The value is P(p'-p > 0.17) = 0.09
From the question we are told that
The population proportion is p=0.19
The sample size is n = 479
Generally given that the sample size is large enough , i.e n > 30 then the mean of this sampling distribution is mathematically represent
[tex]u_{x} =p=0.19[/tex]
Generally the standard deviation is mathematically represented as
σ[tex]=\sqrt{ \frac{p(1-p)}{n}[/tex]
σ= [tex]\sqrt{ \frac{0.19(1-0.19)}{479}[/tex]
σ=0.017
Generally the the probability that the sample proportion will differ from the population proportion by greater than 17% is mathematically represented as
[tex]P(p'-p > 0.17) =P (z > \frac{0.17}{0.017} )[/tex]
[tex]P(p'-p > 0.17) =P (z > 10 )[/tex]
[tex]P(p'-p > 0.17) =P (z > 10 ) - P (z > -10 )[/tex]
From the z table the area under the normal curve to the left corresponding to 10 and - 10 is
[tex]P(p'-p > 0.17) = 0.97042 - 0.87450\\P(p'-p > 0.17) = 0.09[/tex]
So, the value of probability is greater than 17% is P(p'-p > 0.17) = 0.09
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The probability that the sample proportion will be greater than 17% is 0.8677 or 86.77%.
The true proportion of the sample or the mean of the sample = 19%, that is, μ = 19% or 0.19.
The sample size (n) = 479.
The sample proportion is to be calculated at the point 17% or 0.17.
The standard error (s) = √{μ(1 - μ)/n} = √{0.19(1 - 0.19)/479} = 0.0179.
We are asked to calculate the probability that the sample proportion is greater that 17% or 0.17.
This is written as P(X > 0.17) = P(Z > {(0.17-0.19)/0.0179}) = P(Z > -1.1173) = 1 - P(Z ≤ -1.1173) = 1 - 0.1304 = 0.8696 or 86.96%.
To calculate this using the calculator, we use the calculator function:
Normalcdf(0.17,10000000,0.19,0.0179) = 0.8677 or 86.77%.
Thus, the probability that the sample proportion will be greater than 17% is 0.8677 or 86.77%.
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Given that (7-2x),9,(5x+17) are consecutive terms of a geometric progression with common ratio, r>0, find the value of x.
This are also referred to as exponential sequence. The common ratio if r > 0 is 2
Geometric sequenceThis are also referred to as exponential sequence. Given the following sequence
(7-2x),9,(5x+17)
If they are in geometric progression, hence;
9/7-2x = 5x+17/9
Cross multiply
7-2x(5x+17) = 9(9)
Expand
35x+119-10x²-34x = 81
-10x²+x+119-81=0
10x²-x-38 = 0
Factorize
10x²-20x +19x-38 = 0
10x(x-2)+19(x-2)= 0
x - 2 = 0
x = 2
Hence the common ratio if r > 0 is 2
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PLEASE HELP! You are covering the metal wedge below with a thin layer of high-conducting silver (surface area). The measurements shown are in centimeters. Find the cost of covering the wedge in silver, if silver plating costs $3 for every 2 square centimeters.
The cost of covering the triangular prism wedge in silver is: $108.
What is the Surface Area of a Triangular Prism?Surface area = (s1 + s2 + s3)L + bh.
Given the following:
s1 = 10s2 = 8s3 = 6L = 0.5b = 6 h = 8Plug in the values into the formula
Surface area of the triangular prism metal wedge = (10 + 8 + 6)0.5 + (6)(8)
Surface area of the triangular prism metal wedge = 72 cm²
Cost of covering = 72/2 × 3 = $108
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The area of a rectangle is 59.5 square inches. The base of the
rectangle is 7 inches.
What is the height of the rectangle, in inches?
O A. x = 52.5 in
OB. x = 8.5 in
OC. x= 416.5 in
OD. x= 22.75 in
Answer:
Step-by-step explanation:
Givens
Area = 59.5 in^2
Base = 7 inches
height = h
Solution
Area = Base * height Substitute what you know in the formula
59.5 = 7 * h Divide both sides by 7
59.5/7 = 7h / 7
h = 8.5
Answer height = 8.5
Answer:
Answer B is correct
Step-by-step explanation:
The formula to find the area of a rectangle is :
Area = Base × Height
Given that,
Area ⇒ 59.5 in²
Base ⇒ 7 in
Height ⇒?
Let the height of the rectangle be x.
First, let us make an expression to find the value of h.
Area = Base × Height
59.5 = 7 × x
And now let us solve for x.
59.5 = 7h
Divide both sides by 7.
x = 8.5 in
Which ordered pair is a solution of the equation 3x + y = 15?
Answer: 3(3)+6=15
Step-by-step explanation:
X=3 and the Y=6
( ) means multiplying so it 3 multiplied (3) and add 6 which Is the Y then you got the answer which is 15.
cChoose all that apply. If a population is decreasing in size, you would expect lambda to be ___________________ and r to be _______________________.
If the population can be shown to be decreasing in size, then the lambda would be positive while the r would be negative.
What happens when the population is decreasing?When the population is decreasing, the rate would be negative because the population is shrinking. This is why r - which is rate - will be negative.
Lambda on the other hand will be positive to show that the population started from a higher value and is now decreasing.
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The points (-3 r) and (9 2) lie on the line with slope 1/4. find the missing coordinate
Answer: -1
Step-by-step explanation:
I assume the points are (-3, r) and (9,2).
Substituting into the slope formula,
[tex]\frac{r-2}{-3-9}=\frac{1}{4}\\\\\frac{r-2}{-12}=\frac{1}{4}\\\\r-2=-3\\\\r=-1[/tex]
Given the system
4x + 2y 2z = 10 (A)
2x + 8y + 4z = 32 (B)
30x+12y - 4z = 24 (C)
The values of the variables are x = -2, y = 6 and z = -3
How to solve by elimination?The system is given as:
4x + 2y - 2z = 10 (A)
2x + 8y + 4z = 32 (B)
30x + 12y - 4z = 24 (C)
The easiest variable to eliminate is z.
Combine A and B
2[4x + 2y - 2z = 10]
⇒
8x + 4y - 4z = 20
+ 2x + 8y + 4z = 32
⇒ 10x + 12y = 52
Combine B and C
2x + 8y + 4z = 32
30x + 12y - 4z = 24
⇒ 32x + 20y = 56
Divide through by 4
8x + 5y = 14
So, we have:
10x + 12y = 52
and
8x + 5y = 14
Multiply 10x + 12y = 52 by 8/10
8/10[10x + 12y = 52]
⇒ 8x + 9.6y = 41.6
Combine 8x + 9.6y = 41.6 and 8x + 5y = 14
8x + 9.6y = 41.6
- [8x + 5y = 14]
⇒ 4.6y = 27.6
Divide
y = 6
Substitute y = 6 in 8x + 5y = 14
8x + 5 * 6 = 14
8x + 30 = 14
Subtract 30
8x = -16
Divide
x = -2
Substitute y = 6 and x = -2 in (A)
4x + 2y - 2z = 10
4(-2) + 2(6) - 2z = 10
-8 + 12- 2z = 10
Evaluate the like terms
-2z = 6
Divide
z = -3
Hence. the values of the variables are x = -2, y = 6 and z = -3
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a nunebr is chosen at random from 1 to 50 find the probability of selecting numbers greater than 30 and less than 45
Answer:
7/25
Step-by-step explanation:
there are 14 numbers greater than 30 and less than 45
31 32 33 34 ......42 43 44 <=====14 numbers
14 choices out of 50 = 14/ 50 = 7/25
y=f(x)graph Select the interval where fff is positive.
The interval where f is positive is [tex]0 \le x < 1.5[/tex]
How to determine the positive interval?The missing function is added as an attachment
From the attached graph, the function f(x) is positive from x = 0 to x = 1.5
As an interval notation, this can be represented as:
[tex]0 \le x < 1.5[/tex]
Hence, the interval where f is positive is [tex]0 \le x < 1.5[/tex]
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find the zeros of 7=x^2-8x-3 by completing the square
Using the completing the square method, for the equation, we have the zeros as x = √26 + 4 and x = 4 - √26
How can the zeros be found using completing the square method?The given equation is presented as follows
[tex]7 = \mathbf{ {x}^{2} - 8x - 3}[/tex]
Which, by completing the square, gives;
[tex] {x}^{2} - 8x - 3 - 7 = 0[/tex]
[tex] {x}^{2} - 8x - 10 = 0[/tex]
[tex] {x}^{2} - 8x + {\left(\frac{8}{2} \right) }^{2} - 10 - {\left(\frac{8}{2} \right) }^{2} = 0[/tex]
[tex] \mathbf{{(x - 4)}^{2} } =26[/tex]
The zeros of the equation;
[tex]7 = {x}^{2} - 8x - 3[/tex]
are;
[tex] \underline{x = \pm \sqrt{26} + 4}[/tex]
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turn y=6x-5 (explicit) into a recursive equation
Answer:
[tex]a_1=1\\a_n=a_{n-1}+6[/tex]
Step-by-step explanation:
So to define a recursive equation, you need to find how much each term is increasing or decreasing by. You also need to find the first term. To find the first term you can simply plug in 1 into x: [tex]a_1=6(1)-5 = 6-5 = 1[/tex]. And as you can see the slope is 6, so each term is increasing by 6. So you get the recursive function: [tex]a_1=1\\a_n=a_{n-1}+6[/tex]
If my savings of $x grows 10% each year, how much will I have in 2 years?
Answer:
1.21x
Step-by-step explanation:
we can write 100% as 1
then 10% is 0.1
then 1.1x = is first
1.1*1.1x = 1.21x or 121% of x
The savings of $x grows 10% each year after 2 year it will become 1.21x .
What is compound interest?Compound interest is an interest accumulated on the principal and interest together over a given time period. The interest accumulated on a principal over a period of time is also accounted under the principal.
The formula of Compound interest :
[tex]A= P(1+\frac{r}{100} )^{t}[/tex]
where,
A = Final amount
P = initial Principal
t = Time in years
r = rate of interest per annum
According to the question
Principal = $x
Rate of interest per annum = 10%
Time in years = t
By using formula of Compound interest :
[tex]A= P(1+\frac{r}{100} )^{t}[/tex]
Now ,
Substituting the values in the formula
[tex]A= x(1+\frac{10}{100} )^{2}[/tex]
[tex]A= x(1.1} )^{2}[/tex]
[tex]A= 1.21x[/tex]
Hence, the savings of $x grows 10% each year after 2 year it will become 1.21x .
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I need help asap with thissssssssssss
Answer:
D
Step-by-step explanation:
The domain is the x value which in this case would be the hours of training
In an election, 1200 total votes were cast for the 3 candidates. The second-place candidate received 155 fewer votes than the winner and 200 votes more than the third-place candidate. How many votes did the winner receive
The winner received 570 votes.
Let the winner candidate be c1
Let the second-place candidate be c2
Let the third-place candidate be c3
[tex]c2=c1-155\\[/tex].........equation 1
[tex]c2=c3+200\\[/tex]
[tex]c3=c2-200 \\[/tex]
[tex]c3=c1-155-200\\[/tex].........by equation 1
[tex]c3=c1-355[/tex]........equation 2
Now we know,
[tex]c1+c2+c3=1200[/tex]
[tex]c1+(c1-155)+(c1-355)=1200[/tex] .....by equations 1 and 2
[tex]3c1-510=1200[/tex]
[tex]3c1=1200+510\\3c1=170\\c1=570[/tex]
Hence, The winner received 570 votes.
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What is an equation for the line parallel to y = −x + 2 going through the point (−3, −5)?
The equation for the line parallel to y = −x + 2 going through the point (−3, −5) is y = -x - 8
Equation of a lineThe equation of a line in point slope form is expressed as:
y - y1 = m(x-x1)
Given the equation y = -x + 2, the slope of the line parallel to the line is -1
Substitute the slope and point (-3, -5)
y -(-5) = -1(x - (-3))
y+5 = -(x + 3)
y+5 =-x - 3
y = -x - 3 - 5
y = -x - 8
Hence the equation for the line parallel to y = −x + 2 going through the point (−3, −5) is y = -x - 8
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Try It #3
There is a straight road leading from the town of Timpson to Ashburn 60 miles east and 12 miles north. Partway down the road, it junctions with a second road, perpendicular to the first, leading to the town of Garrison. If the town of Garrison is located 22 miles directly east of the town of Timpson, how far is the road junction from Timpson?
The distance of the road junction form Timpson is given as 21.57 miles.
We have to solve this using the Pythagoras theorem methodWe have AT = [tex]\sqrt{TN^{2}+AN^{2} }[/tex]
√60² + 12² = 12√26
∠TMG = LN = 90 degrees
Therefore we have the system
[tex]\frac{TM}{60} = \frac{22}{12\sqrt{26} }[/tex]
When we cross multiply we would have to solve for TM
TM = 21.57 miles
Hence the distance of the road junction form Timpson is given as 21.57 miles.
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What is the difference? −9 4/5−(−3 2/3)
Subtraction is a mathematical operation that reflects the removal of things from a collection. The difference between −9 4/5 and −3 2/3 is -6 2/15.
What is subtraction?Subtraction is a mathematical operation that reflects the removal of things from a collection. The negative symbol represents subtraction.
The difference between −9 4/5 and −3 2/3 is,
−9 4/5 − (−3 2/3)
= −9 4/5 + 3 2/3
= (−9+3) + (−4/5 + 2/3)
= −6 + (-2/15)
= -6 2/15
Hence, The difference between −9 4/5 and −3 2/3 is -6 2/15.
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Can someone please help
Answer: 2.5
Step-by-step explanation:
[tex]1 \times 3=3\\\\3-\frac{1}{2}=2.5[/tex]
Jordan's grades improved in arithmetic when he was fitted with hearing aids. Why does he no longer have an SCD
Jordan can now hear the math teacher, whose classroom instruction was crucial in addition to what Jordan read in his textbook.
What are hearing aids?A hearing aid is a small electronic device that you wear in or behind your ear. It is used by people who cannot hear properly. Wearing this device makes sounds louder so that a person who cannot hear can listen, and talk to other people. A hearing aid can help people hear in every situation.
What is an SCD?SCD is nothing but a specific learning disorder.
How is it different from intellectual disability?An SLD is specific to underachievement in academic skills that are not attributable to intellectual disability, developmental delay, or physical cause.
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The sum of two numbers is 79. Three
times the first number added to 5 times
the second number is 283. What are the
two numbers?
Answer:
The two numbers are 23 and 56
Step-by-step explanation:
Let's say the two numbers are A and B.
We are told:
1) A+B=79
2) 3A+5B=283
Let's take the first expression and solve for A:
A+B=79
A=79-B
Now use this value of A in the second expression:
3A+5B=283
3(79-B)+5B=283
237-3B+5B=283
2B = 46
B = 23
Since B=23, we know from 1) that
A+B=79
A+23=79
A = 56
CHECK:
Does A+B=79?
56+23 = 79? YES
Does 3A+5B=283?
3(56)+5(23)=283
168 + 115 = 283? YES
Suppose you have a valid argument with a false conclusion. Given this information, what do you know about the truth value of the argument's premises? The premises must all be false. At least one premise must be false. There must be at least one true premise and at least one false premise. The premises may be any combination of true and false. The premises must all be true.
Suppose you have a valid argument with a false conclusion. Given this information, what do you know about the truth value of the argument's premises? The premises must all be false. At least one premise must be false. There must be at least one true premise and at least one false premise. The premises may be any combination of true and false. The premises must all be true.
"The argument may be either valid or invalid" When trying to determine the validity of an argument in logic, the truth of a premise is a non-factor. Logic is concerned about whether or not an argument would effectively transfer truth from its premises to the conclusion if the premises were true.
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What is tan 30°?
1
60
90°
√3
2
30⁰
OA. √2
OB.
O C.
O D.
√√3
√√3
OE. √3
O F. 1
Answer: [tex]\frac{\sqrt{3}}{3}[/tex]
Step-by-step explanation:
[tex]\tan 30^{\circ}=\frac{\sin 30^{\circ}}{\cos 30^{\circ}}=\frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}}=\frac{1}{\sqrt{3}}=\frac{\sqrt{3}}{3}[/tex]
The value of the trigonometric relation tan 30° = 1/√3
What are trigonometric relations?Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles
The six trigonometric functions are sin , cos , tan , cosec , sec and cot
Let the angle be θ , such that
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
tan θ = sin θ / cos θ
cosec θ = 1/sin θ
sec θ = 1/cos θ
cot θ = 1/tan θ
Given data ,
Let the trigonometric relation be represented as A
Now , the value of A is
A = tan 30°
And , tan θ = sin θ / cos θ
On simplifying , we get
sin 30° = 1/2
cos 30° = √3/2
Substituting the values in the equation , we get
tan 30° = sin 30° / cos 30°
tan 30° = ( 1/2 ) / ( √3/2 )
tan 30° = 1/√3
Hence , the value of relation tan 30° is 1/√3
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If a snowball melts so that its surface area decreases at a rate of 1 cm2/min, find the rate at which the diameter decreases when the diameter is 12 cm. (Give your answer correct to 4 decimal places.) cm/min
The rate at which the diameter decreases is 0.0159cm/min.
Given that a snowball melts and its surface area decreases at a rate of 1cm²/min.
The surface area of a solid object may be a measure of the entire area that the surface of the thing occupies.
The surface area of the snowball is A=4πr² because the snowball is spherical.
Here, r is the radius of the snowball.
Let D be the diameter of the snowball.
As the radius is half of the diameter
The surface area of a snowball can also be rewritten as
A=4π(D÷2)²
A=4π(D²÷4)
A=πD²
Given that the surface area decreases by 1cm²/min, so,
dA÷dt=-1cm²/min.
Differentiating both sides in A=πD² and get
dA÷dt=2πD(dD÷dt)
Given that the diameter is 12cm.
Substitute these values in the formula and find dD÷dt
-1=2π×12×(dD÷dt)
-1=24π×(dD÷dt)
-1÷24π=dD÷dt
-0.0159≈dD÷dt
Hence, the diameter decreases at the rate of 0.0159 cm/min when the diameter is 12 cm.
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Find a quadratic polynomial whose zeroes are reciprocals of the zeroes of the polynomial x²-x-6
Zeros of this function
x²-x-6=0x²-3x+2x-6=0x(x-3)+2(x-3)=0(x+2)(x-3)=0x={-2,3}ZEros of reciprocal function
x={-1/2,1/3}The equation
x²-(-1/2+1/3)x-(1/2)(1/3)=0x²-1/6x-1/6=0Which is the graph of y = - root(7, x) - 8 ?
Answer:
Step-by-step explanation:
Which of the following properly describe "slope"? Select all that apply.
Y₂
x₂-x
0
x₂7x
y₂-yi
Orun / rise
Orise / run
Oratio of the change in y-values (rise) for a segment of the graph to the corresponding change in x-values (run)
Answer:
I would assume you're referring to this test? if so the answer is
a, d and e
The expression that describes the slope properly are:
A. m = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]
D. m = rise/run
E. Ratio of the change in y-values (rise) for a segment of the graph to the corresponding change in x-values (run).
We have,
The slope of a line is a measure of its steepness or inclination.
It represents the rate of change between two points on the line, specifically the ratio of the vertical change (rise) to the horizontal change (run).
Mathematically, the slope (m) is calculated as:
m = change in vertical distance/change in horizontal distance
or
m = rise/run
or
m = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]
Thus,
The expression that describes the slope properly are:
A. m = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]
D. m = rise/run
E. Ratio of the change in y-values (rise) for a segment of the graph to the corresponding change in x-values (run).
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12(x + 4) + 8 = 9
y = 4(x + 4)
y=
Answer:
y= 1/3
Step-by-step explanation:
12(x + 4) + 8 = 9
12(x + 4) + 8 -8 = 9 -8
12(x + 4) = 1
12(x + 4)/12 = 1/12
(x + 4) = 1/12
y = 4(x + 4)
y= 4(1/12)
y= 4/12
y= 1/3
A toy manufacturer wants to know how many new toys children buy each year. A sample of 1492 children was taken to study their purchasing habits. Construct the 99% confidence interval for the mean number of toys purchased each year if the sample mean was found to be 8.8. Assume that the population standard deviation is 2.2. Round your answers to one decimal place.
By assuming the standard deviation of population 2.2 the confidence interval is 8.67 toys,8.94 toys.
Given sample size of 1492 children,99% confidence interval , sample mean of 8.8, population standard deviation=2.2.
This type of problems can be solved through z test and in z test we have to first find the z score and then p value from normal distribution table.
First we have to find the value of α which can be calculated as under:
α=(1-0.99)/2=0.005
p=1-0.005=0.995
corresponding z value will be 2.575 for p=0.995 .
Margin of error=z*x/d
where x is mean and d is standard deviation.
M=2.575*2.2/[tex]\sqrt{1492}[/tex]
=0.14
So the lower value will be x-M
=8.8-0.14
=8.66
=8.67 ( after rounding)
The upper value will be x+M
=8.8+0.14
=8.94
Hence the confidence interval will be 8.67 toys and 8.94 toys.
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How many solutions does this system have?
x+4y=6
y=2x-3
Oone
Otwo
Oan infinite number
Ono solution
Pls I need help
Answer:
-x+3y=9
i think this is answer
What is the solution of the equation (x – 5)2 3(x – 5) 9 = 0? use u substitution and the quadratic formula to solve.
The value of x in the equation [tex](x-5)^{2} +3(x-5)+9=0[/tex]is x=(7+3[tex]\sqrt{3}i[/tex])/2,
(7-3[tex]\sqrt{3}i[/tex])/2.
Given equation [tex](x-5)^{2} +3(x-5)+9=0[/tex] .
We have to find the solution of the equation.
Equation is solved to find the value of variables. The number of values of the variable depends on the highest power of variables.
let (x-5)=u-------------------1
equation becomes [tex]u^{2} +3u+9=0[/tex]
solution of a quadratic formula
x=-b±[tex]\sqrt{b^{2} -4ac}[/tex]/2a
on comparing with general form a=1,b=3, c=9
u=-3±[tex]\sqrt{3^{2} -4*1*9} /2[/tex]
=-3±[tex]\sqrt{9-36}/2[/tex]
=-3±[tex]3\sqrt{-27}/2[/tex]
=-3±[tex]3\sqrt{3} i/2[/tex]
[tex]u_{1} =-3[/tex]+3[tex]\sqrt{3}/2[/tex] , [tex]u_{2}[/tex]=-3-3[tex]\sqrt{3}/2[/tex]
put the values of [tex]u_{1}[/tex] in equation 1
x-5=[tex]u_{1}[/tex]
x-5=-3+[tex]3\sqrt{3} /2[/tex]
x=-3+3[tex]\sqrt{3}i/2+5[/tex]
x=7+3[tex]\sqrt{3} i/2[/tex]
put the values of [tex]u_{2}[/tex] in equation2
x-5=[tex]u_{2}[/tex]
x-5=-3-3[tex]\sqrt{3} /2[/tex]
x=7-3[tex]\sqrt{3}/2[/tex]
Hence the values of x are 7+3[tex]\sqrt{3}i/2[/tex], 7-3[tex]\sqrt{3}i/2[/tex].
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