Unpacking the expression we have,
[tex](\sqrt{x})(\sqrt[4]{x})[/tex]
Its better to work with this in terms of exponents so we rewrite the expression as [tex]x^{\frac{1}{2}}*x^{\frac{1}{4}}[/tex]. (cause [tex]\sqrt[n]{x}=x^{\frac{1}{n}}[/tex]) This can be a little tricky when learning it for the first time.
Then by the exponent sum rule [tex]x^{\frac{1}{2}}*x^{\frac{1}{4}}=x^{\frac{1}{2}+\frac{1}{4}}=x^{\frac{3}{4}}[/tex] (more straightforward, you probably know this from class).
I assume this is what you mean by rational exponent form. But you could also write it as [tex]\sqrt[4]{x^3}[/tex].
suppose that alpha and omega have identically sized working-age populations but that total annual hours of work are much greater in alpha than in omega. what are two possible reasons for this difference?
If workers in Alpha are more productive than those in Omega, they may be able to accomplish more work in the same amount of time, resulting in more total annual hours of work in Alpha. This could be due to a variety of factors, such as differences in technology, education levels, or infrastructure.
There could be several reasons why the total annual hours of work are much greater in Alpha than in Omega, even though both countries have identically sized working-age populations. Here are two possible reasons:
Differences in labor force participation: It is possible that a larger proportion of the working-age population in Alpha is participating in the labor force than in Omega. Labor force participation refers to the percentage of the working-age population that is either employed or actively seeking employment. If more people in Alpha are working or looking for work, then the total annual hours of work would be higher in Alpha than in Omega.
Differences in productivity: Another possible reason for the difference in total annual hours of work is differences in productivity levels between Alpha and Omega. Even if both countries have the same number of people in their working-age population, the productivity of those workers can vary significantly. If workers in Alpha are more productive than those in Omega, they may be able to accomplish more work in the same amount of time, resulting in more total annual hours of work in Alpha. This could be due to a variety of factors, such as differences in technology, education levels, or infrastructure.
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On a certain hot summers day, 402 people used the public swimming pool. The daily prices are 1. 50$ for children and 2. 00$ for adults. The receipts for admission totaled 648. 50$. How many children and how many adults swam at the public pool that day?
From the given information provided, there were 311 children who swam at the pool that day.
Let's use C to represent the number of children who swam at the pool and A to represent the number of adults who swam at the pool.
From the problem, we know that:
C + A = 402 (Equation 1) (The total number of people who used the pool was 402)
1.50C + 2.00A = 648.50 (Equation 2) (The total receipts from admission were $648.50)
To solve for C and A, we need to eliminate one of the variables. We can do this by multiplying Equation 1 by 1.50, which will give us:
1.50C + 1.50A = 603 (Equation 3)
Now we can subtract Equation 3 from Equation 2 to eliminate C:
2.00A - 1.50A = 648.50 - 603
0.50A = 45.50
A = 91
So there were 91 adults who swam at the pool that day. To find the number of children, we can substitute A = 91 into Equation 1:
C + 91 = 402
C = 311
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the equations 6x + 5y = 28 and 10x + 14y = 58 represent the cost for lunch and dinner for a family eating out on vacation. if x is the number of adults and y is the number of children, how many adults are in the family?
There are 3 adults in the family by using the method of substitution and elimination.
What is Substitution?Substitution is a method used in mathematics to replace one or more variables in an equation or expression with a value or expression that is equivalent to the variable(s). This is done in order to simplify an equation or expression or to solve for a variable.
What is Elimination?Elimination is a method used in mathematics to solve a system of equations by eliminating one variable. This method involves manipulating the equations in such a way that one of the variables is eliminated, leaving a simpler equation with only one variable that can be solved easily.
In the given question,
Here's how we can solve for x, the number of adults:
Multiply the first equation by 2 to get rid of the coefficient of x in the second equation:
12x + 10y = 56
10x + 14y = 58
Subtract the first equation from the second equation to eliminate y:
10x + 14y - (12x + 10y) = 58 - 56
-2x + 4y = 2
Divide both sides by -2 to isolate x:
x - 2y = -1
x = 2y - 1
Substitute x = 2y - 1 into one of the original equations (let's use the first one) and solve for y:
6x + 5y = 28
6(2y - 1) + 5y = 28
12y - 6 + 5y = 28
17y = 34
y = 2
Substitute y = 2 into the equation x = 2y - 1 to solve for x:
x = 2(2) - 1
x = 3
Therefore, there are 3 adults in the family.
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a lawn sprinkler sprays water 7 feet in every direction as it rotates. what is the area of the watered lawn? use 3.14 for π and be sure to put the correct unit of measure.
If a lawn sprinkler sprays water 7 feet in every direction as it rotates, the area of the watered lawn is approximately 153.94 square feet.
Assuming the sprinkler is placed at the center of the lawn, the area of the watered lawn can be found by calculating the area of a circle with a radius of 7 feet. The formula for the area of a circle is A = πr^2, where A is the area and r is the radius.
Plugging in the given value of the radius, we get:
A = π(7 feet)^2
A = 153.94 square feet (rounded to two decimal places)
It's important to include the correct unit of measure, which is square feet in this case, to avoid confusion.
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FARMING A dairy farmer has 2650 dairy cows on his farm. If each dairy cow produces 2320 gallons of milk per year, how much milk does the dairy farm yield in one year? Write your answer in scientific notation.
Answer:
To calculate the total milk yield in one year, we need to multiply the number of dairy cows by the amount of milk each cow produces per year:
Total milk yield = 2650 dairy cows × 2320 gallons of milk per cow per year
Total milk yield = 6,188,000 gallons per year
To write this answer in scientific notation, we need to express the number 6,188,000 as a number between 1 and 10 multiplied by a power of 10. We can do this by moving the decimal point to the left until we have a number between 1 and 10, and counting the number of decimal places we moved. In this case, we need to move the decimal point 6 places to the left:
Total milk yield = 6.188 × 10^6 gallons per year
Therefore, the dairy farm yields 6.188 × 10^6 gallons of milk per year.
5. Twenty students in Mr. Martin's class each took a survey about the number of minutes they played outside. The box
plots represent the amount of time the students spent outside playing in the summer and in the winter. Which statement is
best supported by the data?
SUMMER WINTER
30
45
60
NUMBER OF MINUTES
75
90
A. The range of number of minutes outside is the same in the
summer and in the winter.
B. The median number of minutes outside in the summer is
equal to the maximum number of minutes outside in
the winter.
C. The interquartile range for the number of minutes outside is
the same in the summer and in the winter.
D. The minimum number of minutes outside in the summer is
the same as the first quartile in the winter.
The statement "The median number of minutes outside in the summer is equal to the maximum number of minutes outside in the winter" is best supported by the data (option B).
How to find the maximum number of minutes outside?Looking at the plot;
Winter: Minimum= 0 Maximum= 60 Median= 30
Range = 60 - 0 = 60
Summer: Minimum= 20 Maximum= 90 Median= 60
Range = 90 - 20 = 70
So the median number of minutes outside in the summer is
equal to the maximum number of minutes outside in the winter.
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Missing information:
The question is incomplete and the complete question is shown in the attached image.
- The Graduates Choice designs and sells two types of class rings, the GPA and the MVP. They
can produce up to 24 rings per day using at most 60 total hours of labor. It takes 3 hours to
make one GPA ring and 2 hours to make one MVP ring. How many of each ring type should be
made daily in order to maximize the company's profit if the profit on the GPA ring is $40 and
the profit on the MVP ring is $35?
The 12 of each type of the ring would give max profit for the company.
How many of each type should be made daily to maximize the company's profit?Let x = number of VIP rings: let y = number of SST rings
:
The total production inequality;
x + y =< 24
y = 24 - x; arranged to plot graph (purple)
:
The labor inequality;
3x + 2y =< 60
2y = 60 - 3x
y = 60/2 - (3/2)x
y = 30 - 1.5x; arranged to plot the graph (red).
From the graph, the 3 corners of the area of feasibility (at or below the lines whichever is lower):
: x/y;.....profit on each type;... total profit
0,24; 40(0) + 35(24) = 0 + 840 = $840
12,12; 40(12) + 35(12) = 480 + 420 = $900
20,0; 40(20) + 35(0) = 800 + 35(0) = $800.
Therefore, the 12 of each type of the ring would give max profit for the company.
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the slant height of a cone measures 26 centimeters. The height of the cone measures 24 centimeters.
What is the exact surface area of the cone?
help!!
Enter your answer in the box.
The value of the exact surface area of the cone is 360π
What is the exact surface area of the cone?To find the surface area of a cone, we need to calculate the area of the circular base and the curved lateral surface.
The radius of the circular base can be found using the Pythagorean theorem:
r = √(s^2 - h^2)
where s is the slant height and h is the height.
In this case, we have:
r = √(26^2 - 24^2)
r = 10
So, the surface area is
S = πr² + πrl
This gives
S = π * 10² + π * 10 * 26
S = 360π
Hence, the exact surface area of the cone is 360π
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Which line models the data points better and why? (1 point) Oblue, because it is longer Oblue, because the data points are all close to the line Ored, because it goes through one of the points Ored, because there are three points above the line and three points below the line
The line that models the data points better is Red, because it goes through one of the points.
What is data in math?Data is information that has been organized and processed in a meaningful way. It is the raw material of digital systems and the foundation of all computer-based operations. It can be stored, retrieved, and manipulated in a variety of ways, and it is used to generate insights, drive decisions, and build solutions. Data can come from a variety of sources, including manual entry, sensors, databases, and the internet.
This is a better model than Blue, because the data points are not all close to the line, and having the line go through one of the points ensures that the line is better representing the points. Additionally, having three points above the line and three points below the line helps to make the line a better model of the data points, as it is more evenly distributed.
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Martha has read 52 pages of her book. This is
20% of the book. How many pages does the
book have?
A right triangle has a leg of 9 cm and a hypotenuse of 18 cm.
What is the length of the other leg?
Round to the nearest tenth.
Answer:
Using the Pythagorean theorem, we know that:
a^2 + b^2 = c^2
where a and b are the legs of the right triangle, and c is the hypotenuse.
We can plug in the values given:
9^2 + b^2 = 18^2
Simplifying:
81 + b^2 = 324
b^2 = 243
b = sqrt(243) = 15.6 (rounded to the nearest tenth)
Therefore, the length of the other leg is approximately 15.6 cm.
Step-by-step explanation:
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Two fishermen, Ashraf and Khalid, went fishing. Ashraf caught x fish, Khalid caught y fish and in total they cau 69 fish. (a) Write down an equation in x and y. Ashraf caught 30% more fish than Khalid. (b)Write down another equation in x and y. (c)Solve your equations to find the number of fish caught by Ashraf and the number of fish caught h Khalid
The number of fish caught by Ashraf and Khalid by solving the equation formed is 39 and 30 respectively.
What is the Substitution method for solving equations?
In a system of linear equations to solve, we have N variables and N equations between them to solve. In substitution, we represent one variable in terms of another and replace it in the equation to convert it to a 1-variable equation and solve it.
a) Given, the number of fishes caught by Ashraf is "x" and by Khalid is "y".
As the total number of fish caught is 69, the equation is :
[tex]x + y = 69[/tex]
b) It is stated in the question that the number of fish caught by Ashraf i.e. x is 30% more than that caught by Khalid i.e. y.
The equation formed is :
x = 30% greater than y
[tex]= y + 30y/100[/tex]
[tex]= (100+30)y/100[/tex]
[tex]= 13y/10[/tex]
Hence, the equation is : [tex]10x = 13y[/tex]
c) Here, we have 2 equations and 2 variables. We use the substitution method to find the values of the variables :
[tex]y + 13y/10 = 69[/tex]
[tex](10+13)y/10 = 69[/tex]
[tex]23y/10 = 69[/tex]
[tex]y = 69 * 10 /23[/tex]
[tex]y = 30[/tex]
Putting the value of y in the first equation :
[tex]x + 30 = 69[/tex]
[tex]x = 39[/tex]
Hence, the number of fish caught by Ashraf is 39, and by Khalid is 30.
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Identify the area of the polygon with vertices P(1,2), Q(1,4), R(-1,6), and S(-3,2).
A = 16 units²
A= 10 units²
A= 6 units²
A = 14 units²
The area of the polygon with vertices P(1,2), Q(1,4), R(-1,6), and S(-3,2) is given as 10 units. Option B
How to find the areaWe can find the area of the polygon with the given vertices by dividing it into triangles and adding their areas.
One way to divide the polygon into triangles is to draw a diagonal from vertex P to vertex R. This creates two triangles, PQR and PRS.
[tex]\frac{1 }{2} ((4 - 2) + (6--4) + (-2 - - 18) + (-6 - 2)[/tex]
= 1 / 2 ( 2 + `10 + 16 - 8)
= 1 / 2 ( 20
= 10
The area of the polygon is 10 units
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at 99% confidence, how large a sample should be taken to obtain a margin of error of for the estimation of a population proportion? assume that past data are not available for developing a planning value for . round up to the next whole number.
To estimate a population proportion with a margin of error of 1% and a 99% confidence interval, we would need a sample size of at least 6644 individuals.
The formula to calculate the sample size is:
n = [z² x p(1-p)] / e²
where:
n is the sample size
z is the z-score corresponding to the desired confidence level (in this case, 2.576 for a 99% confidence level)
p is the planning value for the population proportion, which we don't know in this case, so we will assume the worst-case scenario of p=0.5 (which gives us the maximum sample size needed)
e is the desired margin of error
Plugging in the values, we get:
n = [(2.576)² x 0.5(1-0.5)] / (0.01)²
n = 6643.04
Since we need to round up to the next whole number, the minimum sample size needed is 6644.
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what is the center od dilation type ( Number, number)
the center of dilation for the triangle is (0,0)
Define center of dilationThe center of dilation is a point in a plane about which a dilation, a type of transformation, is performed. A dilation is a transformation that changes the size of a geometric figure, while preserving its shape and orientation. The center of dilation is the fixed point that serves as the reference for the scaling or shrinking of the figure.
In a dilation, each point of the original figure is moved away from or towards the center of dilation, by a certain factor called the scale factor.
The coordinate of yellow triangle and scaled triangle both passes through center of axes.
So, the center of dilation is (0,0).
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What is the measure of
∠1 if
∠1 is (8x)
∘ and
∠2 is (2x - 3)
∘?
∠1 + ∠2 = 180
Substituting the given expressions for ∠1 and ∠2:
8x + (2x - 3) = 180
Simplifying and solving for x:
10x - 3 = 180
10x = 183
x = 18.3
Now we can substitute x back into the expression for ∠1 to find its measure:
∠1 = 8x = 8(18.3) = 146.4 degrees.
Therefore, if ∠1 and ∠2 add up to 180 degrees and ∠1 is given as 8x° and ∠2 is given as (2x - 3)°, then ∠1 measures 146.4 degrees
Answer:
<1=146.4
<2=34.6
Step-by-step explanation:
<1+<2=180 degrees
So,
8x+(2x-3)=180
10x-3=180
10x=183
X=18.3
subsitute:
<1=8x
<1=8(18.3)
<1=146.4
<2=2x-3
<2=2(18.3)-3
<2=34.6
a laptop has a listed price of 882.99 before tax. if the sales tax rate is 6.25% , find the total cost of the laptop with sales tax included. round your answer to the nearest cent, as necessary.
The total cost of the laptop with the sales tax included is 938.18.
The total cost of the laptop with the sales tax included is the sum of the original price and the tax amount. The formula to calculate the total cost is given below:
Total Cost = Original Price + (Original Price * Sales Tax Rate)
In this case, the Original Price is 882.99 and the Sales Tax Rate is 6.25%. Therefore, the Total Cost of the laptop with the sales tax included is calculated as follows:
Total Cost = 882.99 + (882.99 * 0.0625)
Total Cost = 882.99 + 55.19
Total Cost = 938.18
Rounding to the nearest cent, the total cost of the laptop with the sales tax included is 938.18.
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coupling tetraalkylammonium and ethylene glycol ether side chain to enable highly soluble anthraquinone-based ionic species for nonaqueous redox flow battery
Coupling tetraalkylammonium and ethylene glycol ether side chain is an effective method to enable highly soluble anthraquinone-based ionic species for nonaqueous redox flow battery. The side chains of the tetraalkylammonium are modified with the ethylene glycol ether, which is a highly polar solvent, allowing for better solubility in nonaqueous electrolyte solutions. Additionally, the ethylene glycol ether has the ability to modify the stability of the ionic species, preventing aggregation and ensuring the longevity of the battery. This increases the redox capacity and enhances the performance of the flow battery.
The ethylene glycol ether-tetraalkylammonium coupling has been proven to be an effective method for improving the solubility and stability of anthraquinone-based ionic species. For example, it has been observed that the coupling of ethylene glycol ether to anthraquinone-based ionic species enhanced the current density of the battery by more than 3 times. Furthermore, the coupling process has also been found to improve the energy efficiency and storage capacity of the nonaqueous redox flow battery.
Overall, coupling tetraalkylammonium and ethylene glycol ether side chain is an effective method for enabling highly soluble anthraquinone-based ionic species for nonaqueous redox flow battery. This process has been proven to improve the performance of the battery, including current density, energy efficiency, and storage capacity.
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(7) The area of a rectangle is 14
square units. It has side lengths a
and b. Given the following value
for a, find b. a = 2 & 1/3
The value of sides b for different value of a in a rectangle are;
a=2 and b=7
a=1/3 and b=42
Define rectangleA rectangle is a type of quadrilateral with four sides and four right angles (90-degree angles). It is a two-dimensional shape with opposite sides that are parallel and equal in length. The opposite sides of a rectangle are also perpendicular to each other, which means they meet at 90-degree angles.
A = l x w, where A is the area, l is the length, and w is the width, calculates the area of a rectangle.
In this case, we are given that the area is 14 square units, so we can set up the equation:
14 = a x b
Given;
a=2
Using this value as a replacement in the formula, we obtain:
14 = (2) x b
b=7
Taking another value of a=1/3
Using this value as a replacement in the formula, we obtain:
14=1/3×b
b=42
Therefore, The value of b for different value of a are;
a=2 and b=7
a=1/3 and b=42
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Consider the following hypothetical survey results of 18- to 34-year-olds in a certain country, in response to the question "Are you currently living with your family.
Yes No Totals
Men 106 141 247
Women 92 161 253
Totals 198 302 500
a. Develop the joint probability table for these data and use it to answer the following questions
b. What are the marginal probabilities?
c. What is the probability of living with family given you are an 18- to 34-year-old marn in the U. S. ?
d. What is the probability of living with family given you are an 18- to 34-year-old woman in the U. S. ?
e. What is the probability of an 18- to 34-year-old in the U. S. Living with family?
f. If, in the U. S. , 49. 4% of 18-to 34-year-olds are male, do you consider this a good representative sample? Why?
After considering the following hypothetical survey results of 18- to 34-year-olds in a certain country, in response to the question "Are you currently living with your family?" we get the following probabilities.
a. The joint probability table for the given data is:
Yes No Totals
Men 0.212 0.282 0.494
Women 0.184 0.322 0.506
Totals 0.396 0.604 1
b. The marginal probabilities for living with family and not living with family are:
Yes No
Men 0.212 0.282
Women 0.184 0.322
Totals 0.396 0.604
c. The probability of living with family given you are an 18- to 34-year-old man in the U.S. is 0.212/0.396 = 0.5354 or approximately 53.54%.
d. The probability of living with family given you are an 18- to 34-year-old woman in the U.S. is 0.184/0.506 = 0.3636 or approximately 36.36%.
e. The probability of an 18- to 34-year-old in the U.S. living with family is 0.396 or 39.6%.
f. We cannot determine whether the sample is representative solely based on the percentage of males in the survey.
A good representative sample should be randomly selected to accurately reflect the population being studied. The percentage of males in the sample is relevant only if it differs significantly from the percentage of males in the population being studied.
The joint probability table was developed for the survey results of 18- to 34-year-olds on living with family. Marginal probabilities were calculated and the probability of living with the family was found for both men and women. The overall probability of living with the family was also determined. It is unclear if the sample is representative without additional information.
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Use ABC to write the indicated trigonometric ratio
Sin B=
Answer:
b/c
Step-by-step explanation:
sin B = opp/hyp
sin B = b/c
A snack stand sold hot dogs and chips at a recent game. The hot dogs cost $2. 50 and the chips cost $0. 75. After the game, they tallied 175 transactions totaling $262. 50. Represent the linear system in an augmented matrix:
1
1
175
2. 5
0. 75
262. 5
The number of hotdogs sold was
100. The number of chips sold was
The number of hot dogs is 100 while the number of snacks is 75. And it is found by using linear equation.
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are present. The variables in the previous sentence, y and x, are referred to as a "linear equation of two variables" at times.
The linear equation to solve the question will be:-
h+s= 175 ------(1)
2.50h + 0.75s = 262.50 -----(2)
From equation (1), s= 175-h -----(3)
Put qeauation (3) into (2) :-
2.50h + 0.75 = 262.50
2.50 + 0.75 (175-h) = 262.50
2.50 + 131.25 - 0.75 = 262.50
Collect like terms :-
2.50-0.75= 262.50-131.25
1.75= 131.25
h= 131.25/1.75
h= 75
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Pls just say a b c or d
the air speed of a small airplane during the first 25 seconds of takeoff and flight can be modeled as
The air speed of a small airplane during the first 25 seconds of takeoff and flight can be modeled by Newton's Second Law of Motion.
According to Newton's Second Law of Motion, the rate of change of the airplane's momentum is equal to the sum of all the forces acting on the airplane. As the plane takes off and accelerates, the thrust of the engines acting in the forward direction causes the plane's momentum to increase. This increase in momentum results in an increase in air speed. The air resistance acting against the motion of the plane is another force that affects the plane's speed. As the plane accelerates, the air resistance increases, and the plane's speed decreases.
In summary, the air speed of a small airplane during the first 25 seconds of takeoff and flight can be modeled by Newton's Second Law of Motion, where the thrust of the engines and air resistance act as forces that influence the plane's air speed.
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a frozen food company uses a machine that packages okra in six ounce portions. a sample of 54 54 packages of okra has a variance of 0.44 0.44 . construct the 98% 98 % confidence interval to estimate the variance of the weights of the packages prepared by the machine. round your answers to two decimal places.
The confidence interval for variance is (0.29,0.58)
A family of continuous probability distributions is known as the chi-square (X2) distribution. They are frequently employed in hypothesis tests, such as the chi-square test of independence and the goodness of fit test.
The parameter k, which stands for the degrees of freedom, determines the shape of a chi-square distribution.
The distribution of real-world observations rarely has a chi-square shape. Chi-square distributions are primarily used for testing hypotheses rather than for modeling actual distributions.
Since we have given that the sample size n= 54,
variance = 0.44
we need to find a 98% confidence interval to estimate the variance.
So, we will use Chi-square distribution,
For this, we will find
df=n-1 = 54-1 = 53,
the interval would be,
[tex]\frac{(n-1)s^2}{X^2_{\alpha/2}} < \sigma^2 < \frac{(n-1)s^2}{X^2_{1-\alpha/2}}\\\\\alpha=1-0.98=0.02\\\\\alpha/2=0.02/2=0.01\\X^2_{0.01,53}=79.84\\Similarly\\\\1-\alpha/2=0.99\\\\X_{1-\alpha/2}^2,df=X^2_{0.99,53}=40.308\\\\So,\\\frac{53*0.44}{79.84} < \sigma^2 < \frac{53*0.44}{40.308}\\\\0.29 < \sigma^2 < 0.58[/tex]
Hence the confidence interval is (0.29,0.58)
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A city has a population of 370,000 people. Suppose that each year the population grows by 4. 75%. What will the population be after 11
years?
The population of the city will be approximately 597,543 people after 11 years.
We can solve this problem using the formula for exponential growth:
[tex]N = P(1 + r)^t[/tex]
where:
N = final population
P = initial population
r = annual growth rate (as a decimal)
t = number of years
In this case, we have:
P = 370,000
r = 0.0475 (since the annual growth rate is 4.75%)
t = 11
Substituting these values into the formula, we get:
[tex]N = 370,000(1 + 0.0475)^{11}[/tex]
Using a calculator, we can simplify this expression to:
N = 597,542.64
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Can the segment form a triangle? Why or why not?
A. 6 + 5 is not greater than twelve
B. Yes 6+5 is equal to twelve
C. No 6+5 is not equal to 12
D. Yes 6+5 equals less than twelve
Answer: b
Step-by-step explanation:
The length in inches of each side of a square is given by the expression x 2 . the area of the square can be represented by (x 2)2−16=0 when the area is 16 square inches. what is the value of x?
The value of x is 2 inches.
We are given that the area of the square is 16 square inches and can be represented by the expression,
(x+2)^2 - 16 = 0
We can simplify this equation by expanding the square,
x^2 + 4x + 4 - 16 = 0
x^2 + 4x - 12 = 0
Now we can use the quadratic formula to solve for x
x = (-b ± sqrt(b^2 - 4ac)) / 2a
Where a = 1, b = 4, and c = -12.
Plugging in these values, we get
x = (-4 ± sqrt(4^2 - 4(1)(-12))) / 2(1)
x = (-4 ± sqrt(16 + 48)) / 2
x = (-4 ± sqrt(64)) / 2
x = (-4 ± 8) / 2
We get two solutions,
x = (-4 + 8) / 2 = 2
x = (-4 - 8) / 2 = -6
Since we are dealing with the length of a side of a square, we can eliminate the negative solution and conclude that the value of x is 2 inches.
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The given question is incomplete, the complete question is:
The length in inches of each side of a square is given by the expression x + 2 . the area of the square can be represented by (x+2)^2−16=0 when the area is 16 square inches. what is the value of x?
assume that the width of a ci for the mean of a normal distribution is 3.4. you know that the population variance is 22, the sample average is 25 and the sample size is 15. what is the confidence level of the ci?
The confidence level of the CI is 95%.
The formula for the confidence interval of a normal distribution is
CI = X ± Zα/2 × σ/√n
Where
CI is the confidence interval
X is the sample mean
Zα/2 is the Z-score corresponding to the desired confidence level α/2
σ is the population standard deviation
n is the sample size
We know that the width of the confidence interval is 3.4, so
3.4 = 2 × Zα/2 × σ/√n
We also know that σ = √22 = 4.69, X = 25, and n = 15. Plugging these values into the equation and solving for Zα/2
3.4 = 2 × Zα/2 × 4.69/√15
Zα/2 = 1.96
The Z-score corresponding to a 95% confidence level is 1.96. Therefore, the confidence level of the CI is 95%.
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is the real-estate market heating up? to estimate the mean sales price, a realtor in a large city randomly selected 100 home sales from the previous 6 months in her city. these sales prices are displayed in the boxplot.
The truth regarding the conditions for constructing a confidence interval for a population mean for the real estate market is that E. All conditions have been met.
What conditions are needed to construct a confidence interval ?For a confidence interval to be construction, sample should be randomly selected, sample size should be no more than 10% of the population size, and the sampling distribution should be approximately normal. This can be achieved if the sample size is large (typically n ≥ 30) and the data doesn't have strong skewness or outliers.
The question states that the realtor is working in a large city, and it is reasonable to assume that 100 home sales are less than 10% of all homes sold in the previous 6 months in this large city. So, this condition is met.
The realtor has randomly selected 100 home sales, so the random condition is met. All conditions have therefore been met to construct a confidence interval.
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Options for this question include:
The 10% condition is not met. It is not reasonable that 100 < 10% of all homes sold in the previous 6 months in this large city. Random: This condition is not met because the sample was selected from only one city. The Normal/Large Sample condition has not been met because the boxplot is strongly skewed to the right with outliers. The Large Counts condition has not been met because np = 100 and n(1-P) are not both at least 10. All conditions have been met.