the error term of the 96% confidence interval for the population proportion of people having a plan to buy an electronic car is approximately 0.076.
To calculate the error term of a confidence interval for the population proportion, we first need to calculate the margin of error using the following formula:
Margin of error = z* * sqrt(p_hat*(1-p_hat)/n)
where:
z* is the critical value of the standard normal distribution for the desired level of confidence. For a 96% confidence level, the critical value is 1.750.
p_hat is the sample proportion, which is calculated as p_hat = x/n, where x is the number of people in the sample who have a plan to purchase an electronic car (18 in this case) and n is the sample size (85 in this case).
Using these values, we have:
Margin of error = 1.750 * sqrt(0.2118*(1-0.2118)/85) ≈ 0.076
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In AABC, if AB = 14 and BC = 9, AC may be equal to
A. 13
B. 23
C. 25
D. 5
Answer:
A
Step-by-step explanation:
By the triangle inequality theorem, 5<AC<23.
So, the answer is A.
Which of the following terms are possible in the domain of a sequence? Select all that apply.
The terms that are possible on the domain of a sequence are given as follows:
13, 25, 60.
What is a sequence?A sequence is a list containing numbers, that may be related or not. It has a 1st term, 2nd term, and so on until the nth term.
The domain is the indexes of the terms, which starts at one and goes until n, hence the possible numbers are:
13, 25, 60.
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Estimate the product 5.25 × 8.89.
Answer:
47.25
Step-by-step explanation:
8.89 is about 9.
So, we have 9(5.25)=9(5)+9(0.25)=45+2.25=47.25
The gross domestic product of the United States in 2020 was $20,940,000,000. What is the gross domestic product of the United States in 2020 expressed in scientific notion?
Answer:
2.094 x 10¹⁰ I have to add more words soo
factorize all the question.
Answer:
5a(a - 2)
2(a^2 - 4)
(x + 5)(x - 5)
(x - 4)(x^2 + 4x + 16)
(a - 3)(a - 2)
(x^2 + x + 1)(x^2 - x - 1)
Step-by-step explanation:
5a^2 - 10a factor out GCF
5a(a - 2)
2a^2 - 8 factor out GCF
2(a^2 - 4)
x^2 - 25 difference of squares
(x + 5)(x - 5)
x^3 - 64 difference of cubes
(x - 4)(x^2 + 4x + 16)
a^2 - 5a + 6 factors of 6 that add to -5
a^2 - 2a - 3a + 6
a(a - 2) - 3(a - 2)
(a - 3)(a - 2)
x^4 - x^2 - 2x - 1 group last three terms
x^4 + (-x^2 - 2x - 1)
x^4 - (x^2 + 2x + 1) factors of 1 that add to 2
x^4 - (x + 1)(x + 1)
x^4 - (x + 1)^2 difference of squares
(x^2 + (x + 1))(x^2 - (x + 1)) simplify
(x^2 + x + 1)(x^2 - x - 1)
sort the sequence according to whether they are arithmetic gemoentic or neither
98.3, 94.1, 89.9, 85.7 (Arithmetic)
1, 0, -1, 0 (Neither)
1.75, 3.5, 7, 14 (Geometric)
-1, 1, -1, 1..... (Geometric)
Determining the type of a sequenceAn arithmetic sequence has a common difference
A geometric sequence has a common ratio
Considering the given sequences one after the other:
For 98.3, 94.1, 89.9, 85.7,..........
The common difference, d = 94.1 - 98.3 = -4.2
Therefore, 98.3, 94.1, 89.9, 85.7 is an arithmetic sequence
For 1, 0, -1, 0......
The sequence does not have a common difference or a common ratio. Therefore, it is neither an arithmetic nor geometric sequence
For 1.75, 3.5, 7, 14,.....
The common ratio = 3/1.75 = 2
Therefore, it is a geometric sequnec
For -1, 1, -1, 1.....
The common ratio = 1/-1 = -1
It is a geometric sequence
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Zachary is a salesperson who sells computers at an electronics store. He makes a base pay amount each day and then is paid a commission as a percentage of the total dollar amount the company makes from his sales that day. Let P represent Zachary's total pay on a day on which he sells x dollars worth of computers. The table below has select values showing the linear relationship between x and P. Determine the percentage commission Zachary makes on his daily sales.
The tabular values can be used to derive the formula relationship between x and P which gives the percentage commission of Zachary as 1%
How can the percentage commission be calculated?From the above table, we have;
P = x × y% + bWhere;
y = The fixed percentage commission Zachary makes
b = Zachary's base pay
Therefore;
105 = 3000 × y + b... (1)110 = 3500 × y + b... (2)125 = 5000 × y + b... (3)Subtracting equation (1) from (2), gives;
110 - 105 = (3500 - 3000) × y + b - b = 0
5 = 500•y
y = 5/500 = 0.01 = 1%
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Someone please helpppp
Answer:
3. Completing the Square
4. 0, 1, or 2
Step-by-step explanation:
Hello!
3) Which of the following is NOT a method to find the x-intercepts of a quadratic equation?a) Graphing
Graphing is a useful method as it lays the answer out in front of you. Once you graph the parabola, you simply take the intersections of the graph and x-axis as your x-intercepts. Therefore, it is a method.
b) Factoring
Factoring can be used to find x-intercepts, and after factoring, you can set each factor to 0 and solve for x, which are the x-intercepts. This method is also called the Zero Product Property.
c) Quadratic Formula
The quadratic formula is meant to solve for the x-intercepts, as the formula uses values of the coefficients to isolate x and solve for it.
Standard form of a Quadratic: [tex]ax^2 + bx + c = 0[/tex]
Quadratic Formula: [tex]x = \frac{-b\pm\sqrt{b^2 - 4ac}}{2a}[/tex]
Plugging in the values of a, b, and c give you the solutions for x.
d) Completing the Square
Completing the square CAN be used to find the x-intercepts, but not directly so. It is used to convert standard form into a different form, known as the vertex form. It is meant so find the vertex, not the x-intercepts.
Therefore, Completing the Square is NOT a method to find the x-intercepts.
4) How many solutions (x-intercepts) can a quadratic equation have?The number and types of solutions depend on the discriminant of the quadratic (the part under the square root in the QF).
Types of roots:
If positive: 2 real rootsIf negative: 2 imaginary roots (technically 0 roots)If equal to 0: 1 real root (double root)That means that a quadratic equation can have 0, 1, or 2 roots.
Answer:
Completing the square and 2, 1, and 0.
Step-by-step explanation:
Person above is correct!!
Can someone help me with these problems having trouble and show work please !!
Answer:
(2x-5)(2x-5), 81 meters
Step-by-step explanation:
All of the sides of a square are equal, so to find the area we need to multiply 2x-5 by 2x-5: (2x-5)(2x-5)
Using this equation we can plug in 7 for x:
(2(7)-5)(2(7)-5) =
(14-5)(14-5) =
9*9 = 81
Find the volume of the prism. Round to the nearest tenth if necessary.
Answer:
27.2
Step-by-step explanation:
V = (1/2)(2.6)(5.1)(4.1), which is 27.2 to the nearest tenth
(2x+5/60-95x-3/30=3/2
Answer:
x = -0.01685
(Is the equation written correctly? This feels like a very unfortunate number)
Step-by-step explanation:
(2x+5/60-95x-3/30=3/2
2x+(5/60)-95x-(3/30)=3/2
2*(2x+(5/60)-95x-(3/30))=3 [Multiply both sides by 2]
4x+(10/60)-190x-(6/30))=3
(2/30)-186x-(6/30))=3 [Simplify]
-186x-(4/30)=3
-186x=3+(4/30)
-186x=(90/30)+(4/30)
x = (94/30)/(-186)
x = -0.01685
18 pieces of furniture by this Saturday. The materials for each bookcase cost him $20.00 and the materials for each TV stand cost him $40.00. He has $600.00 to spend on materials. Andrew makes a profit of $60.00 on each bookcase and a profit of $100.00 for each TV stand. Find how many of each piece of furniture Andrew should make so that he maximizes his profit.
Andrew should make 6 bookcase and 12 tv stand to maximize his profut $1560.
Given that 18 pieces of furniture is made and the materials for each bookcase cost him $20.00 and the materials for each TV stand cost him $40.00 and he has $600.00 to spend on materials. He makes a profit of $60.00 on each bookcase and a profit of $100.00 for each TV stand.
Let x represent the number of book case and let y represent number of tv stand.
Total number of book case and total number of tv stand is x+y≤18 ......(1)
Total amount of book case and total amount of tv stand is 20x+40y≤600 ......(2)
minimum amount of book case is x≥0 and minimum amount of tv stand is y≥0.
Now, solve the inequality (1) by converting it into equality and substituting x=0 and y=0, we get
x+y=18
When x=0 then
0+y=18
y=18
When y=0 then
x+0=18
x=18
Now, solve the inequality (2) by converting it into equality and substituting x=0 and y=0, we get
20x+40y=600
When x=0 then
20(0)+40y=600
40y=600
y=15
when y=0 then
20x+40(0)=600
20x=600
x=30
Further, we will grph the inequalities and we get feasible region and taking boundary point from graph.
From the graph the vertices of the feasible region is (0,0),(6,12),(0,15) and (18,0)
Further, we will find the maximization profit for the equation Z=60x+100y
When (x,y)=(0,0) then
Z=60(0)+100(0)
Z=0
When (x,y)=(6,12) then
Z=60(6)+12(100)
Z=360+1200
Z=1560
When (x,y)=(0,15) then
Z=60(0)+12(15)
Z=0+1500
Z=1500
When (x,y)=(18,0) then
Z=60(18)+100(0)
Z=1080
Hence, maximum profit is $1560 when andrew should build 6 bookcase and 12 tv stand.
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If you have a savings account, contact your bank and find out the interest rate on that account. (If you don’t have your own account, contact a local bank to ask what the interest rate would be if you set up a savings account today.)
a. State the interest rate the bank quoted.
b. Write an exponential growth equation that models the yearly growth if you put $625 in the account and left it there for years.
c. What will be the value of the account in 25 years?
d. Which of the following would result in more money: $625 deposited in your bank at the current interest rate for 6 years, or deposit $625 into a money market account with a 5% rate for 1 year? Show how you determined your answer.
Deposit $625 into a money market account with a 5% rate for 1 year would result in more money.
The interest rate of the bankTo do this, we make use of 1.50% interest rate
The exponential growth equationHere, we have:
Initial, a= 625
Rate, r = 1.5%
The exponential growth equation is
A(t) = a * (1 + r)^t
So, we have:
A(t) = 625 * (1 + 1.5%)^t
Evaluate
A(t) = 625 * 1.015^t
Hence, the exponential growth equation is A(t) = 625 * 1.015^t
The value in 25 yearsHere, t = 25.
So, we have:
A(25) = 625 * 1.015^25
Evaluate
A(25) = 906.84
Hence, the value in 25 years is $906.84
The investment with more money#Investment A
a = 625
r = 1.5%
t = 5
So, we have:
A(5) = 625 * 1.015^5
Evaluate
A(5) = 673.3
#Investment B
a = 625
r = 5%
t = 1
So, we have:
A(1) = 625 * 1.5^1
Evaluate
A(1) = 937.5
By comparison, 937.5 is greater than 673.3
Hence, deposit $625 into a money market account with a 5% rate for 1 year would result in more money.
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When a person convicted of a crime appeals a conviction, he or she asks a higher court to examine the trial court's decisions to determine whether the proper procedures were followed.
The statement when a person convicted of a crime appeals a conviction, he or she asks a higher court to examine the trial court's decisions to determine whether the proper procedures were followed is True.
What is Appeals?Appeal occur when a person convicted of a crime want another court to reverse a decisions or to examine and re-check the judgement or outcome of a trial court outcome because the convicted person was not satisfied with the outcome or the result of the trial court .
Hence, the statement is true because an offender that was convicted of a crime can tend to files an appeal with a higher court or appellate court so as to examine the trial court's decisions.
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the sum of three numbers is 78. the third number is 3 times the first. the first number is 7 more than the second. what are the numbers?
Answer:
17
Step-by-step explanation:
x+3x+x-7=78
5x-7=78
5x=78+7
5x=85
x=85/5
x=17
Answer:
The three numbers are 17, 10 and 51.
Step-by-step explanation:
Let the first, second, and third numbers be [tex]x[/tex], [tex]y[/tex], and [tex]z[/tex] respectively.
• From the question, we know:
sum of the numbers is 78.
∴ [tex]x + y + z = 78[/tex] ----------(1st equation)
Let's express both [tex]x[/tex] and [tex]z[/tex] in terms of [tex]\bf y[/tex] :
• We know that:
the third number is 3 times the first.
∴ [tex]z = 3x[/tex]
⇒ [tex]x = \frac{z}{3}[/tex] ----------(2nd equation)
• We also know that:
the first number is 7 more than the second.
∴ [tex]\boxed{x = 7 + y}[/tex]
Substituting [tex]x = \frac{z}{3}[/tex] (from 2nd equation)
⇒ [tex]\frac{z}{3} = 7 + y[/tex]
⇒ [tex]\boxed{z = 21 + 3y}[/tex]
• We can now substitute [tex]x = 7 + y[/tex] and [tex]z = 21 + 3y[/tex] into the first equation:
[tex]x + y + z = 78[/tex]
⇒ [tex](7 + y) + y + (21 + 3y) = 78[/tex]
⇒ [tex]5y + 28 = 78[/tex]
⇒ [tex]5y = 50[/tex]
⇒ [tex]y = \bf 10[/tex]
∴ [tex]x = 7 + 10\\[/tex]
⇒ [tex]x = \bf 17[/tex]
[tex]z = 21 + 3(10)[/tex]
⇒ [tex]z = \bf 51[/tex]
∴ The three numbers are 17, 10 and 51.
A prism with a heart-shaped base is sliced parallel to the base. What shape is formed?
The shape formed, when a prism with a heart-shaped base is sliced parallel to the base, will be congruent to its base. Hence, it will also be heart-shaped.
A prism is a polyhedron made up of n parallelogram faces that connect the n-sided polygon base, the second base, which is a translated duplicate of the first base, and the n faces. The bases are translated into all cross-sections that are parallel to them.
In the question, we are informed that a prism with a heart-shaped base is sliced parallel to the base.
We are asked what shape is formed.
From the above discussion, we know that the bases are translated into all cross-sections that are parallel to them, that is, all cross-sections parallel to the base, will be congruent to the base.
Thus, the shape formed, when a prism with a heart-shaped base is sliced parallel to the base, will be congruent to its base. Hence, it will also be heart-shaped.
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Answer:
Step-by-step explanation:
Heart Shaped
How does the volume of a cylinder with a radius of 4 units and a height of 12 units compare to the volume of a rectangular prism with dimensions 8 units x 8 units x 6 units
Answer:
The volume of the cylinder is smaller than the rectangular prism.
Step-by-step explanation:
36a^(4)b^(10)-81a^(16)b^(20) factor the given expression using the difference of squares pls
The factorized expression using difference of squares is as follows,
9a²b⁵ (2+3a⁶b⁵)(2-3a⁶b⁵)
Difference of Squares
Difference of squares is a factorization method where an expression can be factored as (a + b) (a - b) when considered as the difference of two perfect squares, a²-b². For instance, factoring x²-25 results in (x+5) (x-5). By enlarging the parentheses in (a + b) (a - b), the pattern (a + b) (a - b)=a²-b² is used as the foundation for this technique.
Factorization Using Difference of Squares
Given expression is,
36a⁴b¹⁰ - 81a¹⁶b²⁰
= (6a²b⁵)² - (9a⁸b¹⁰)²
Using square of differences, we have
a² - b² = (a + b) (a - b)
Here, a = 6a²b⁵ and b = 9a⁸b¹⁰
Thus, we get,
(6a²b⁵ + 9a⁸b¹⁰)(6a²b⁵ - 9a⁸b¹⁰)
Further Factorization
We can take out 3 common from both the bracket terms after applying difference of squares
3×3(2a²b⁵ + 3a⁸b¹⁰)(2a²b⁵ - 3a⁸b¹⁰)
= 9(2a²b⁵ + 3a⁸b¹⁰)(2a²b⁵ - 3a⁸b¹⁰)
Further, we can take out a²b⁵ as common from both the bracket terms
= 9a²b⁵ (2+3a⁶b⁵)(2-3a⁶b⁵)
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12. The average bowling score of the 5-member in Regional High School bowling team is 128. If all the members of the team get the same score except for one, who bowls a 160, what is the score of the rest of the players? (A) 32 (B) 96 (C) 120 (D) 144
Answer:
C
Step-by-step explanation:
The average is the total of the scores divided by 5.
128 x 5 Gives us the total scores of 640. I know that one bowler had a score of 160. I will subtract that from the total of 640. 640-160 = 480. Since the 4 bowlers left, all had the same score, I will divide 480 by 4 to get 120
Can someone help me with these problems please!
Answer:
I have just wrote answers
A pyramid with a rectangular base is stacked on top of rectangular prism. The height of the composite figure is 10. The lengths of the rectangular base are 8 and 6 units. The height of the rectangular prism is 4. Which expression represents the volume, in cubic units, of the composite figure
The expression that represents the volume of the composite figure is: 1/3(8)(6)(6) + (8)(6)(4).
What is the Volume of a Composite Figure?The volume for the given composite figure = volume of the rectangular pyramid + volume of rectangular prism.
= 1/3(l)(w)(h) + (l)(w)(h)
Thus, with the given dimensions, plug in the values to get the expression represents the volume of the composite figure:
Volume = 1/3(8)(6)(6) + (8)(6)(4)
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a triangle has two sides of length 2 and 5 and that the angle between these two sides is 60 degrees, what is the length of the third side of the triangle
The length of the third side of the triangle is 4. 33
How to determine the side
We have the length of the two sides to be;
2 and 5
If the angle between them is 60 degrees, then the third side is the opposite side
To find the opposite side, we use the sin ratio, which is
sin 60 = opposite/hypotenuse
sin 60 = x/ 5
Cross multiply
sin 60 × 5 = x
x = 0. 8660 × 5
x = 4. 33
Thus, the length of the third side of the triangle is 4. 33
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Write the following inverse proportion: y is inversely proportional to x, when y = 5 and x = 8.
The inverse proportionality expression is y =40/x
Inverse proportionIf the variable y is inversely proportional to x, this is expressed as;
y = k/x
where
k is the constant of proportionality
If y = 5 and x = 8. then;
5 = k/8
k = 5 * 8
k = 40
Determine the inverse proportionality
Recall that y = k/x
y = 40/x
Hence the inverse proportionality expression is y =40/x
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What is the ratio?
Help me please I appreciate it :)
Answer:
I'm assuming that it is 4:1
Step-by-step explanation:
The pressure, p, with which water passes through a pipe varies inversely as the square of the pipe's radius, 2. If k is the constant of
variation, which equation represents this situation?
Opr²-k
Op=r²2²+k
Op+r²2²=k
Op=kr²
The variation equation is p = kr^2
How to determine the variation equation?The variables are give as:
Pressure = P
Radius= r
The direct variation from p to the square of r is represented as:
[tex]p\ \alpha\ r^2[/tex]
Express as an equation
p = kr^2
Where k represents the constant of variation
Hence, the variation equation is p = kr^2
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Answer:
The correct answer is the 3rd option
The volume of a certain right circular cone is 30 cubic inches. What is the volume, in cubic inches, of a second right circular cone with half the radius and twice the height of the first cone
Answer:
V = 15 in.³
Step-by-step explanation:
The original cylinder has radius r and height h.
V = πr²h
Its volume is 30 in.³, so
πr²h = 30 in.³
The new cylinder has radius (1/2)r and height 2h.
Its volume is
V = π(r/2)²(2h)
V = πr² × 2h/4
V = πr²h/2
πr²h is the volume of the original cylinder, and it is 30 in.³.
V = 30 in.³/2
V = 15 in.³
If 5/6 is 180, what is 1/6?
(please explain as well)
Answer: 36
Step-by-step explanation:
If 5/6 = 180
lets find what 1/6 equals
To do this lets divide 180 by 5 to find 1/6
[tex]\frac{180}{5} =36[/tex]
Therefore, 1/6 = 36
We know 180/5 will give us the answer because 180 is already 5/6 of the total; dividing by 5 will give us 1/6 of the total. Ex: if we had 4/6 of the total, we would divide by 4 to find 1/6.
Anyways, we can check our answer by doing:
36*5 = 216 then taking 5/6 of 216, which should equal 180
[tex]216*\frac{5}{6} =180[/tex]
Therefore, we know 36 is the correct answer
Which is the correct equation of the line for the following graph?
Answer:
(c) y = -3x +6
Step-by-step explanation:
The equation can be written in slope-intercept form when we know the slope and the y-intercept.
Slope-intercept formThe slope-intercept form of the equation of a line is ...
y = mx +b . . . . . . where m is the slope and b is the y-intercept
Y-interceptThe y-intercept is the y-value where the line crosses the y-axis. It is 6. This eliminates choices A and D, leaving choices ...
y = 3x +6 . . . . . choice By = -3x +6 . . . . .choice CSlopeThe line goes down to the right. This is a negative slope, eliminating choice B.
The equation of the line is y = -3x +6.
__
Additional comment
The line intersects the x-axis at x=2. This means the "rise" of the line is -6 units for a "run" of 2 units. The numerical value of the slope is ...
m = rise/run = -6/2 = -3
Now, we know the parameters of the equation are m=-3, b=6, and the equation of the line is
y =-3x +6
Which of the following equations describes the graph?
Identify a transformation of the function f(x) = x by observing the equation of the function g(x) = x − 90.
The base graph has been shifted down 90 units.
The base graph has been shifted right 90 units.
The base graph has been shifted left 90 units.
The base graph has been shifted up 90 units.
Using translation concepts, the change of f(x) = x to g(x) = x - 90 can be described as follows:
The base graph has been shifted down 90 units.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
In this problem, we have that g(x) = f(x) - 90, that is, the base graph was shifted down 90 units.
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It takes the pit crew 15 seconds to change a
tire. How long is this in minutes?
Answer:
Hey there :) The answer is 0.25 minutes.
Step-by-step explanation:
1 minute = 60 seconds
So, 15 ÷ 60 = 0.25 minutes