the object.
Volume is the amount of space available in an object. Each shape has its surface area as well as volume.Surface area is the total area of the faces of a three-dimensional shape. Surface area is measured in square units.Thus , The farmer calculate surface area in unit of [tex]yd^{2}[/tex]
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Yiadom is y
years now.
What would be
his age in the next ten
years.
Answer:
(y+10 ) years
Step-by-step explanation:
If Yiadom is y years now.
Then after 10 years, his anew age will be = (y+10) yrs
Find xAssume that segments that appear tangent are tangent
Step-by-step explanation:
I assume the length that got cut off is 18.
Use Pythagorean theorem:
x² + 36² = (x + 18)²
x² + 1296 = x² + 36x + 324
972 = 36x
x = 27
URGENT, PLEASE HELP ! (2/5) - 50 POINTS - ! please no wrong answers for points. ! Which scatter plot represents the data?
Answer:
A has the points plotted correctly
Step-by-step explanation:
We need to plot the data
A has the points plotted correctly
B has the point ( 10,5) plotted on (9,5)
C is missing (-6,-5)
D is missing (-6,-5) and has (-2,1) instead of (-2,-1)
Answer:
A.
Step-by-step explanation:
It would be very helpful to write the points individually from the data. Take the x value and place it with its corresponding y value:
(1,4) ; (2,2) ; (-2,-1) ; (-2,-6) ; (5,-4) ; (-6,-5) ; (10,5)
Now find the graph that has each of these points. You can write these down and cross them out if you find them on the graph, and once you find the graph where all of these points are crossed out, that's the correct graph.
The correct graph is A.
:Done
The algebraic expression for the product of five and the cube of a number decreased by 40
Answer:
5a³ - 40
Step-by-step:
The algebraic expression is:
5a³ - 40
The local resale store buys used designer jeans for $15. The
store increases their purchase price by 400%. What is the
sale price of the designer jeans?
the answer to your question is $75
PLEASE ANSWER ASAP!!!
Melissa is able to Rollerblade 100 feet in 3.8 seconds. Calculate how fast she Rollerblade in miles per hour?
Answers options given will be in picture
any unrelated answer will be reported
Answer:
A
Step-by-step explanation:
100fps=68.182mph
68.182/3.8=17.94
Mellissa's speed will be 17.94 mph.
What is speed?Speed is defined as the ratio of the time distance travelled by the body to the time taken by the body to cover the distance.
It is given that Melissa is able to Rollerblade 100 feet in 3.8 seconds.
We know that 100fps is equal to 68.182mph.
Mellissa's speed in meters per hour is calculated as:-
S = 68.182/3.8=17.94mph
Therefore, Mellissa's speed will be 17.94 mph.
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radical 16 * redical 12
[tex]\sqrt{16}\times\sqrt{12}[/tex]
$=\sqrt{4^2}\times\sqrt{2^2\cdot3}$
$=4\times2\sqrt3=8\sqrt3$
Find the equation of the line passing through the pair points (-8,6) (-9,-9). The equation of the line in the form is Ax+By=C.
Answer:
15x - y = - 126
Step-by-step explanation:
will make it simple and short
first we need to find the slope (m) first in order to get the equation
given: (-8,6) (-9,-9)
y2 - y1 -9 - 6
Slope = m = ----------- = ------------------ = 15
-x2 - x1 -9 - (-8)
so the equation of the line using point (-8,6) and slope 15 is y - 6 = 15( x + 8)
y - 6 = 15x + 120
using the form equation Ax + By = C, 15x - y = -120-6
therefore... 15x - y = - 126 is the answer
omplete the following multiplication problems.
a. 0.34 × 6
b. 0.11 × 4
c. 17 × 0.07
d. 28 × 0.003
e. 3.8 × 5
f. 5.931 × 7
g. 14.07 × 13
h. 3.005 × 32
i. 0.8 × 0.3
j. 0.45 × 0.05
k. 0.09 × 0.02
l. 0.074 × 0.08
m. 2.3 × 0.9
n. 7.25 × 0.3
o. 4.53 × .003
p. 53.67 × 0.056
q. 1.1 × 3.7
r. 3.76 × 18.9
s. 4.57 × 6.1
t. 24.13 × 1.48
How far from the base of the house do you need to place a 13-foot ladder so that it exactly reaches the top of a 10-feet wall?
Answer:
√69 or 8.3 feets
Step-by-step explanation:
Hypotenuse=13
Therefore
13²=x²+10²
x²=169-100
x²=69
x=√69 feets
The distance from the base of the house is 8.3 feet.
What is the pythagoras theorem?The pythagoras theorem is used to obtain the sides of a right angled triangle.
Given that;
The hypotenues of the triangle is 13-foot
The length of the opposite side is 10 feet
Thus;
13^2 = 10^2 + a^2
a^2 = 13^2 - 10^2
a = √13^2 - 10^2
a = 8.3 feet
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What is the solution set for StartAbsoluteValue z + 4 EndAbsoluteValue greater-than 15? 11 less-than z less-than 19 Negative 19 less than z less-than 11 z less-than negative 19 or z greater-than 11 z less-than 19 or z greater-than 11
Answer:
z less-than negative 19 or z greater-than 11Step-by-step explanation:
Given the inequality [tex]|z+4|>15[/tex], we are to find the solution set of the inequality. Since the the function is an absolute value, this means that the function will be positive and negative.
For the positive value of the function;
[tex]z+4>15\\\\subtract\ 4\ from \ both \ sides\\z+4-4 > 15 -4\\\\z>11[/tex]
For the negative value of the function we have;
[tex]-(z+4) > 15\\\\-z-4> 15\\add\ 4 \ to\ both \ sides\\\\-z-4+4> 15+4\\\\-z> 19\\\\[/tex]
Multiplying both sides of the inequality by -1 will change the sense of the inequality sign;'
[tex]-(-z)< -19\\\\z<-19[/tex]
Hence the solution sets are [tex]z> 11 \ and \ z< -19 \\[/tex] OR z less-than negative 19 or z greater-than 11
Answer:
z less-than negative 19 or z greater-than 11
Step-by-step explanation:
[tex]f(x) = sqr root x+3 ; g(x) = 8x - 7[/tex]
Find (f(g(x))
[tex]f(x)=\sqrt{x+3}\\g(x)=8x-7\\\\f(g(x))=\sqrt{8x-7+3}=\sqrt{8x-4}[/tex]
