The margin of error at 90% confidence and its interpretation is;
0.085; we are 90% confident that the true proportion of sophomores who will attend Homecoming is within 0.085 of the sample proportion
How to find the margin of error?The margin of error is defined as a term used in statistics to find the confidence interval. It is denoted by E.
The formula for margin of error is;
E = z(√(p(1 - p)/n)
The parameters are given as;
Sample size; n = 92
sample of success; x = 51
Sample proportion; p = 51/92 = 0.554
z at 90% CL = 1.645
Thus;
E = 1.645(√(0.554(1 - 0.554)/92)
E = 0.085
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y=-1/2x-1
y=1/4x-4
graphing method
The solution of the system of equations is (4, -3)
How to solve the system of equations graphically?Here we want to solve the next system of equations:
y = -(1/2)x - 1
y = (1/4)x - 4
Graphically.
To do so, we just need to graph both of these lines on the same coordinate axis and find the point where the lines intersect. Below is the graph of the system of equations, there we can see that the lines intersect at the point (4, -3), so that is the solution of the system.
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13 AM
23.
Big Ideas
You make necklaces and key chains to sell at a
crafts fair. The table shows the amounts of time
and money it takes to make a necklace and a
key chain, and the amounts of time and money
you have available for making them.
Time
(hours)
Cost
(dollars)
Necklace Key
0.5
2
O 0.52 +0.25y ≤ 20
O 0.5x+0.25y ≥ 20
2x+3y ≤ 120
2x+3y ≥ 120
Ox+y ≥ 20
chain
0.25
3
Available
Let a represent the number of necklaces and y
represent the number of key chains you make.
Given z>0 and y ≥ 0, select all the
inequalities that represent the situation.
AirF 2023Algebra 1 MOY Items Question #27
20
120
Which combinations of
necklaces and key chains can
you make given the situation?
Select all that apply.
30 necklaces and 20
key chains
50 necklaces and 10
key chains
30 necklaces and 30
key chains
40 key chains
60 necklaces
All the inequalities that represent the situation are as follows;
A. 0.5x + 0.25y ≤ 20.
C. 2x + 3y ≤ 120.
A combinations of necklaces and key chains you can make given the situation include the following:
A. 30 necklaces and 20 key chains.
How to write the required system of linear inequalities?In order to write a system of linear inequalities to describe this situation, we would assign variables to the number of necklaces and number of key chains respectively, and then translate the word problem into algebraic equation as follows:
Let the variable x represent the number of necklaces.Let the variable y represent the number of key chains.Based on the table of values (see attachment) and given x ≥ 0 and y ≥ 0, a system of linear inequalities to describe this situation include the following:
0.5x + 0.25y ≤ 20.
2x + 3y ≤ 120.
Next, we would use an online graphing calculator to plot the above system of linear inequalities in order to determine its solution as shown in the graph attached below.
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Charlie is studying the time it takes members of his company to travel to the office.
He stands by the door to the office from 0840 to 0850 one morning and asks workers, as they arrive, how long their journey was.
State the sampling method Charlie used.
Charlie could have used quota sampling instead of non-random sampling.
What are sampling methods?Sampling means selecting the group that you will actually collect data from in your research. For example, if you are researching the opinions of students in your university, you could survey a sample of 100 studentsGiven is that Charlie is studying the time it takes members of his company to travel to the office. He stands by the door to the office from 08 : 40 A.M. to 08 : 50 A.M. one morning and asks workers, as they arrive, how long their journey was.
Charlie could have used quota sampling instead of non-random sampling. He could have selected a sample that reflects the characteristics of the whole population.
Therefore, Charlie could have used quota sampling instead of non-random sampling.
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{COMPLETE QUESTION IS -
Charlie is studying the time it takes members of his company to travel to the office.
He stands by the door to the office from 0840 to 0850 one morning and asks workers, as they arrive, how long their journey was.
State and briefly describe an alternative method of non-random sampling Charlie could have used to obtain a sample of 40 workers.}
Please help :) 10 points (Geometry)
Answer: (2,0)
Step-by-step explanation:
Midpoint formula( [tex]\frac{x1+x2}{2}[/tex],[tex]\frac{y1+y2}{2}[/tex])
P(-4, 6)
Q(8, -6)
Substitute into formula
-4+8/2
4/2
x = 2
6-6/2
0/2
y = 0
Answer (2,0)
Pls help thank you will mark the Brainliest
Option d) [tex]y= 30.5(0.7)^x[/tex] is the function that best models the number of game systems sold in millions x years since 2015.
Describe Function?In mathematics, a function is a rule that associates each element in one set (called the domain) with a unique element in another set (called the range). The rule specifies how the input values (the elements of the domain) are transformed into output values (the elements of the range).
A function can be represented using various notations, such as f(x), where f is the name of the function and x is the input value, or y = f(x), where y is the output value and x is the input value. The function can be defined explicitly, as in[tex]f(x) = x^2,[/tex] or implicitly, as in the equation of a circle, [tex]x^2 + y^2 = r^2[/tex], where y is a function of x.
To determine which function best models the number of game systems sold, we need to observe the trend in the data.
We can see that the number of game systems sold is decreasing as time goes on, which means the function should be decreasing as well.
Option a) [tex]y=21.35(0.7)^x[/tex] is an exponential function with a base less than 1, which means it would also be decreasing. However, it starts with a higher initial value than the data suggests.
Option b) [tex]y= 30.5(21.35)^x[/tex] is an exponential function with a base greater than 1, which means it would be increasing. This function does not match the trend in the data.
Option c) [tex]y= 30.5(1.3)^x[/tex] is an exponential function with a base greater than 1, which means it would be increasing. This function also does not match the trend in the data.
Option d) [tex]y= 30.5(0.7)^x[/tex]is an exponential function with a base less than 1, which means it would be decreasing. Additionally, this function passes through all three data points, and it has a starting value that matches the first data point. Therefore, option d) is the function that best models the number of game systems sold in millions x years since 2015.
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a certain species of virulent bacteria is being grown in a culture. it is observed that the rate of growth of the bacterial population is proportional to the number present. if there were 4000 bacteria in the initial population and the number doubled after the first 30 minutes, how many bacteria will be present after 3 hours?
For a certain species of virulent bacteria with the rate of growth of the bacterial population as proportional to the number the bacteria present after 3 hours is 256000.
What is exponential function?A mathematical function called an exponential function is employed frequently in everyday life. It is mostly used to compute investments, model populations, determine exponential decline or exponential growth, and so forth.
When there is exponential growth, the quantity grows initially extremely slowly and subsequently quickly. Over time, the rate of change quickens. As time goes on, the rate of increase accelerates. It is intended for the quick growth to be a "exponential increase".
The species of bacteria follow an exponential growth pattern.
The exponential growth is given as:
[tex]A(t) = A_0e^{kt}[/tex]
Where, A₀ is the initial population = 4000
k = constant
t = time = 30 minutes = 1/2 hour.
The bacteria doubles in 30 minutes, thus A(t) = 2(4000) = 8000.
Substituting the values in the equation:
[tex]8000 = 4000e^{k(\frac{1}{2} )}\\\\2 = e^{k(\frac{1}{2} )}[/tex]
Takin ln on both sides of the equation:
ln(2) = 1/2 k
2(ln(2)) = k
k = 1.38
The number of bacteria present after 3 hours:
[tex]A(t) = 4000e^{(1.38)(3)}\\\\[/tex]
A(t) = 256000
Hence, for a certain species of virulent bacteria with the rate of growth of the bacterial population as proportional to the number the bacteria present after 3 hours is 256000.
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PLEASE HURRY!! Which of the following statements are true regarding the graph of this linear function? Select all that apply.
By making linear equation for given graph, slope of line will be 9.75 which is the amount she makes in an hour i.e. E.
What exactly is a linear equation?
The equation is referred to as linear when a variable's maximum power is 1. A one-degree equation is another name for it. A linear equation in one variable has the conventional form Ax + B = 0. This equation has three variables: x, A, and B. A is a coefficient. A linear equation in which there are only two variables typically takes the form Ax + By = C. In addition to the constant C, there are three other constants: the variables x and y, the coefficients A and B, and the variables.
Now,
As given she has a debt of $25 that will be y-intercept.
and as we can see from graph she earns $39 in 4 hours that means $9.75 in an hour which will be slope of line also, then the line will be represented as
y=9.75x-25 where x=hours worked and y=amount earned
hence,
slope of line will be 9.75 which is the amount she makes in an hour.
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I think the difference 6.96 - 0.04 is greater or less than 7
The difference 6.96 - 0.04 is greater than 7.
. A rectangle’s length is twice its width. Its perimeter is 156 meters. What is the rectangle’s length?
Answer:
26 meters,
hope this helps!
Melanie is raising money for a school trip by selling candy bars and bags of chips. The price of each candy bar is $1.50 and the price of each bag of chips is $1.25. Yesterday Melanie made $33.25 and sold 13 more candy bars than bags of chips. Determine the number of candy bars sold and the number of bags of chips sold.
The number of chips sold is 10
The number of candy bars sold is 23
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 3 = 9 is an equation.
We have,
The price of each candy bar = $1.50.
The price of each bag of chips = $1.25.
Number of chips = x
Number of candy bar = x + 13
Yesterday Melanie made $33.25.
So,
x + x + 13 = 33.25
Solve for x.
x + x + 13 = 33.25
2x + 13 = 33.25
2x = 33.25 - 13
2x = 20.25
x = 10.125
x = 10
Now,
Number of chips = 10
Number of candy bar = 10 + 13 = 23
Thus,
Number of chips sold = 10
Number of candy bar sold = 23
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Determine the given lengths in the rectangle
Step-by-step explanation:
AC =18 (ac = bd opposite sides of a rectangle)
AB= 40(AB = CD)
AD = 22 ( ad = cb diagonals of a rectangle)
Someone help me with this equation please!!
The given statement is transitive property.
What is transitive property?Transitive property is also called transitive property of equality when we have two equal values and either of this value is equal to third value.
DE≅XY AND [tex]\hat{DE}$$\approx\hat{XY} and \hat{XY}$$\approx$$\YZ, then\hat{DE}$$\approx$$\hat{YZ}[/tex]
This is a transitive property.
Here we have three values, initially first two values are equal and second & third values are equal.
Which gives any one of the value of first and second equals third value.
This is the transitive property.
Hence, the given statement is transitive property.
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how do i do these types of problems?
Answer:
1/24.
Step-by-step explanation:
There are 2 events here and they are independent, so the single probabilities are multiplied.
P(4 when die is rolled) = 1/6
P(A on the spinner) = 1/4
So, P(4 and A)
= 1/6 * 1/4
= 1/24.
solve the using cramers rule
Using Cramers Rule, X = 10.34, Y = 0.85. See the computations below.
What is Cramers Rule?Cramer's rule is an explicit formula in linear algebra for solving a system of linear expressions with as many equations as unknowns, and it is true whenever the system has a unique solution.
Given:
10x - 4y = 100; ..................1) and
8x - 100y = -2; ...................2)
First things first, let's pick off the variables we will need for Cramer's equation:
Standard equation 1 = ax + by = c and Standard equation 2 = dx + ey = f. Therefore:
a = 10, b = -4, c = 100, d = 8, e = -100, f = -2
Step 1, calculate the denominator Delta (Δ):
Δ = a * e - b * d
Δ = (10 * -100) - (-4 * 8)
Δ = -1000 - -32
Δ = -968
Step 2, calculate the numerator for x
Numerator(x) = c * e - b * f
Numerator(x) = (100 * -100) - (-4 * -2)
Numerator(x) = -10000 - 8
Numerator(x) = -10008
X = Numerator (x) / Δ
x = -10008/-968
x = 10.338842975207
x [tex]\approx[/tex] 10.34
y = Numerator(y)/Δ
y = -820/-968
y = 0.84710743801653
y [tex]\approx[/tex] 0.85
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what is the area of this figure?
Answer:
213 km
Step-by-step explanation:
a square $10$ cm on each side has four quarter circles drawn with centers at the four corners. how many square centimeters are in the area of the shaded region? express your answer in terms of $\pi$.
A square of 10 cm on each side has four quarter circles drawn with centers at the four corners, then the area of the shaded region is 21.46 centimeter square
The side of the square a = 10 cm
The area of the square = a^2
Substitute the values in the equation
The area of the square = 10^2
= 100 centimeter square
There are 4 quarter circle in the figure. We know 4 quarter circle is one circle
The area of the circle = πr^2
Where r is the radius of the circle
The radius of the circle = 5 cm
The area of the circle = π × 5^2
= 78.54 centimeter square
The area of the shaded region = The area of the square - The area of the circle
= 100 - 78.54
= 21.46 centimeter square
Therefore, the area of shaded region is 21.46 centimeter square
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find the gcf 24x^3+36^2
The greatest common factor of the 24x³ + 36x² is 12x².
What is the greatest common factor?It is the greatest factor common to all the numbers given such that there are no greater factors common other than that.
Example:
4 is the gcd of 12, 8, 16.
We have,
24x³ + 36x²
Taking out the common factor.
= 12x² (2x + 3)
Thus,
GCF of the expression is 12x².
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6. Ming uses 3/ 4 cup of peanuts and 1/ 4 cup of raisins to make a snack. Which statement correctly compares the fractions?
*
10 points
A. 3/4 = 1/4
B. 1/4 > 3/4
C 3/4 < 1/4
3/4 > 1/4
Answer:
3/4 > 1/4
Step-by-step explanation:
3/4 is 75%, and 1/4 is 25 percent. 3/4 is greater than 1/4!
Write the scale factor of abcde to zyxwv
The scale factor of abcde to zyxwv is obtained dividing one side length of zyxwv by the equivalent side length of abcde, for example:
k = zy/ab.
What is a dilation?A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.
The figures for this problem are given as follows:
Original: abcde.Dilated: zyxwv.Hence the scale factor of abcde to zyxwv is obtained dividing one side length of zyxwv by the equivalent side length of abcde, for example:
k = zy/ab.
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A line is graphed on the coordinate plane.
Type in the equation for this line? Use x as your independent variable and y as the dependent variable.
The equation of the given line is [tex]y= \frac{1}{3}x+2[/tex]
What is the slope of a line?
A line's steepness and direction are measured by the line's slope. Any two different points on a line can be used to calculate the slope of any line. The ratio of "vertical change" to "horizontal change" between two different locations on a line is calculated using the slope of a line formula.
Given a straight line in a graph, we need to find the equation of this line
from the graph, we can see that the line passes through the axes at (0, 2) and (-6, 0)
now, the slope of the line is [tex]\frac{y2 - y1}{x2 - x1}[/tex]
[tex]= \frac{0 - 2}{-6 - 0} \\= \frac{1}{3}[/tex]
The line makes an intercept of 2 on the Y-axis, as we can see clearly
The slope-intercept form of the line is y = mx + c, where 'c' is the intercept and 'm' is the slope of the line
The equation of the given line is [tex]y = \frac{1}{3}x + 2[/tex]
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32% of the 384 students in the eighth grade walk to school, about how many eighth graders walk to school?
Answer: 123 students
32 % of 384 is 122.88. Since a percent of a person can't walk to school, we should round up. This means 123 students in the eighth grade walk to school each day.
I hope this helps and good luck <3!!
At the art store, Maria bought a poster board for $0.65, glitter for $3.29, and glue for $1.99. She told Carl that she paid $5.00 for everything. True or False?
Answer:
False
If we wanted to solve this equation, we can use this expression:
0.65 + 3.29 + 1.99 = 5.93Maria must have spent $5.93, making her statement false.
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What is the greatest common factor of 21, 14, and 7
Answer:
Submit Answer
The greatest common factor ( GCF ) of 21 , 14 and 7 is given by A = 7
What is HCF and LCM?The Greatest Common Divisor GCF or the Highest Common Factor HCF is the highest number that divides exactly into two or more numbers. It is also expressed as GCF or HCF
Least Common Multiple (LCM) is a method to find the smallest common multiple between any two or more numbers. A common multiple is a number which is a multiple of two or more numbers
Product of HCF x LCM = product of two numbers
Given data ,
Let the GCF of the numbers be represented as A
Now , the equation will be
Let the first number be p = 21
Let the second number be q = 14
Let the third number be r = 7
Now , the factors of 21 = 1 , 2 , 3 , 7 and 21
The factors of 14 = 1 , 2 , 7 and 14
The factors of 7 = 1 and 7
So , the greatest common factors of 21 , 14 and 7 is 7
Hence , the GCF is 7
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How do you prove that between any two irrationals there is a rational number and vice versa?
To prove that there exists a rational number between any two irrational numbers, we can use the fact that there exists a rational number between any two real numbers.
Let a and b be two irrational numbers with the property that a b. Then a and b are not rational by definition, which means they cannot be written in the form p/q, where p and q are integers and q is not equal to zero.
We can define a new number c = (a + b) / 2 because a b. This number is a rational number because it can be expressed as a fraction in lowest terms as (a + b) / 2.
As a result, we have demonstrated that a rational number c exists between any two irrational numbers a and b.
A similar argument can be used to demonstrate that there exists an irrational number between any two rational numbers.
Consider a and b to be two rational numbers such that a b. We can then define a new number c = (a + b) / 2.
If c is also rational, we're done because we can just use c as our desired number between a and b. However, if c is irrational, we have found our desired number between a and b, which is also irrational.
Assume that a and b are both even integers to see why c must be irrational in some cases. Then their average c is also even, implying that c can be written as p/q, where p and q are integers and q is not equal to zero, with both p and q being even. However, because p and q are both even, this contradicts the fact that they must have no common factors.
As a result, we have demonstrated that there exists an irrational number c between any two rational numbers a and b.
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Please help, I’ll give brainliest!!!!!!!!!!!!
Answer: (2, -1)
Step-by-step explanation:
true or false? a. a 95% confidence interval for the odds ratio between mi (yes, no) and treatment (placebo, aspirin) is (1.44, 2.33). if we form the table with aspirin in the first row (instead of placebo), the confidence interval is (1/2.33, 1/1.44)
The statement is true. A confidence interval is a range of values that is likely to contain the true value of the parameter with a certain degree of confidence.
In this case, we are interested in the odds ratio between MI (yes, no) and treatment (placebo, aspirin).
If the 95% confidence interval for the odds ratio between MI and placebo is (1.44, 2.33), this means that we can be 95% confident that the true odds ratio falls between these two values. This implies that the odds of having an MI are between 1.44 and 2.33 times greater for those taking the placebo compared to those taking aspirin.
When we switch the rows so that aspirin is in the first row, we need to take the reciprocal of the upper and lower bounds of the confidence interval to get the new interval. This is because the odds ratio is calculated as the odds of MI for one group divided by the odds of MI for the other group, and switching the groups changes the ratio.
So, if we take the reciprocal of the lower and upper bounds of the original interval, we get:
1/2.33 and 1/1.44
which is the new 95% confidence interval for the odds ratio when aspirin is in the first row. Therefore, the statement is true.
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1. Which of the following are methods for solving systems of equations (select all that apply)
a) graphing
b) substitution
c) Using a Protractor
d) elimination
Answer:
1- graphing
2- substitution
3- elimination.
Find the area of the figure. Use 3.14 for pie
The area of the figure is 254.8 m²
What is area?Area is the region occupied by an object.
How to find the area of the figure?Since the figure is a rectangle and containing two semi-circles, we find the area of the figure by finding the area of the rectangle and the two semi-circles.
What is the area of the rectangle?The area of the rectangle is given by A = LW where
L = length of rectangle and W = width of rectangleGiven that
L = 16 m and W = 12 mA = LW
= 16 m × 12 m
= 192 m²
What is the area of a semi-circle?The area of a semi-circle with diameter d is A = πd²/4
Now for the first semi-circle, its diameter d' = 8 m.
So, its area A' = πd'²/4
= π(8 m)²/4
= π64 m²/4
= 16π m²
= 16 ×3.14 m²
= 50.24 m²
Also, for the fsecond semi-circle, its diameter d" = 4 m.
So, its area A' = πd'²/4
= π(4 m)²/4
= π16 m²/4
= 4π m²
= 4 × 3.14 m²
= 12.56 m²
So, the area of the figure is A₁ = A + A' + A"
= 192 m² + 50.24 m² + 12.56 m²
= 254.8 m²
So, the area of the figure is 254.8 m²
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Teboho wants to order a new CD from Germany. He has R250 in his savings account. The CD costs €5. Once he has bought the CD. how much money will he have left in ZAR? If he can order the same CD from Canada for $7, where must he order it from for the best price provided the shipment cost is the same.
Answer: Let's assume the exchange rate between ZAR and EUR is given by E1, and the exchange rate between ZAR and CAD is given by E2.
First, let's calculate the cost of the CD in ZAR:
5 EUR * E1 = 5 * E1 ZAR
Next, let's calculate how much money Teboho will have left after purchasing the CD:
250 ZAR - 5 * E1 ZAR = 245 ZAR - 5 * E1 ZAR
Now, let's calculate the cost of the CD in CAD:
7 CAD * E2 = 7 * E2 ZAR
We need to determine the value of E1 and E2 in order to compare the prices. However, without knowing the current exchange rates, we cannot determine the best option for Teboho. If the exchange rate between ZAR and EUR is favorable and the cost of the CD in ZAR is lower than the cost of the CD in CAD, Teboho should order the CD from Germany. On the other hand, if the exchange rate between ZAR and CAD is favorable and the cost of the CD in CAD is lower than the cost of the CD in EUR, Teboho should order the CD from Canada.
Step-by-step explanation:
Given the following segment lengths,
find the value of x.
If AB = 19 and AC = 17 then the value of x be 95/9 or 10.5555.
What is meant by angle bisector?In geometry, a line that divides an angle into two equal angles is referred to as an angle bisector. By definition, a bisector is something that divides an object or a shape into two equal parts. A ray is said to be an angle bisector if it divides an angle into two equal portions of the same measure.
The ray, line, or segment that divides an angle into two equal portions is known as the angle bisector in geometry. A 60-degree angle, for instance, will be split into two angles of 30 degrees each by an angle bisector. To put it another way, it separates one angle into two smaller congruent angles.
The segment AD bisects angle BAC.
Given: AB = 19 and AC = 17
AD is an angle bisector of BAC and divides the opposite side into segments that are proportional to the other two sides, that is
Let the equation be
[tex]$& \frac{B D}{C D}=\frac{A B}{A C}(\text { substitute values ) } \\[/tex]
[tex]$& \frac{x}{20-x}=\frac{19}{17}(\text { cross- multiply) } \\[/tex]
Simplifying the above equation, we get
[tex]$$x \cdot 17=380-19 x$$[/tex]
36x = 380
Divide both sides by 36, we get
[tex]$\frac{36 x}{36}=\frac{380}{36}$$[/tex]
x = 95/9 = 10.5555
Therefore, the value of x be 95/9 or 10.5555.
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