Answer:
[tex]z=\frac{0.45 -0.47}{\sqrt{\frac{0.47(1-0.47)}{631}}}=-1.007[/tex]
Now we can find the p value with the alternative hypothesis and using this probability:
[tex]p_v =P(z<-1.007)=0.157[/tex]
Since the p value is higher than the significance level given of 0.05 we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true proportion of interest is not significantly lower than 0.47
Step-by-step explanation:
Information given
n=631 represent the random sample selected
X=284 represent the people who said that they thought unemployment would increase
[tex]\hat p=\frac{284}{631}=0.45[/tex] estimated proportion of people who said that they thought unemployment would increase
[tex]p_o=0.47[/tex] is the value that we want to test
[tex]\alpha=0.05[/tex] represent the significance level
z would represent the statistic
[tex]p_v{/tex} represent the p value
System of hypothesis
We want to verify if the proportion of Australians in November 1997 who believe unemployment would increase is less than the proportion who felt it would increase in July 1997 (0.47), then the system of hypothesis are:
Null hypothesis:[tex]p\geq 0.47[/tex]
Alternative hypothesis:[tex]p < 0.47[/tex]
The statistic would be given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
Replacing the info given we got:
[tex]z=\frac{0.45 -0.47}{\sqrt{\frac{0.47(1-0.47)}{631}}}=-1.007[/tex]
Now we can find the p value with the alternative hypothesis and using this probability:
[tex]p_v =P(z<-1.007)=0.157[/tex]
Since the p value is higher than the significance level given of 0.05 we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true proportion of interest is not significantly lower than 0.47
Determine which consecutive integers do not have a real zero of f(x) = x^3 + 9x^2 + 8x – 5 between them.
A.) (–8, –7)
B.) (4, 5)
C.) (0, 1)
D.) (–2, –1)
Answer:
Option B (4,5)
Step-by-step explanation:
The integers (4, 5) do not have real zero.
What is zero of a function?Knowing what zeros represent can assist us in determining when and how to locate the zeros of functions given their expressions and a function's graph. The value of x when the function itself reaches zero is typically referred to as a function's zero.
A function's zero can take many different forms, but as long as they have a y-value of zero, we will consider them to be the function's zero.
Given Expression
f(x) = x³ + 9x² + 8x - 5
to find which is not a real zero,
condition of real zero is for any function f(a , b) if f(a).f(b) < 0 the function have at least a zero.
1: (-8, -7)
f(-8).f(-7) = [(-8)³ + 9(-8)² + 8(-8) - 5][(-7³) + 9(-7)² + 8(-7) - 5]
f(-8).f(-7) = (-5)(37)
f(-8).f(-7) = -185 < 0 points have at least a zero
2: (4, 5)
f(4).f(5) = [(4)³ + 9(4)² + 8(4) - 5][(5³) + 9(5)² + 8(5) - 5]
f(4).f(5) = 235 x 385
f(4).f(5) = 94,475 > 0
points do not have any zeros
3: (0, 1)
f(0).f(1) = [(0)³ + 9(0)² + 8(0) - 5][(1³) + 9(1)² + 8(1) - 5]
f(0).f(1) = -5 x 13
f(0).f(1) = -65 < 0
points have a zero
4: (–2, –1)
f(-2).f(-1) = [(-2)³ + 9(-2)² + 8(-2) - 5][(-1³) + 9(-1)² + 8(-1) - 5]
f(-2).f(-1) = 7 x (-5)
f(-2).f(-1) = -35 < 0
points have a zero
Hence only point (4, 5) do not have a zero.
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A university found that 20% of its students withdraw without completing the introductory statistics course. Assume that 20 students registered for the course. (Round your answers to four decimal places.) (a) Compute the probability that 2 or fewer will withdraw. (b) Compute the probability that exactly 4 will withdraw. (c) Compute the probability that more than 3 will withdraw. (d) Compute the expected number of withdrawals.
Answer:
(a) Probability that 2 or fewer will withdraw is 0.2061.
(b) Probability that exactly 4 will withdraw is 0.2182.
(c) Probability that more than 3 will withdraw is 0.5886.
(d) The expected number of withdrawals is 4.
Step-by-step explanation:
We are given that a university found that 20% of its students withdraw without completing the introductory statistics course.
Assume that 20 students registered for the course.
The above situation can be represented through binomial distribution;
[tex]P(X =r) = \binom{n}{r} \times p^{r} \times (1-p)^{n-r};x=0,1,2,3,......[/tex]
where, n = number of trials (samples) taken = 20 students
r = number of success
p = probability of success which in our question is probability
that students withdraw without completing the introductory
statistics course, i.e; p = 20%
Let X = Number of students withdraw without completing the introductory statistics course
So, X ~ Binom(n = 20 , p = 0.20)
(a) Probability that 2 or fewer will withdraw is given by = P(X [tex]\leq[/tex] 2)
P(X [tex]\leq[/tex] 2) = P(X = 0) + P(X = 1) + P(X = 2)
= [tex]\binom{20}{0} \times 0.20^{0} \times (1-0.20)^{20-0}+ \binom{20}{1} \times 0.20^{1} \times (1-0.20)^{20-1}+ \binom{20}{2} \times 0.20^{2} \times (1-0.20)^{20-2}[/tex]
= [tex]1 \times1 \times 0.80^{20}+ 20 \times 0.20^{1} \times 0.80^{19}+ 190\times 0.20^{2} \times 0.80^{18}[/tex]
= 0.2061
(b) Probability that exactly 4 will withdraw is given by = P(X = 4)
P(X = 4) = [tex]\binom{20}{4} \times 0.20^{4} \times (1-0.20)^{20-4}[/tex]
= [tex]4845\times 0.20^{4} \times 0.80^{16}[/tex]
= 0.2182
(c) Probability that more than 3 will withdraw is given by = P(X > 3)
P(X > 3) = 1 - P(X [tex]\leq[/tex] 3) = 1 - P(X = 0) - P(X = 1) - P(X = 2) - P(X = 3)
= [tex]1-(\binom{20}{0} \times 0.20^{0} \times (1-0.20)^{20-0}+ \binom{20}{1} \times 0.20^{1} \times (1-0.20)^{20-1}+ \binom{20}{2} \times 0.20^{2} \times (1-0.20)^{20-2}+\binom{20}{3} \times 0.20^{3} \times (1-0.20)^{20-3})[/tex]
= [tex]1-(1 \times1 \times 0.80^{20}+ 20 \times 0.20^{1} \times 0.80^{19}+ 190\times 0.20^{2} \times 0.80^{18}+1140\times 0.20^{3} \times 0.80^{17})[/tex]
= 1 - 0.4114 = 0.5886
(d) The expected number of withdrawals is given by;
E(X) = [tex]n\times p[/tex]
= [tex]20 \times 0.20[/tex] = 4 withdrawals
What can be determined by looking at the factored form of the polynomial f(x) = (x + 7)(x - 2) ?
A
The graph of the polynomial has zeros at (0,-7) and (0,2)
В
The graph of the polynomial has zeros at (7,0) and (-2,0)
C
The graph of the polynomial has zeros at (-7,0) and (2,0)
D
The graph of the polynomial has zeros at (0,7) and (0,-2)
Answer:
C . The graph of the polynomial has zeros at (-7,0) and (2,0)
Step-by-step explanation:
f(x) = (x + 7)(x - 2)
Zero's obtained:
(x+7)(x-2) = 0x+7 = 0 ⇒ x = -7x-2 = 0 ⇒ x = 2Coordinates:
(-7, 0) and (2, 0)Correct answer choice is:
C . The graph of the polynomial has zeros at (-7,0) and (2,0)
A 5000-seat theater has tickets for sale at $28 and $40. How many tickets should be sold at each price for a sellout performance to generate a total revenue of $153 comma 200?
Answer:
Let's denote:
x: number of ticket 28$
y: number of ticket 40$
Then, we have:
x + y =5000
28x + 40y = 153200
=> 28(5000 - y) + 40y = 153200
=> 12y = 153200 - 140000
=> 12y =13200
=> y = 1100 (ticket 40$)
=> x = 5000 - 1100 = 3900 (ticket 28$)
Bob, Paula and Sam invest $50000 in a business. Bob invests $4000 more than Paul does and Paul invests $5000 more than Sam does. If the total profit was $70000, select the correct answer. Note that the profit is distributed proportionally based on the respective amount each invested. A. The ratio of the investment of Bob, Paula and Sam is 11:15:10. B. The ratio of the investment of Bob, Paula and Sam is 12:17:21. C. The ratio of the investment of Bob, Paula and Sam is 12:5:4. D. The profit of Paula was $23,800
Answer:
D
Step-by-step explanation:
since sam invest the least, let a be the amount invested by sam
sam = a
paul = a + 5000
bob = a + 5000 + 4000
3a + 14000 = 50000
3a = 36000
a = 12000
thus sam is 12000, paul is 17000 and Bob is 21000
therefore the ratio of B:P:S is 21:17:12
profit by paula is 17/50 x 70000 = 23800
The profit by Paula is 17/50 x 70000 = 23800.
We have given that Bob, Paula and Sam invest $50000 in a business. Bob invests $4000 more than Paul does and Paul invests $5000 more than Sam does. If the total profit was $70000
Since sam invest the least, let a be the amount invested by sam
Therefore we get,
sam = a
What is the investment of Paul?
The investment of Paul = a + 5000
Bob = a + 5000 + 4000
3a + 14000 = 50000
3a = 36000
divide both sides by 3 so we get,
a=36000/3
a = 12000
Therefore, sam is 12000,
paul =5000+12000=17000 and
Bob =12000+9000= 21000
Therefore the ratio of B:P:S is 21:17:12
The profit by Paula is 17/50 x 70000 = 23800.
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Jim just found a job with a take-home pay of $950 per month. He must pay $400 for rent and $100 for groceries each month. He also spends $100 per month on transportation. If he budgets $50 each month for clothing, $100 for restaurants and $50 for everything else, how long will it take him to save $1,800?
Answer:12 months
Step-by-step explanation:
400+400=800 so 950-800=150 1800/150=12
Which expression has the same value as the one below?
22+(-32)
○ 22+(-22)+(-10)
○22+(22)+(-10)
○22+(-22)+(10)
○22+0+32
Answer:
Option A
Step-by-step explanation:
22+(-32) is the same thing as 22-32.
[tex]22-32=-10[/tex]
Let's see if the given options are equal:Option A:
[tex]22+(-22)+(-10) \\22-22-10\leftarrow \text{Distribute -1 into the Parentheses.} \\0-10\\\boxed {-10}[/tex]
Option A's expression has the same value as the expression given.
Option B:
22+(22)+(-10)
[tex]22+22-10\\44-10\\\boxed {34}[/tex]
Option B's expression does not have the same value as the expression given.
Option C:
[tex]22+(-22)+(10)\\22-22+10\\0+10\\\boxed {10}[/tex]
Option C's expression does not have the same value as the expression given.
Option D:
[tex]22+0+32\\22+32\\\boxed{54}[/tex]
Option D's expression does not have the same value as the expression given.
The correct answer should be A: 22+(-22)+(-10).Answer:
the answer is A
hoped this helped
True or false
Writing a check on an account with insufficient funds is allowed under certain conditions?
How far can a dog run into the woods?
Answer:
Half way
Step-by-step explanation:
Half way, because the dog can run all the way through the woods, but only half of the time he is going in, the rest of the time he is going out.
In the right triangle shown DF=EF=3. How long is DE?
Answer:
4.24
Step-by-step explanation:
To solve this, use the Pythagorean therom. A^2 + b^2 = C^2
in this case a = 3 and b = 3
so 9 + 9 = sqrt 18
4.24
Answer:3√(2)
Step-by-step explanation:
DF=3
EF=3
DE=√(3^2 + 3^2)
DE=√(3x3 + 3x3)
DE=√(9+9)
DE=√(18)
DE=√(2 x 9)
DE=√(2) x √(9)
DE=√(2) x 3
DE=3√(2)
A bag contains 3 red marbles and 6 blue marbles. A second bag contains 6 green marbles and 4 yellow marbles. You choose a marble from bag A and then a marble from bag B, what would be the probability of selecting one blue marble and one yellow marble?
Answer:
4/15
Step-by-step explanation:
Bag A
3 red marbles and 6 blue marbles. = 9 marbles
P(blue) = blue/total =6/9 = 2/3
Bag B
6 green marbles and 4 yellow marbles. = 10 marbles
P(yellow) = yellow/total=4/10 = 2/5
P(blue,yellow) = 2/3 * 2/5 = 4/15
Solve this system of equations.
2x + 6y = −6,
4x − 3y = −12
What is the solution to the system of equations?
Answer:
x = -3 and y = 0
Step-by-step explanation:
It would be more direct to apply elimination in this problem, rather than substitution:
2x + 6y = -6 ⇒ 2x + 6y = -6 ⇒ 10x = - 30
+ 2(4x - 3y = -12) + 8x - 6y = -24
Now let us solve for x through simply algebra:
10x = -30,
x = -3
Substitute this value of x into the first equation to get the value of y:
2( -3 ) + 6y = -6,
-6 + 6y = -6,
6y = 0,
y = 0
Answer:
-3 and 0
Step-by-step explanation:
i hope this helps :)
The number of cars sold at a dealership over several weeks is given below.
14, 23, 31, 29, 33
What is the standard deviation for this set of population data?
Standard deviation: Sigma = StartRoot StartFraction (x 1 minus mu) squared + (x 2 minus mu) squared + ellipsis + (x N minus mu) squared Over N EndFraction EndRoot
6.9
12.4
15.4
47.2
Answer:
A. 6.9
Step-by-step explanation:
Edge 2020
The standard deviation for the set of population data given in the question is 6.9
How to determine the meanData = 14, 23, 31, 29, 33Number of data (n) = 5Summation of data = 14 + 23 + 31 + 29 + 33 = 130Mean (μ) =?Mean = summation of data / number
μ = 130 / 5
μ = 26
How to determine the standard deviationData = 14, 23, 31, 29, 33Mean (μ) = 26Number of data (n) = 5Standard deviation (σ) =?σ = √[[(x₁ - μ)² + (x₂ - μ)² + (x₃ - μ)² + (x₄ - μ)² + (x₅ - μ)²] / n]
σ = √[[(14 - 26)² + (23 - 26)² + (31 - 26)² + (29 - 26)² + (33 - 26)²] / 5]
σ = √[236 / 5}
σ = 6.9
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What is the amplitude of y=3sin(2x−1)+4?
Answer:
3
Step-by-step explanation:
Amplitude is the number in front of the sin or the number multiplied by the whole equation. In this case its 3
the length of a rectangle is 4 unit less than the width. which expression represents the perimeter of the rectangle
Answer:
Length: 11
Width: 5
Step-by-step explanation:
Let W = width
Let L = length
Length is 4 less than 3 times the width ==> L = 3*W - 4
Let P = Perimeter = 2*W + 2*L
Perimeter is 22 more than twice the width ==> P = 2*W + 22
Setting the 2 expressions for the perimeter equal to each other gives
2*W + 2*L = 2*W + 22
2*L = 22
L = 11
So 11 = 3*W - 4
3*W = 15
W = 5
The length is 11 and the width is 5
Check: 3*W - 4 = 11 = Length
Perimeter = 32 = 22 more than 2*5 = 10
What is the Surface Area of the figure below?
A
60 units2
B
60 units3
C
104 units2
D
104 units3
Answer:
D
Step-by-step explanation:
I'm really sry if it's wrong!
The number of new contributors to a public radio station's annual fund drive over the last ten years is 63, 58, 61, 72, 98, 103, 121, 147, 163, 198 Using Microsoft Excel, develop a linear regression model that predicts the number of new contributors. Explain the slope of this model. Based on this model, how many new contributors would you predict for the following year?
Answer:
The number of potential members predicted in next year's estimate becomes 193. The further explanation is given below.
Step-by-step explanation:
The slope of the model,
m = 15.345
c = 24
After comparing with the equation,
⇒ [tex]y=mx+c[/tex]
we get,
⇒ [tex]=15.345x + 24[/tex]
The slope seems to be a positive value which also means that another always improves this as component decreases. Which ensures that perhaps the number of contributors rising as time went by.
So that the above is the right answer.
What’s the correct answer for this?
Answer:
c
Step-by-step explanation:
The altitude of an airplane is decreasing at a rate of 44 feet per second. What is the change in altitude of the airplane over a period of 34 seconds?
Answer:
1320 feet
Step-by-step explanation:
All we have to do is multiply the rate of change of altitude by the time it took the altitude to change.
The altitude of an airplane is decreasing at a rate of 44 feet per second. After 30 seconds, the change is altitude is:
44 * 30 = 1320 feet
The altitude of the airplane has changed by 1320 feet.
BRAINLIEST ASAP! LENGTH OF AC?
Answer:
2.33 units
Step-by-step explanation:
[tex]\tan 25\degree =\frac{AC}{5}\\\\0.46630 = \frac{AC}{5}\\\\AC = 0.46630 \times 5\\AC =2.3315\\AC = 2.33 \: units[/tex]
A movie theater decreased the size of its popcorn bags by 20%. If the old bags held 15 cups of popcorn, how much do the new bags hold
Answer:
Your answer will be [tex]12[/tex] cups of popcorn.
Step-by-step explanation:
To find out how much the new bags hold, you need to find out the discount.
[tex]\frac{20}{100 } = .2[/tex]
[tex]15 * .2 = 3[/tex]
We know that the discount is [tex]3[/tex].
To figure out how much the new bags hold, subtract by the old bags.
[tex]15 - 3 = 12[/tex]
The new bags hold 12 cups of popcorn.
don't know if my answer is right
Answer:
168
Step-by-step explanation:
SA= 2B + hp
h=9
p=16
B= 1/2 bh
B= 1/2 6(4)
B=12 x 2 = 24
9 x 16= 144
144+24= 168
BRAINLIEST really needed!!
At Silver Gym, membership is $35 per month, and personal training sessions are $30 each. At Fit Factor,
membership is $85 per month, and personal training sessions are $20 each. In one month, how many
personal training sessions would Sarah have to buy to make the total cost at the two gyms equal?
Sarah would have to buy
equal.
personal training sessions to make the total cost at the two gyms
Answer:
5 sessions each
Step-by-step explanation:
Let the personal training sessions be x.
Then at Silver Gym Sarah would spend:
35 + 30xAnd at Fit Factor she would spend:
85 + 20xSince total costs are same, the amounts will be equal:
35+30x = 85 + 20x30x - 20x = 85 - 3510 x = 50x= 50/10x= 5So Sarah would buy 5 training sessions for each of the gyms.
And she would spend $185 at each.
if a line is perpendicular to y=-2/3x+2, will it be perpendicular to 2x+3y=12?
Answer:
3x + 2y = -2
Step-by-step explanation:
Given Equation is − 2 x + 3 y = 12
3 y = 2 x + 12
y = ( 2 /3 ) y + 12
Slope of this line is m = 2/ 3
Slope of Line A m a = 2
Slope of Line B m b = 2/ 3
Slope of Line C m c = − ( 2 /3 )
Slope of Line D m d = − ( 3 /2 )
since m d = − 1 /m , D is perpendicular to the given line
The moon has a diameter of approximately 2,200 miles. If the circumference of a circle can be found using the formula C = πd, what is the circumference of the moon? (Use 3.14 for π)
Answer:6908 (miles) ^2
Step-by-step explanation:
diameter=2200 miles
π=3.14
Circumference=π x diameter
Circumference=3.14 x 2200
Circumference=6908 (miles)^2
Answer:
The circumference is 6908 miles.
Step-by-step explanation:
so your answer is B.
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A colony of 300 bacteria doubles in size every 22 minutes can be represented by the exponential function y=300(2)x. If you want to know how many bacteria will be present about 66 minutes, what should you plug in for x?
Answer:
[tex] y = 300 (2)^x[/tex]
Where x represent the number of period of times of 22 minutes. If we want to know the value of the population after 66 minutes we need to find the value of x on this way:
[tex] x = 66 minutes *\frac{1period}{22 minutes}= 3[/tex]
So then we need to replace the value of x =3 and we got:
[tex] y= 300 (2)^3 = 2400[/tex]
Step-by-step explanation:
For this case we have the following function:
[tex] y = 300 (2)^x[/tex]
Where x represent the number of period of times of 22 minutes. If we want to know the value of the population after 66 minutes we need to find the value of x on this way:
[tex] x = 66 minutes *\frac{1period}{22 minutes}= 3[/tex]
So then we need to replace the value of x =3 and we got:
[tex] y= 300 (2)^3 = 2400[/tex]
Which best describes a fraction?
» A fraction is the denominator divided by the numerator.
» A fraction is the numerator divided by the denominator.
1.) A fraction is the numerator multiplied by the denominator.
()) A fraction is the denominator multiplied by the numerator.
A fraction is the numerator divided by the denominator best describes a fraction.
Given,
- A fraction is the denominator divided by the numerator.
- A fraction is the numerator divided by the denominator.
- A fraction is the numerator multiplied by the denominator.
- A fraction is the denominator multiplied by the numerator.
We need to find which option best describes a fraction.
What is a fraction?A fraction has two parts: Numerator and Denominator.
It is in the form of Numerator / Denominator.
We have,
- A fraction is the denominator divided by the numerator.
It is written as denominator / Numerator.
- A fraction is the numerator divided by the denominator.
It is written as Numerator / Denominator
- A fraction is the numerator multiplied by the denominator.
It is written as Numerator x Denominator.
- A fraction is the denominator multiplied by the numerator.
It can be written as Denominator x Numerator.
We see that the option "a fraction is a numerator divided by the denominator" is the correct answer.
Thus A fraction is the numerator divided by the denominator best describes a fraction.
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in the first quarter of the game the Giants gained 5 yards lost 13 yards gained 2 yards gained 6 yards and unfortunately lost 12 yards in their final play
Answer:
They lost a total of -12 yards.
Step-by-step explanation:
Do the calculation.
5- 13= -8
-8 + 2 + 6= 0
0 - 12 = -12
what kind of novel is nutshell?
Answer:
i dont know what is it
den
Consider the triangle.
Which statement is true about the lengths of the sides?
45°
Each side has a different length.
Two sides have the same length, which is less than the
length of the third side.
D. The three sides have the same length.
D. The sum of the lengths of two sides is equal to the
length of the third side.
45°
Answer:
Assuming this is a 45 - 45 - 90 right triangle, The answer would be B) Two sides have the same length, which is less than the length of the third side
Hence statements stated true false along with reason
What is triangle?A triangle is a three-sided polygon with three edges and three vertices in geometry. The sum of a triangle's interior angles equals 180 degrees is the most significant feature of a triangle.
Triangle of Isosceles: Triangle with Obtuse Angle
Triangle Inequality in the Scalene Triangle
Triangle Surface Area: Triangle with Sharp Angle
Triangle with Right Angles: Triangle Form of Pascal...
How to solve?Given a triangle and statements related to it let's check
Each side has a different length.
-This statement can't always be true as in equilateral triangle all sides are equal
Two sides have the same length, which is less than the
length of the third side.
-this statement is correct but when it is a right angles triangle where other two anges are 45degrees each then this can't be true.
The three sides have the same length.
-this statement is true for equilateral triangle
D. The sum of the lengths of two sides is equal to the
length of the third side.-
-This statement is true when we talk of only right angled triangle
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