Answer:
Use the Rational Zero Theorem to list all possible rational zeros of the function. Use synthetic division to evaluate a given possible zero by synthetically dividing the candidate into the polynomial. Repeat step two using the quotient found with synthetic division.
Step-by-step explanation:
One of the methods to finding zeros and factors of higher degree polynomial functions is using the Remainder theorem.
What are the zeros of the polynomial function?The zeros of polynomial refer to the values of the variables present in the polynomial equation for which the polynomial equals 0.
The methods to finding zeros and factors of higher degree polynomial functions
Evaluate a polynomial using the Remainder Theorem.Use the Rational Zero Theorem to find rational zeros.Use the Factor Theorem to solve a polynomial equation.Use synthetic division to find the zeros of a polynomial function.Hence, one of the methods to finding zeros and factors of higher degree polynomial functions is using the Remainder theorem.
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In a study in Scotland (as reported by Devlin 2009), researchers left a total of 320 wallets around Edinburgh, as though the wallerts were lost. Each contained contact information including an address. Of the wallets, 146 were returned by the people who found them. With the following steps, use the data to estimate the proportion of lost wallets that are returned, and give a 95% confidence interval for this estimate.
Required:
a. What is the observed proportion of wallets that were returned (rounded to the nearest thousandths)?
b. Calculate p to use in the Agresti-Coull method of calculating a 95% confidence interval for the population proportion rounded to the nearest thousandths).
c. Calculate the lower bound of the 95% confidence interval (rounded to the nearest thousandths)
d. Calculate the upper bound of the 95% confidence interval (rounded to the nearest thousandths)
Answer:
a) The observed proportion of wallets that were returned
p = 0.45625
b) 95% of confidence intervals for Population proportion
0.40168 , 0.51082)
c) The lower bound of the 95% confidence interval = 0.40168
d) The upper bound of the 95% confidence interval = 0.51082
Step-by-step explanation:
Step(i):-
a)
Given data the researchers left a total of 320 wallets around Edinburgh, as though the wallets were lost. Each contained contact information including an address. Of the wallets, 146 were returned by the people who found them
Given sample size 'n' = 320
Given data 'x ' = 146
Sample proportion
[tex]p = \frac{x}{n}[/tex]
[tex]p = \frac{x}{n} = \frac{146}{320} = 0.45625[/tex]
Step(ii):-
b) 95% of confidence intervals for Population proportion
Level of significance = 95% or 0.05%
[tex]Z_{\frac{\alpha }{2} } = Z_{\frac{0.05}{2} } = Z_{0.025} = 1.96[/tex]
95% of confidence intervals for Population proportion are determined by
[tex](p - Z_{0.025} \frac{\sqrt{p(1-p)} }{\sqrt{n} } , p + Z_{0.025} \frac{\sqrt{p(1-p)} }{\sqrt{n} })[/tex]
[tex](0.45625 - 1.96\frac{\sqrt{0.45625(1-0.45625)} }{\sqrt{320} } , 0.45625 + 1.96\frac{\sqrt{0.45625(1-0.45625)} }{\sqrt{320} })[/tex]
(0.45625 - 0.05457 , 0.45625 + 0.05457)
( 0.40168 , 0.51082)
c) The lower bound of the 95% confidence interval = 0.40168
d) The upper bound of the 95% confidence interval = 0.51082
Answer this correctly
Answer:
1385.622
Step-by-step explanation:
A=πr2=π·212≈1385.622
hope this helped
Gina has completed her CAD drawing and wants to take a print out. What final step must she take before taking the print out?
A.
select the units for the measurements
B.
select the scale for the drawing
C.
select the color for the different parts of the drawing
D.
delete all the layers created and retain only the final layer
Answer:
It is B I think
Step-by-step explanation:
D is incorrect
Which rays are part of line BE?
AC and
A and
A and A
A and A
Answer:
A and A that is the answer
expand and simplify (4+√2)(6-√2) give your answer in the form b+√2
Answer:
22+2[tex]\sqrt{2}[/tex]
Step-by-step explanation:
Expanded it is
24-4[tex]\sqrt{2}[/tex]+6
This simplified leads to 22+2[tex]\sqrt{2}[/tex]
Hope this helps
What is the range of g?
Answer:
[-4, 9]
Step-by-step explanation:
The range is the vertical extent of the relation.
__
The minimum value of g is marked by the solid dot at (x, y) = (4, -4). That minimum is -4.
The maximum value of g is the peak at (x, y) = (-2, 9). That maximum is 9.
The function is continuous between these values, so the range includes all values between -4 and +9, inclusive.
range: [-4, 9]
Answer:
Step-by-step explanation:
range: [-4, 9]
what is 1/2*1^12 1/2
Answer: 0.5
Step-by-step explanation: I think that the answer.
What’s the correct answer for this?
Answer:
x = 5
Step-by-step explanation:
Since TV bisects (equally divides) EF hence <EKT = 90°
Also <EKT = 5x+65
So
5x+65 = 90
5x = 90-65
5x = 25
Dividing both sides by 5
x = 5
What is the inverse of the function f(x) = 2x + 1? h(x) = one-halfx – one-half h(x) = one-halfx + one-half h(x) = one-halfx – 2 h(x) = one-halfx + 2
Step-by-step explanation:
To find the inverse we just switch f(x) and x so we get :
x = 2f(x) + 1
2f(x) = x - 1
h(x) = 1/2x - 1/2
Hope this helps!
Answer:
x = 2f(x) + 1
2f(x) = x - 1
h(x) = 1/2x - 1/2
Step-by-step explanation:
The sum of two numbers is 15. One of the
numbers is 12 times the other. Find the
bigger number.
Answer:
The Sum of two number is 15: x + y = 15
One of the numbers is 12 times the other: x = 12y:
System of equations:
x + y = 15
x = 12y
Plug x = 12y into equation one(x + y = 15)
12y + y = 15
13y = 15
y = 15/3
y ≈ 1.15
Now we know x = 12y
x = 12(15/13) = 180/13
x = 180/13
x ≈ 13.85
The biggest number is x = 180/13.
275 feet in 10 seconds =
Ocean fishing for billfish is very popular in the Cozumel region of Mexico. In the Cozumel region about 41% of strikes (while trolling) resulted in a catch. Suppose that on a given day a fleet of fishing boats got a total of 29 strikes. Find the following probabilities. a) 12 or fewer fish were caught.b) 5 or more fish were caught.c) between 5 and 12 fish were caught.
Answer:
a) 59.10% probability that 12 or fewer fish were caught.
b) 99.74% probability that 5 or more fish were caught.
c) 58.84% probability that between 5 and 12 fish were caught.
Step-by-step explanation:
I am going to use the normal approximation to the binomial to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
In this problem, we have that:
[tex]n = 29, p = 0.41[/tex]
So
[tex]\mu = E(X) = np = 29*0.41 = 11.89[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = 2.6486[/tex]
Find the following probabilities.
a) 12 or fewer fish were caught.
Using continuity correction, this is [tex]P(X \leq 12 + 0.5) = P(X \leq 12.5)[/tex], which is the pvalue of Z when X = 12.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{12.5 - 11.89}{2.6486}[/tex]
[tex]Z = 0.23[/tex]
[tex]Z = 0.23[/tex] has a pvalue of 0.5910
59.10% probability that 12 or fewer fish were caught.
b) 5 or more fish were caught.
Using continuity correction, this is [tex]P(X \geq 5 - 0.5) = P(X \geq 4.5)[/tex], which is 1 subtracted by the pvalue of Z when X = 4.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{4.5 - 11.89}{2.6486}[/tex]
[tex]Z = -2.79[/tex]
[tex]Z = -2.79[/tex] has a pvalue of 0.0026
1 - 0.0026 = 0.9974
99.74% probability that 5 or more fish were caught.
c) between 5 and 12 fish were caught.
Using continuity correction, this is [tex]P(5 - 0.5 \leq X \leq 12 + 0.5) = P(4.5 \leq X \leq 12.5)[/tex], which is the pvalue of Z when X = 12.5 subtracted by the pvalue of Z when X = 4.5. So.
From a), when X = 12.5, Z has a pvalue of 0.5910
From b), when X = 4.5, Z has a pvalue of 0.0026.
So
0.5910 - 0.0026 = 0.5884
58.84% probability that between 5 and 12 fish were caught.
What is the y-intercept of the line?
x 16 24 32
y 44 64 84
Answer:
The y-intercept of the line is 2
Step-by-step explanation:
You could try to find the slope of the line and then find the intercept with y axis by sloving b = y - ax
But here it seems easy enough once you see that the x values in the table increase by a factor of 8 and the y values in the table increase by a factor of 20.
(By the way, this is enough to give you the slope, because it is 8/20 ). But why bother?
Just extrapolate the table to the left, and you will find the y value where x = 0
x 0 8 16 24 32
y 2 22 44 64 84
So the y-intercept of the line is 2.
Extra:
The full equation of the line is:
y = 8/20x + 2
Answer:
(0,4)
Step-by-step explanation:
How to solve 3/7+3/14
Answer:
About 0.642
Step-by-step explanation:
Please answer this correctly
Answer: Rectangular pyramid
Step-by-step explanation:
When you think about it, a pyramid has 3 faces that are triangular!
If you found this answer helpful, give it a five-star rating and a thanks! I would really appreciate it!
You can even give it a brainliest if you want! ;)
You operate a gaming Web site, www.mudbeast.net, where users must pay a small fee to log on. When you charged $3 the demand was 1100 log-ons per month. When you lowered the price to $2.50, the demand increased to 1375 log-ons per month.
A) Construct a linear demand function for your Web site and hence obtain the monthly revenue R as a function of the log-on fee x.
B) Your Internet provider charges you a monthly fee of $30 to maintain your site. Express your monthly profit P as a function of the log-on fee x.
C) Determine the log-on fee you should charge to obtain the largest possible monthly profit. What is the largest possible monthly profit?
Answer:
A) The linear relation between price and demand is:
[tex]d=-550x+2750[/tex]
The revenue R is:
[tex]R=-550x^2+2750x[/tex]
B) The profit functionP is:
[tex]P=-550x^2+2750x-30[/tex]
C) The largest monthly profit is obtained with a log-on fee of $2.5 per month. This corresponds to a profit of $3407.5.
Step-by-step explanation:
We have a site where the number of log-ons depends on our monthly fee. A linear relation is established between the price (log-on fee) and the number of log-ons.
We have two points for this linear relationship:
At price x=3, the demand is d=1100.At price x=2.5, the demand is d=1375.We will model the relation:
[tex]d=mx+b[/tex]
We can calculate the slope m as:
[tex]m=\dfrac{\Delta d}{\Delta x}=\dfrac{d_2-d_1}{x_2-x_1}=\dfrac{1375-1100}{2.5-3}\\\\\\m=\dfrac{275}{-0.5}=-550[/tex]
Then, replacing one point in the linear equation, we can calculate the intercept b:
[tex]d_1=mx_1+b\\\\1100=(-550)\cdot 3+b\\\\1100=-1650+b\\\\b=1100+1650=2750[/tex]
Then, the linear relation between demand and price is:
[tex]d=-550x+2750[/tex]
The revenue R can be expressed as the multiplication of the price and the demand:
[tex]R=x\cdot d=x(-550x+2750)=-550x^2+2750x[/tex]
If we have a fixed cost of $30 per month, the profit P is:
[tex]P=R-FC=-550x^2+2750x-30[/tex]
We can maximize the profit by deriving the profit function and making it equal to zero.
[tex]\dfrac{dP}{dx}=0\\\\\\\dfrac{dP}{dx}=-550(2x)+2750(1)=0\\\\\\-1100x+2750=0\\\\x=\dfrac{2750}{1100}=2.5[/tex]
This corresponds to a profit of:
[tex]P(2.5)=-550(2.5)^2+2750(2.5)-30\\\\P(2.5)=-550\cdot 6.25+6875-30\\\\P(2.5)=-3437.5+6875-30\\\\P(2.5)=3407.5[/tex]
Which graph is the solution to Ixl > 10?
Answer: D with the open circles at -10 and 10 with a line in between them.
Step-by-step explanation:
Since x has an absolute value sign around it this means that all the values will be positive which includes negative numbers.
Since the solution must be less than 10 we need all values under 10 which is 1-9.9 repeating. we can show the 9.9 repeating with an open circle on the value of 10. This also goes for the negative values for x as we can go up to -9.9 repeating because it will become positive.
The only graph that shows these values is D with the open circles at -10 and 10 with a line in between them.
Answer:
D
Step-by-step explanation:
Hope this helps
Find the volume of a cone with the radius of radius of 80 and height of 21
Answer:
140672
Step-by-step explanation:
formula for cone volume=pi*r^2*h*1/3
80^2*3.14*21=422016
422016*1/3
=140672
Explain how you could calculate the surface area of a square pyramid
Answer:
calculate the area of a square using the length * width formula, and then add the areas of the other triangles, of which you can calculate by using the base * height formula
Step-by-step explanation:
Answer:
Multiply the side length of the base by the slant height and divide by two. Then, multiply by 4. This will give you the lateral surface area of the pyramid.Step-by-step explanation:
Chords XY and ZW intersect in a circle at P. If
XP = 7, PY=12, and WP= 14, find PZ.
Answer:
Length of segment PZ = 6 units
Step-by-step explanation:
As per theorem of intersecting chords in a circle ;
"Product of lengths of line segments on each chord are equal".
From the figure attached,
Chords XY and WZ are intersecting at point P in a circle.
By theorem; XP × PY = WP × PZ
7 × 12 = 14 × PZ
PZ = [tex]\frac{84}{14}[/tex]
PZ = 6 units
Therefore, length of the segment PZ = 6 units.
What is the volume of the shape?
Volume of the bottom rectangle:
12 x 4.5 x 5.5 = 297 cubic cm
Volume of triangle:
1/2 x 12 x 5 = 30 x 4.5 = 135 cubic cm
Total volume = 297 + 135 = 432 cubic cm
2. The perimeter of a rectangular pool is 98 feet.
The ratio of the width to the length is 3:4.
What are the dimensions of the pool?
Answer:
56 and 42
Step-by-step explanation:
3:4
3 + 4 = 7
98 / 7 = 14
14 x 3 = 42
14 x 4 = 56
56 + 42 = 98
The dimensions of the pool can be categorized as below:
Length equals 28 feet
Width equals 21 feet
What is the perimeter?The perimeter of a rectangle is the outside length of the rectangle. To find the perimeter we add all the 4 sides of the rectangle.
Perimeter = 2(length) + 2 (width )
The ratio of the width to the length is 3:4. The width of the rectangle is 3x
We know,
Length of the rectangle is 4xWidth =3x
Length = 4x
Substitute it in the perimeter formula and solve for x.
Given that,
Perimeter of a rectangle = 98 feet
Perimeter = 2(length )+2(width)
98 = 2(4x)+2(3x)
98 = 8x+6x
98 = 14x
∵ x = 7
Now, we will find out the length and width of the pool.
Length = 4x
= 4(7)
= 28 ft.
and,
Width = 3x
= 3(7)
= 21 ft.
Thus, the length of the pool is 28 feet and the width of the pool is 21 feet
Learn more information about 'Perimeter' here: brainly.com/question/89866
6+7=73.5
7+8=84
11+12=126
12+24=390.6
24+28=?
Answer:
52
Step-by-step explanation:
24+28 = 52
52 - 24 = 28
Solve the system of equations.
y=x2-5
y=-2x+3
A. (2-1) and (4.-5)
B. -2.7) and (4-5)
C. (-411) and (2-1)
O D. (-4, 11) and (-27)
1. Michel buys a leash for his dog. The leash is 6 ft 3 inches. How long, in inches, is the leash?(1 ft = 12 inches)
A) 48 inches
B) 51 inches
C) 72 inches
D) 75 inches
2. What is the area of a triangular garden with base of 6 ft and a height of 9 ft? (A = 1/2BH)
A) 27 square feet
B) 48 square feet
C) 54 square feet
D) 24 square feet
Answer:
1. D) 75 inches
2. A) 27 square feet
Step-by-step explanation:
1. You need to convert 6 feet to inches. In one foot, there are 12 inches. Multiply 6 by 12 to find the number of inches in 6 feet. Add 3 inches to the product to find the total number of inches.
6 × 12 = 72
72 + 3 = 75
You will have 75 inches in total.
2. Use the formula to solve. You are given the base and the height already. Simply plug in and solve.
A = 1/2BH
A = 1/2(6)(9)
A = 3(9)
A = 27 ft²
The area is 27 ft².
Answer:
Step-by-step explanation:
Can I please get some help on this...I have tried to many times...
Answer: A
Step-by-step explanation:
First, the problem is g(f(x)). You would plug in f(x) wherever you see an x in g(x). To find the domain, you take the bottom function, and set it equal to 0.
[tex]\sqrt{x-2} =0[/tex]
When you solve that, you get x=2. You know your domain is x≥2, but there is as asymptote at x=11. That means the graph never reaches x=11, but gets very close. You find that by setting the entire equation equal to 0 and solve from there.
Set up each situation and simplify if possible. Then, choose all situations that are best modeled by a rational inequality.
Answer:
Problem: 3x/5x + 5 ≤ 8 + 2x
Solution: x ≥ -15/7
Step-by-step explanation:
Example of this inequality is:
3x/5x + 5 ≤ 8 + 2x
3x/5x - 2x ≤ 8 - 5
(3x - 10x)/5 ≤ 3
-7x ≤ 15
x ≥ -15/7
match each linear equation with the name of its form
Answer:
2x - 5y = 9 // standard form
y + 6 = -3 (x-1) // point slope form
y = -x + 8 // slope intercept form
Step-by-step explanation:
Abigail had a fish tank that was in the shape of a box. The dimensions were 1 foot deep by 24 inches wide, by 18 inches tall. How many cubic inches of water will it take to completely fill the tank?
Answer:
volume= 5,184 cubic inches
Step-by-step explanation:
25. If the area of a circle is 144cmthen find
a. lts diameter
b. Its circumference
Answer:
a. lts diameter = 13.540550005146 cm
b. Its circumference = 42.538892421732 cm
Step-by-step explanation:
suppose A the area ; d the Diameter ; P the circumference and r the radius
A = πr²
P = d×r = 2πr
then
r² = A/π = 144÷π = 45.836623610466
then
→ r = √(45.836623610466) = 6.770275002573
d = 6.770275002573×2 = 13.540550005146
→ P = 13,.540550005146×π = 42.538892421732
