The 95% confidence interval for the proportion of respondents who say yes is of:
(0.5562, 0.6176)
What is a confidence interval of proportions?A confidence interval of proportions has the bounds given by the rule presented as follows:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which the variables used to calculated these bounds are listed as follows:
[tex]\pi[/tex] is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
The remaining parameters, which are the sample size and the estimate, are given as follows:
[tex]n = 990, \pi = \frac{581}{990} = 0.5869[/tex]
The lower bound of the interval is of:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.5869 - 1.96\sqrt{\frac{0.5869(0.4131)}{990}} = 0.5562[/tex]
The upper bound of the interval is of:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.5869 + 1.96\sqrt{\frac{0.5869(0.4131)}{990}} = 0.6176[/tex]
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Which symbol replaces the box to make the statement true? 18÷6+3□6+12÷3 Responses > greater than < less than =
The correct expression of the inequality expression is 18 ÷ 6 + 3 □ 6 + 12 ÷ 3
How to complete the inequality expression?From the question, the expression is given as
18 ÷ 6 + 3 □ 6 + 12 ÷ 3
We start by converting the above expression to the same form
So, we start by solving the quotients
This gives
3 + 3 □ 6 + 4
Next, we evaluate the sum
So, we have
6 □ 10
In the above expression, we have
6 and 10
By convention, the number 6 is less than the number 10
This is so because 6 has a smaller value and 10 has a higher value
When the above numbers are compared, we have
6 is less than 10
This means that we make use of the inequality symbol <
So, we have
18 ÷ 6 + 3 < 6 + 12 ÷ 3
Hence, the complete inequality is 18 ÷ 6 + 3 □ 6 + 12 ÷ 3
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Tim needs 6 lb of a metal that contains 54 % silver. If Tim combines one metal with 29%
silver, and another with 80 % silver, how much of each metal does Tim need?
After solving the Algebraic expression we gets Tim needs 3.05 lbs. and 2.95 lbs. Metal.
What is algebra ?Algebraic expressions are constructed using integer constants, variables, and the addition, subtraction, multiplication, and division operations of basic arithmetic.
To form the Algebraic expression
Let x be the quantity of silver at 29% and y the quantity at 80%
Then x*28% + y*61% = 6*54%
and x + y = 6
Let y = 6-x then
29*x + (6-x)*80= 324
29*x + 480- 80*x = 324
51*x = 156 and x = 156/51 = 3.05 lbs.
so y = 6 - x = 2.95 lbs.
Hence,
Tim needs 3.05 lbs. and 2.95 lbs. Metal.
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Question 8 of 10
What is the complete factorization of the polynomial below?
x3+3x²+ 9x+27
OA. (x+3)(x+3/)(x-3)
OB. (x-3)(x+3)(x+3)
OC. (x-3)(x+3)(x-3/)
D. (x+3)(x+3)(x+3/)
The factorization of the expression [tex]x^3+3x^2+9x+27[/tex] is [tex](x+3)(x^2+9)[/tex].
What is factorization?
The greatest common factors among the terms in the provided algebraic expression are identified, and the terms are then grouped in accordance with these factors to factorise the equation. A factorization is just the procedure by which an algebraic expression gets expanded in the opposite direction. The greatest common factors among the terms in the provided algebraic expression are identified, and the terms are then grouped in accordance with these factors to factorise the equation. Factorization is the reverse process of expansion of an algebraic statement. If an algebraic expression is a product of prime factors, it has undergone complete factorization.
Here the given polynomial expression is ,
=> [tex]x^3+3x^2+9x+27[/tex]
=> [tex]x^2(x+3)+9(x+3)[/tex]
=> [tex](x+3)(x^2+9)[/tex]
Hence the complete factorization of the given expression is [tex](x+3)(x^2+9)[/tex].
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If q is 2.00 what is the distance from C to A?
Answer: 4.00
Step-by-step explanation:
If the q is 2.00 A to C is double the q. So, 2.00x2= 4.00.
Answer:
AC = 4.00Step-by-step explanation:
Given is a parallelogram.
One of the properties of a parallelogram is its diagonals bisect each other.
It gives us:
AC = 2qAC = 2*2.00 = 4.00If India works overtime, she receives an
hourly rate of 1-times her regular hourly 1/2
rate. What is her hourly overtime rate?
After solving, 50% is her hourly overtime rate.
In the given question,
India works overtime, she receives an hourly rate of 1-times her regular hourly 1/2 rate.
We have to find her hourly overtime rate.
India is working overtime so her regular hourly rate is 1/2.
Evaluating the expression
We find her hourly overtime rate in percentage.
She receive overtime rate for 1 time is 1/2 rate.
We can write 1/2 as 0.5.
To express it as percentage we multiply and divide by 100.
= 0.5 × 100/100
= 50%
Hence, 50% is her hourly overtime rate.
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A rectangular wall measures 15 ft along the floor. The area of
the wall is 180 ft². What is the height of the wall?
Answer:
The height is 12ft
Step-by-step explanation:
In order to find the height, you have to divide the area by the width which is 180ft divided by 15ft, you get 12ft, and if you double-check 15 x 12 gets you 180, which is the area.
Find the Surface Area for the following:
(Use 3.14 for . Do not round and do not type your units.)
Surface Area = ______ in²
The shape has a surface area of: Surface Area = 282.6 in²
How to determine the surface area?The given parameter is represented on the figure
In this case, the figure is a cone with the following parameters
Radius, r = 5 inches
Height, h = 12 inches
The surface area of the cone is then calculated as
A = πr * (r + √(h² + r²))
Substitute the known values in the above equation, so, we have the following representation
A = 3.14 * 5 * (5 + √(12² + 5²))
Evaluate the expression
A = 282.6
Hence, the surface area is 282.6 square inches
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A quadratic function y = f(x) is plotted on a graph and the vertex of the resulting
parabola is (-5, 3). What is the vertex of the function defined as g(x) = f(x) + 2?
Answer:
Submit Answer
Vertex of g(x) is: (-2, -4)
What is vertex?An element of a line is a line segment. A line segment that can be extended endlessly is known as a ray.An angle is created when two line segments or rays cross one another. A vertex is created by definition whenever two lines come together to produce an angle. Thus, we can state that a vertex is formed when two line segments or rays intersect.acc to our question:
Vertex form of a quadratic function:
f(x) = (x - h)² + k
We have (h, k) = (3, -4)
The function f(x) is:
f(x) = (x - 3)² - 4
The function g(x) is: g(x) = f(x + 5) =
(x + 5 - 3)² - 4 = (x + 2)² - 4Vertex of g(x) is:(-2, -4)
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What is -1/6 divided by 2/9
Answer:
Step-by-step explanation:
1. List out the numbers and divide
-1/6/2/9=
2. In division for fractions, the number or numbers on the right of the division side flip and change to multiply!
-1/6/2/9= -1/6*9/2= -9/12
3. Simplify!
-9/12= -3/4
Answer:
-3/4
Step-by-step explanation:
so you leave -1/6 but then you change the sign to multiply and the other fraction change it so if you had 2/9 it will be 9/2
so we get -1/6×9/2.
if you don't know how to multiply fractions i can explain just ask.
A student earned the scores in the data set in one course.
{88, 72, 68, 78, 94}
What is the mean of the scores?
Answer:
80
Step-by-step explanation:
the mean of a data set is calculated as
mean = [tex]\frac{sum}{count}[/tex] = [tex]\frac{88+72+68+78+94}{5}[/tex] = [tex]\frac{400}{5}[/tex] = 80
For d the question is asking after four months, the heat is turned off. The excess amount, electricity from the solar panels begins to build back up according to the function. E(d)=38d+500. How do you interpret the 38 in the 500 and this model, we’re doing our presents the number of days since the heat was turned off. How would I solve this?
From the equation E(d) = 38d + 500, The initial electricity is 500W and the build up is 38W per day
What is an equation?An equation is an expression showing the relationship between two or more numbers and variables.
The standard equation of a straight line is:
y = mx + b
Where m is the rate of change and b is the y intercept
Let E represent the electricity from the solar panels after d days.
Since:
E(d) = 38d + 500
The y intercept is 500 and the slope is 38
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Line x is the perpendicular bisector of segment ZY
what does b=
Based on the definition of perpendicular bisector, the value of b = 5.
What is a Perpendicular Bisector?A perpendicular bisector can be described as any line that bisects another line segment at right angles.
This means, the measure of the angles at the point of bisection are right angles (90 degrees).
Therefore:
12b + 30 = 90 [definition of perpendicular bisector]
Solve for b
12b + 30 - 30 = 90 - 30
12b = 60
Divide both sides by 12
12b/12 = 60/12
b = 5
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A laundromat has a wash-and-fold service for a monthly fee of $28.00. The laundromat will wash and fold clothes at $0.61 per pound for those customers with a laundry service. One customer paid $41.42 in total for the month.
Which equation can be used to determine the pounds of laundry the customer brought in to be washed and folded that month?
A. 0.61x + 28.00 = 41.42
B. 0.61x + 41.42 = 28.00
C. 28.00 - 0.61x = 41.42
D. 41.42 + 28.00 = 0.61x
The required equation can be used to determine the pounds of laundry the customer brought in is A. 0.61x + 28.00 = 41.42
What is an equation?An equation is a mathematical expression that shows the relationship between two variables.
How to find equation can be used to determine the pounds of laundry the customer brought in to be washed and folded that month?To find the given equation,
Let x be the number of pounds of clothes washed and folded at the laundromat.
Given that the laundromat will wash and fold clothes at $0.61 per pound for those customers with a laundry service, the total amount paid for the number of poundsof clothes is P = rate × number of pounds = $0.61 × x = 0.61x
Also, the laundromat has a wash-and-fold service for a monthly fee of $28.00.
So, the total amount paid is T = P + $28.00 = $0.61x + $28.00
Now, since one customer paid $41.42 in total for the month, since this is the total amount paid, then T = $41.42
So, $0.61x + $28.00 = $41.42
So, the required equation is A. 0.61x + 28.00 = 41.42
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Apples cost 1.85 per kilogram
Work out the cost of 1.6 kilogram of apples
for 20 points
Answer:
1.6 kg = $2.96
Step-by-step explanation:
The given statement is,
→ 1 kg of apple = $1.85
→ a = 1.85
Now the cost of 1.6 kg of apple is,
→ 1.6 × a
→ 1.6 × 1.85
→ $2.96
Hence, 1.6 kg of apple is $2.96.
In the triangle below, with right angle I, suppose that m< J= (2x+22)° and m < K = (5x-2)
Find the degree measure of each angle in the triangle.
m < I =
M< J =
m < K =
Answer:
Step-by-step explanation
so basically you need to see what m<I equals and do the same for the rest of them and you should get your answer and that would be let me see and m<k= -44 degrees and m<I and J= -10 degrees and there you have if this is not right i tried have the same step and ask another person
Divide. If the polynomial does not divide evenly, include the remainder as a fraction.
2
(13q² +82q - 55) ÷ (q + 7)
The division of the given polynomial is [tex]13q - 9 + \frac{8}{q+7}[/tex].
What is the quotient of polynomials?
Any quotient of polynomials a(x)/b(x) can be expressed as q(x)+r(x)/b(x), where r(x) is a real number and b is a real number (x). For instance, x-2+3 can be used to represent (x2-3x+5)/(x-1) (x-1).
We have,
[tex]\frac{(13q^{2} + 82q - 55)}{ (q + 7)}[/tex]
By dividing,
[tex]\frac{(13q^{2} + 82q - 55)}{ (q + 7)} / \frac{(13q^{2} + 82q - 55)}{ (q + 7)}[/tex]
[tex]= 13q + \frac{-9q - 55)}{ (q + 7)}[/tex]
[tex]\frac{-9q - 55}{q+7} / \frac{-9q - 55}{q+7}[/tex]
[tex]= 13q - 9 + \frac{8}{q+7}[/tex]
Hence, the division of the given polynomial is [tex]13q - 9 + \frac{8}{q+7}[/tex].
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17).
A chef has 31 litres of cooking oil. He uses 7, of it during an evenings cooking.
How much does he
a).
use,
b).
have left over ?
Answer:
a) He obviously used 7 liters of cooking oil.
b) He has 24 liters of cooking oil left.
(HELP ASAP) ABC Is Isosceles m
Answer:
m∠A = 55°-----------------------------
A and C are congruent angles opposite to congruent sides of the isosceles triangle.
m∠A = m∠C3x + 40 = x + 503x - x = 50 - 402x = 10x = 5Find the measure of ∠A
m∠A = 3×5 + 40 = 15 + 40 = 55Answer:
The angle A is 55°.
Step-by-step explanation:
We know that,
→ <A = <C
Now the value of x will be,
→ 3x + 40 = x + 50
→ 3x - x = 50 - 40
→ 2x = 10
→ x = 10/2
→ [ x = 5 ]
Then the value of m<A is,
→ A = 3x + 40
→ A = 3(5) + 40
→ A = 15 + 40
→ [ A = 55° ]
Hence, the answer is 55°.
Find the sum: (2x² + x + 3) + (3x² + 2x + 1)
A. 3x² + 5x+4
B. 5x²+3x+4
OC. 6x + 2x + 3
OD. 5x²+2x+4
Answer:
B
Step-by-step explanation:
Combine 2x^2 and 3x^2 to get 5x^2.
5x²+x+3+2x+1Combine x and 2x to get 3x.
5x²+3x+3+1Add 3 and 1 to get 4.
5x²+3x+4The correct option is B.K
Find the equation of a line that is perpendicular to the line y=
y= (Type your answer in slope-intercept form.)
keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above
[tex]y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{1}{5}}x+5\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{1}{5}} ~\hfill \stackrel{reciprocal}{\cfrac{5}{1}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{5}{1}\implies -5}}[/tex]
so we're really looking for the equation of a line whose slope is -5 and that it passes through (-4 , 0)
[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{0})\hspace{10em} \stackrel{slope}{m} ~=~ - 5 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{0}=\stackrel{m}{- 5}(x-\stackrel{x_1}{(-4)}) \\\\\\ y -0= -5 (x +4) \implies {\Large \begin{array}{llll} y=-5x-20 \end{array}}[/tex]
Calculate the simple interest and maturity value
The simple interest is $420 and the maturity value is $$6,720
How to find the simple interest?Using this formula to find the simple interest
Simple interest = Principal × Interest rate × Time
Where:
Principal = $6300
Interest rate =4% or 0.04
Time = 20 month = 20/12 = 1.6666666
Let plug in the formula
Simple interest = $6,300 × 0.04 × 1.6666666
Simple interest = $420
Using this formula to find the maturity value
Maturity value = Principal + Interest
Maturity value = $6,300 + $420
Maturity value = $6,720
Therefore the interest is $420.
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A road is 8/9 of a mile long. A crew needs to repave 2/5 of the road. How long is the section that needs to be repaved?
Given that 150 students were interviewed, 85 signed for mathematics, 70 signed for English, and 50 signed for both. Draw a venn diagram to show.
How many signed for only mathematics
How many signed for English only
English or Mathematics
Neither English nor Mathematics
English and Mathematics
1. 35 signed up for only mathematics
2. 20 signed up for only English
3. 85 or 70 is English or mathematics
4. Neither math or English is 45
5. English and Math is 50
How to solve the Venn diagram1. How many signed for only mathematics
We have to define only mathematics as x
while we have math = m
English as E
Math and English as ME
only math
X = M - ME
= 85 - 50
= 35
2. Only English
E - ME
= 70 - 50
= 20
3. English or mathematics =
85 or 75
4. Neither English nor Mathematics
150 - (85 + 70 - 50)
= 45
5. The number for math and English is what is the intersection = 50
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If 3 workers complete a certain task in 12 days, how many workers are needed to finish the same task in 4 days?
A total of 9 workers are needed to finish the same task in 4 days
How to determine the number of workers?From the question, we understand that:
3 workers can complete a certain task in 12 days
This means that
3 workers = 12 days
The proportionality constant is then calculated as
Proportionality constant = Number of workers x Number of days
Substitute the known values in the above equation So, we have the following equation
Proportionality constant = 3 * 12
Evaluate
Proportionality constant = 36
When the number of days is 4, we have
Days = 4
So, we have
Proportionality constant = Number of workers x Number of days
This gives
36 = Number of workers x 4
Divide both sides by 4
Number of workers = 9
Hence, the number of workers is 9
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Select the correct answer from the drop-down menu.
A new park is adding two new walking paths, as indicated by and , which are measured in meters. The park resembles an isosceles trapezoid.
Figure shows a trapezium ABCD. AC and BD are diagonals. The length of BD is 14x plus 4, and AC is 11x plus 31.
Determine the length of each path.
A.
The length of each path is
130
meters.
B.
The length of each path is
140
meters.
C.
The length of each path is
120
meters.
D.
The length of each path is
150
meters.
A.The length of each path is 130 meters.
Given:
The park resembles an isosceles trapezoid.
Figure shows a trapezium . AC and BD are diagonals. The length of BD is 14x plus 4, and AC is 11x plus 31.
we know that:
Diagonals are equal in isosceles trapezoid.
14x + 4 = 11x + 31
14x - 11x = 31 - 4
3x = 27
divide by 3 on both sides
3x/3 = 27/3
x = 9
Diagonal length = 14x + 4.
= 14*9 + 4
= 126 + 4
= 130 meters.
Therefore The length of each path is 130 meters.
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Milan has been given a list of bands and asked to place a vote. His vote must have the names of his favorite, second favorite, and third favorite bands from the list. How many different votes are possible?
The number of possible different votes for Milan, based on the list of bands is 60 different votes.
How to find the number of possible votes?There are 5 lists of bands that Milan has to choose from to place a vote and there are only 3 bands to be chosen out of the 5 lists.
The total number of different votes possible is therefore possible by performing a permutation:
= 5! / ( 5 - 3) !
= 5 ! / 2 !
= (5 x 4 x 3 x 2 x 1) / (2 x 1)
= 60 different votes
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Pls help I’m failing
Answer:
{-9,-8,7,8,10}
A relation is shown: {(3, 2), (5, −1), (6, 7), (3, −8), (4, 2)} Which set of information is true about the relation shown?
The set of information that is true about the relation is:
Domain: {3, 4, 5, 6}
Range: {-8, -1, 2, 7}
The relation is not a function.
How to Determine a Relation that is a Function?A relation that represents a function will have each of its domain elements related to exactly one range element.
All the x-values in a relation are referred to as the domain of a function, while all the y-values are called the range of the function,
Therefore, for a relation to be considered a function, a domain element must not correspond to two different range elements or related to two range elements.
Given the relation, {(3, 2), (5, −1), (6, 7), (3, −8), (4, 2)}:
The domain of the relation is: {3, 4, 5, 6}
The range of the relation is: {-8, -1, 2, 7}
The relation is not a function because the domain element, 3, corresponds to two different range elements, 2 and -8.
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Complete the model to find-9 + 3 Show your work
Answer:
Answer is 0. If you have to owe someone 9 dollars and they give you nine back it is 0. You can also rearrange the problem to 9-9 (same thing) which is 0
Assume z is a standard normal random variable. Then P(–1.20 ≤ z ≤ 1.50) equals
When is a standard normal random variable, the probability of P(–1.20 ≤ z ≤ 1.50) is 0.8181.
What is the probability?The probability illustrates the likelihood of events.
From the information, it's important to note that P(–1.20 ≤ z ≤ 1.50) will be:
= P(Z ≤ 1.50) - P(Z ≤ -1.20)
= P(Z ≤ 1.50) - [1 - P(Z ≤ -1.20)]
It should be noted that by using the normal z table, the probability of the corresponding z score will be 0.9332 and 0.8849.
This will be:
= 0.9332 - (1 - 0.8849)
= 0.8181
Therefore, the probability is 0.8181.
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