The system of equations are solved and the cost are
a) The cost of couch = $ 732
b) The cost of coffee table = $ 366
Given data ,
Let the total cost of the purchase be = $ 1098
Now , the cost of couch is two times the cost of coffee table
Let the cost of couch be a
Let the cost of coffee table be b
where a = 2b
And , 2b + b = 1098
On simplifying the equation , we get
3b = 1098
Divide by 3 on both sides , we get
b = $ 366
So , the cost of coffee table is $ 366
Hence , the cost of couch is $ 732
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26 beats in 1/6 minute
Answer:
If you wanna know how many beats are in a full minute, the answer is 156 beats
Step-by-step explanation:
1/6*6=1
26*6=156
After deducting grants based on need, the average cost to attend the University of Southern California (USC) is $27,175. Assume the population standard deviation is $7,400. Suppose that a random sample of 69 USC students will be taken from this population.
(a)
What is the value of the standard error of the mean? (Round your answer to the nearest whole number.)
$
(b)
What is the probability that the sample mean will be more than $27,175?
(c)
What is the probability that the sample mean will be within $1,000 of the population mean? (Round your answer to four decimal places.)
(d)
What is the probability that the sample mean will be within $1,000 of the population mean if the sample size were increased to 100? (Round your answer to four decimal places.)
a) The standard error of the mean value is 890.
b) 0.5 is the probability that the sample mean will be more than $27,175.
c) \(11%\) of the population means being within \($1,000\) of the sample mean.
d) The population mean is \(71%.\) .
(a) The formula for calculating the standard error of the mean (SE) is as follows:\(SE = / sq rt(n),\) where n is the sample size and is the population standard-deviation.
Inputting the values provided yields:
\(SE = 7,400 sq/69 890\)
The standard error of the mean, rounded to the closest whole number, is \(890.\)
\(= 890\)
(b) We must standardize the sample mean using the following method in order to determine the likelihood that the sample mean will exceed \($27,175:\)
z is equal to\((x - ) / ( / sort(n)).\)
where n is the sample size, x is the sample mean, is the population standard deviation, and is the population mean (which is assumed to be equal to the sample mean because it is not provided).
We obtain the following by substituting the above values: \(z = (27,175 - 27,175) / (7,400 / sqrt(69)) = 0.\)
Obtaining a z-score of \(0\) or above has a \(0.5\) percent chance. As a result, there is a \(0.5\) percent chance that the sample mean will be higher than \($27,175.\)
\(= 0.5%\)
(c) To determine the likelihood that the sample-mean will be within \($1,000\) of the population mean, we must determine the z-scores for the interval's upper and lower boundaries, which are:
\(Z1\) is equal to\((27,175 - 27,175) / (7,400 / sqrt(69)) = 0 Z2\)is equal to \((27,175 + 1,000 - 27,175) / (7,400 / sqrt(69)) 0.14\) \(Z3\) is equal to\((27,175 - 1,000 - 27,175) / (7,400 / sqrt(69)) -0.14\)
The area under the curve between\(z2\) and \(z3\) can be calculated or found using a basic normal distribution table or calculator:
\(P(z2 z3 z2) = P(-0.14 z 0.14) 0.1096\)
Therefore,\(0.1096\), or about \(11%\), of the population means being within \($1,000\) of the sample mean.
\(= 11%\)
(d) If the sample-size were raised to \(100\), we would need to recalculate the standard error of the mean to determine the likelihood that the sample mean will be within \($1,000\) of the population mean:
\(SE = 7,400/7,400/sqrt(100) = 740.\)
We determine the z-scores for the upper and lower boundaries of the interval using the same technique as in (c)
\(z2 = (27,175 + 1,000 - 27,175) / (740) ≈ 1.35\)
\(z3 = (27,175 - 1,000 - 27,175) / (740) ≈ -1.35\)
Once more, we can calculate or use a conventional normal distribution table to get the area under the curve between\(z2\)and\(z3\):
\(P(z2+z+z3) = P(-1.35+z+1.35) = 0.7146\)
Therefore, if the sample size were increased to 100, the likelihood that the sample mean will be within\($1,000\) of the population mean is\(0.7146,\)or roughly \(71%.\)
\(= 71%\)
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Complete Question:
(a) What is the value of the standard error of the mean? (Round your answer to the nearest whole number.)
(b) What is the probability that the sample mean will be more than $27,175?
(c)What is the probability that the sample mean will be within $1,000 of the population mean? (Round your answer to four decimal places.)
(d) What is the probability that the sample mean will be within $1,000 of the population mean if the sample size were increased to 100? (Round your answer to four decimal places.)
Equations on both sides
3x + 5 = 2x -17
Solve it and show the work because i need to show the work
Answer:
x = -22
Step-by-step explanation:
Subtract 5 from both sides
3x + 5 (-5) = 2x - 17 (-5)
3x = 2x - 17
Subtract 2x from both sides
3x (-2x) = 2x (-2) -22
x = -22
Four complex numbers form the vertices of a square in the complex plane. Three of the numbers are $-19 32i,$ $-5 12i,$ and $-22 15i$. What is the fourth number
If the three numbers of a square in the complex plane are \(-19+32i,-5+12i and -22+15i\) , then the fourth complex number \(-2+19i\).
Given \(-19+32i,-5+12i and -22+15i\) are three numbers.
Complex numbers are those numbers which extends the real numbers with an imaginary i. In this \(i^{2}=-1\). Major complex numbers are in the form a+ bi where a and b are real numbers.
let the fourth complex numbers be \(x+yi\). Then according to question;
=\((-22+15i)-(-5+12i)\)
=(cos π/2+i sin π/2) \((x+yi)-(-5+12i)\)
\(-17+3i=-y+12\)\(+(x+5)i\)
Now solving for x and y by equating both sides.
x=-2 and y=29
Put the value of x and y in \(x+yi\)
Z=-2+29i
Hence if the three numbers which forms vertices of a square are \(-19+32i,-5+12i,-22+25i\) then the fourth complex numbers be \(-2+29i\).
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Help please this my last page
Mike’s fitness center charges $30 per month for a membership. All Day fitness center charges $22 per month plus an $80 initiation fee for membership. After how many months will the total amount paid to the two memberships be the same?
Answer:
10 months
Step-by-step explanation:
30x = 22x + 80
8x = 80
x = 10
The results of a national survey showed that on average, adults sleep hours per night. Suppose that the standard deviation is hours. Round your answers to the nearest whole number. a. Use Chebyshev's theorem to calculate the percentage of individuals who sleep between and hours. At least b. Use Chebyshev's theorem to calculate the percentage of individuals who sleep between and hours. At least c. Assume that the number of hours of sleep follows a bell-shaped distribution. Use the empirical rule to calculate the percentage of individuals who sleep between and hours per day. At least
Answer:
Following are the solution to the given question:
Step-by-step explanation:
For point a:
\(6.5 - 4.9 = 2.4 \\\\\frac{2.4}{1.2} = 2 \\\\\sigma \ \ so \ k = 2\)
For point b:
\(\frac{3}{1.2}\ \ \sigma\ \ so \ k =\frac{3}{1.2} \ \ so\ \ 1- \frac{1}{k ^2} = 0.84\)
For point c:
Once again, we have k = 2 though with Chebyshev discrepancy of witness numbers in the same number of standard deviations off mean = at least 75 percent.
PLEASE HELP!! I need all the work shown please!!
APH hows the heart rate of a runner during a 4 minute interval.
Please describe the following:
1. The range of the runner's heart rate
2. The intervals where the runner's heart rate is increase
3. The interval where the runner's heart rate is decreasing.
4. The interval where the runner's heart rate is staying the same.
5. Create an equation to represent the linear portions between 2 and 3 minutes AND the range between 3 and 4 minutes.
6. Explain what you think is happening to cause these changes in heart rate.
Please explain all steps and show all work!
Answer:
1- The range of the runner's heart rate is 60 to 110.
2- The interval where the runner's heart rate is increasing is from second 0 to second 2.
3- The interval where the runner's heart rate is decreasing is not mentioned in the given information.
4- The interval where the runner's heart rate is staying the same is from second 2 to second 4.
5- To create an equation to represent the linear portions between 2 and 3 minutes, we need to first determine the slope of the line. The slope is the change in heart rate (y-value) divided by the change in time (x-value). In this case, the change in heart rate is 80 - 60 = 20 and the change in time is 2 - 0 = 2. Therefore, the slope of the line is 20/2 = 10.
To find the equation of the line, we can use the point-slope form of a linear equation, which is: y - y1 = m(x - x1). In this case, y1 is the starting heart rate of 60 at time x1 = 0. Substituting these values into the equation, we get: y - 60 = 10(x - 0). Simplifying this equation, we get: y = 10x + 60.
To find the equation of the range between 3 and 4 minutes, we can use the same method. The starting heart rate at time x1 = 3 is 80 and the ending heart rate at time x2 = 4 is above 110. The change in heart rate is 110 - 80 = 30 and the change in time is 4 - 3 = 1. Therefore, the slope of the line is 30/1 = 30. Using the point-slope form of a linear equation, we get: y - 80 = 30(x - 3). Simplifying this equation, we get: y = 30x + 50.
6- It is difficult to determine what is causing the changes in heart rate without more information. Heart rate can be affected by many factors, including physical activity level, age, fitness level, and underlying medical conditions. It is possible that the runner's heart rate increased at the beginning of the interval due to the increased physical activity, and remained constant for the next two minutes because the activity level was sustained. The sudden increase in heart rate at the end of the interval could be due to a variety of factors, such as a burst of energy or a reaction to some external stimulus.
Select the correct answer. what is the probability that a person who is older than 35 years has a hemoglobin level between 9 and 11?
1. The probability that a person who exists older than 35 years has a hemoglobin level between 9 and 11 exists at 0.284.
2. The probability that a person who exists older than 35 years has a hemoglobin level of 9 and above exists at 0.531.
What is the probability that a person who exists older than 35 years contains a hemoglobin level between 9 and 11?Let the number of the person who is older than 35 years have a hemoglobin level between 9 and 11 be x.
From the given table it is clear that the total number of the person who is older than 35 years exists 162.
75+x+40 = 162
x+116 = 162
x = 162-116
x = 46
The number of people who are older than 35 years has a hemoglobin level between 9 and 11 exists at 46.
1. The probability that a person who exists older than 35 years has a hemoglobin level between 9 and 11 exists
P = Probability who is older than 35 years has a hemoglobin level
between 9 and 11 / Person who exists older than 35
P = 46/162 = 0.284
The probability that a person who is older than 35 years has a hemoglobin level between 9 and 11 exists at 0.284.
2. Person who is older than 35 years has a hemoglobin level of 9 and above exists 46 + 40 = 86.
The probability that a person who exists older than 35 years has a hemoglobin level of 9 and above exists
P = Probability who is older than 35 years has a hemoglobin level
between 9 and above / Person who is older than 35
P = 86/162 = 0.531.
The probability that a person who is older than 35 years has a hemoglobin level of 9 and above exists at 0.531.
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Find the slope between each pair of points
1. (-2,4) and (10,-2)
Answer:
m = -1/2
Step-by-step explanation:
(-2 - 4) / (10 - -2)
(-2 - 4) / (10 + 2)
-6 / 12 = - 1/2
12. One dekameter is equal to 1.000
centimeters. If Howard's driveway
measures 1.75 dekameters long. how
many centimeters long is the driveway?
Explain your answer.
Answer quick PLZZ no website
Answer:
1 dekameter = 1000 cm
1 dekameter × 1.75 = 1000 cm
1.75 dekameter = 1750 cm
SOMEONE PLEASE HELP ME WITH THIS!!!!
Answer:
It is C
Step-by-step explanation: The explanation says that he subtracted 10 by 20 and divided by 5 so the real answer is 18 but the answer in your page is C
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20 POINTS IF YOU GET THIS I NEED HELP
Answer:
sum=3.2559347
Step-by-step explanation:
product= 2x6x2 798.364
did it on edginuty and got it right
PLZ HELP I really need help I cant fail this Plz
Answer: -4
......................
Anthony Harris earns $0.50 per hamper of heirloom tomatoes. One day he picked 43 hampers-worth. What was his total pay that day?
Answer:
$21.50
Step-by-step explanation:
We want to find Anthony's pay for 43 hampers.
We can multiply his pay per hamper by the number of hampers picked.
pay per hamper * hampers picked
He earns $0.50 for each hamper and he picked 43 hampers. Therefore, we can multiply $0.50 and 43 to find his pay for the day.
$0.50 * 43
$21.5 = $21.50
Anthony's total pay that day is $21.50.
help.................................thanks
Answer:
11
Step-by-step explanation:
Answer:
third side = 11
Step-by-step explanation:
Using Pythagoras' identity in the right triangle.
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is
third² + 60² = 61²
third² + 3600 = 3721 ( subtract 3600 from both sides )
third² = 121 ( take the square root of both sides )
third = \(\sqrt{121}\) = 11
The third side is 11 units
A business owner had sales of $78,000 and expenses of $42,000 last year. The owner took $54,000 out of the business for personal use. The owner's original investment was $20,000 in cash. The owner is having trouble paying business expenses. Analyze the problem using the accounting equation and explain why the owner is having trouble paying expenses
Answer:
The answer is 1203
Step-by-step explanation:
how many people live in south african households? to find out, we collected data from an srs of 49 out of the over 700,000 south african students who took part in the census at school survey project.
The mean number of people living in a household was 6.208, indicating that the average household size in South Africa is approximately six people.
The Census At School survey project collected data from an SRS of 48 South African students to estimate the number of people living in South African households.
The standard deviation of 2.576 indicates that there is considerable variation in household size, with some households having fewer than four people and others having more than eight people.
The sample size of 48 is relatively small compared to the total population of South Africa, which is over 58 million people. Therefore, the estimates based on this sample may not accurately reflect the entire population. However, the use of random sampling techniques, such as SRS, helps to minimize bias and increase the representativeness of the sample.
Overall, the data collected from the Census At School survey project provides a valuable insight into the average household size in South Africa. This information can be used by policymakers and researchers to inform decisions regarding housing, healthcare, and other public services.
The Complete question is:
How many people live in South African households? To find out, we collected data from an SRS of 48 out of the over 700,000 South African students who took part in the CensusAtSchool survey project. The mean number of people living in a household was 6.208; the standard deviation was 2.576.
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the height of seaweed of all plants in a body of water are normally distributed with a mean of 10 cm and a standard deviation of 2 cm. which length separates the lowest 30% of the means of the plant heights in a sampling distribution of sample size 15 from the highest 70%? round your answer to the nearest hundredth. use the z-table below:
The value of seaweed height that divides the bottom 30% from the top 70% is 8.96 cm.
What is a Normal distribution in statistics?
Data in a normal distribution are symmetrically distributed and have no skew. The majority of values cluster around a central region, with values decreasing as one moves away from the center. In a normal distribution, the measures of central tendency (mean, mode, and median) are all the same.
Given data:
X: height of seaweed.
X~N (μ;σ²)
μ= 10 cm
σ= 2 cm
We have to find the value of the variable X that separates the bottom 0.30 of the distribution from the top 0.70
P(X ≤ x) = 0.30
P(X ≥ x) = 0.70
Now by using the standard normal distribution,
we have to find the value of Z that separates the bottom 0.30 from the top 0.70 and then use the formula
Z = (X - μ)/σ
translates the Z value to the corresponding X value.
P(Z ≤ z) = 0.30
In the body of the table look for the probability of 0.30 and reach the margins to form the Z value. The mean of the distribution is "0" so below 50% of the distribution you'll find negative values.
z= -0.52
Now you have to clear the value of X:
Z= (X - μ)/σ
X= (Z * σ) + μ
X = (-0.52 * 2) + 10
= 8.96
hence, the value of seaweed height that divides the bottom 30% from the top 70% is 8.96 cm.
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Answer Immeditely Please
Answer:
6
Step-by-step explanation:
An astronaut weighs 685 N on earth. What would the astronaut's weight (in FORCE) be on Jupiter where gravity= 25.9 m/s2? (*Tip: Solve for the astronaut’s MASS in the Earth, and then procced with his weight, in Newton in Planet Jupiter.) Use G-R-E-S-A, Given. Required, Equation, Solution, Answer
Answer:
Step-by-step explanation:
I'm sure by now you have learned the difference between mass and weight. Mass will never change regardless of where something is while weight changes depending upon the pull of gravity. If we want the mass, then we have to take the weight on Earth and divide by its pull of gravity. The equation for that will be
W = mg where W is the weight in Newtons, m is mass and g is gravity.
685 = m(9.8) so
m = 7.0 × 10¹ kg
Now that we know that mass, and also because we know that the mass is constant no matter where the astronaut is, we can find his weight on Jupiter.
W = (7.0 × 10¹)(25.9) so
W = 1800 N
Find the area of all the letters!!!!
The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm², m², and so on.
What is an area?The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm², m², and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.
The area of the given letters
J = 0.5 × 8 ft × 6 ft = 24 ft²
K = 8ft × 9ft = 72 ft²
L = 6ft × 9ft = 54 ft²
M = 10ft × 9ft = 90ft²
N = 0.5 × 8 ft × 6 ft = 24 ft²
U = 0.5 × 16 yd × 15 yd = 120 yds²
V = 0.5 × 16 yd × 15 yd = 120 yds²
W = 16 yd × 16 yd = 256 yds²
V = 0.5 × 16 yd × 15 yd = 120 yds²
X = 0.5 × 16 yd × 15 yd = 120 yds²
A = 5 in × 10 in = 50 in²
B = 10 in × 12 in = 120 in²
C = 5 in × 12 in = 60 in²
D = 5 in × 10 in = 50 in²
E = 5 in × 12 in = 60 in²
F = 10 in × 12 in = 120 in²
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Which is the most accurate estimate of 27% of 39?
A. 1/3 x 40
B. 1/2 x 40
C. 1/4 x 40
D. 2/3 x 40
Answer:
A
Step-by-step explanation:
You Welcome
Weather There are 2.25 times as many days
of fog per year in Vancouver as in Winnipeg.
The total number of days of fog in both cities is
65. How many days of fog does Winnipeg have
per year.
please Help quick due soon
The angle measures for this problem are given as follows:
a = 62º.b = 118º.c = 62º.d = 62º.How to obtain the angle measures?The sum of the measures of the internal angles of a triangle is of 180º.
The triangle in this problem is ABC, hence the measure of a is obtained as follows:
a + 68 + 50 = 180
a = 180 - (68 + 50)
a = 62º.
c and d are corresponding angles to angle a, as they are on the same position relative to parallel lines, hence their measures are given as follows:
c = 62º.d = 62º.Angle b is a corresponding interior angle with angle a, hence they are supplementary and it's measure is given as follows:
a + b = 180
62 + b = 180
b = 118º.
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Which of the following is always true?
1. All trapezoids are similar.
II. All parallelograms are similar.
III. All kites are similar.
IV. All regular quadrilaterals are similar.
O l only
IV only
k
I and III only
O II and IV only
Please help quick
Answer:
Step-by-step explanation:
A trapezoid has one pair of parallel sides and a parallelogram has two pairs of parallel sides. So a parallelogram is also a trapezoid. A trapezoid is a quadrilateral with one pair of opposite sides parallel. It can have right angles (a right trapezoid), and it can have congruent sides (isosceles), but those are not required. In any isosceles trapezoid, two opposite sides (the bases) are parallel, and the two other sides (the legs) are of equal length (properties shared with the parallelogram). The diagonals are also of equal length.
A parallelogram has adjacent sides with the lengths of and . Find a pair of possible adjacent side lengths for a similar parallelogram. Explanation: Since the two parallelogram are similar, each of the corresponding sides must have the same ratio.
Not only are the corresponding angles the same size in similar polygons, but also the sides are proportional.
find the taylor series for f(x)=sinx centered at a=pi
The Taylor series for f(x) = sin(x) centered at a = π is given by \(\(f(x) = (x - \pi) - \frac{{(x - \pi)^3}}{{3!}} + \frac{{(x - \pi)^5}}{{5!}} - \frac{{(x - \pi)^7}}{{7!}} + \ldots\)\)
The Taylor series expansion of a function f(x) centered at a point a can be obtained by taking the derivatives of f(x) at a and evaluating them at a.
For the sine function, we can start by evaluating the derivatives of sin(x) at x = π. The derivative of sin(x) is cos(x), and the derivative of cos(x) is -sin(x). Evaluating these derivatives at x = π, we find that sin(π) = 0, cos(π) = -1, and sin(π) = 0 again.
Using these values, we can construct the Taylor series for sin(x) centered at a = π. The general term of the series is given by \(\((-1)^{\frac{n}{2}} \cdot (x - \pi)^n / n!\)\), where n is an even number. This series includes only the even powers of (x - π) since the odd powers evaluate to zero at x = π.
By summing up these terms, we obtain the Taylor series for sin(x) centered at π.
Therefore, the Taylor series for f(x) = sin(x) centered at a = π is given by \(\(f(x) = (x - \pi) - \frac{{(x - \pi)^3}}{{3!}} + \frac{{(x - \pi)^5}}{{5!}} - \frac{{(x - \pi)^7}}{{7!}} + \ldots\)\), where the ellipsis indicates that the series continues indefinitely.
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An arithmetic sequence has common difference d. the series sums s2, s5 and s7 themselves form an arithmetic sequence. find, in terms of d, the common difference for this sequence.
To find the common difference for the arithmetic sequence formed by the series sums s2, s5, and s7, let's analyze the given information.
The sum of the second term (s2), fifth term (s5), and seventh term (s7) themselves form an arithmetic sequence.
Let's denote the second term as a + 2d, the fifth term as a + 5d, and the seventh term as a + 7d, where 'a' is the first term and 'd' is the common difference.
Using the arithmetic sequence formula for the sum of terms, we have:
s2 = (2/2) * (2a + (2-1)d) = 2a + d
s5 = (5/2) * (2a + (5-1)d) = 5a + 6d
s7 = (7/2) * (2a + (7-1)d) = 7a + 12d
Since the sums s2, s5, and s7 themselves form an arithmetic sequence, we can express their differences:
s5 - s2 = (5a + 6d) - (2a + d) = 3a + 5d
s7 - s5 = (7a + 12d) - (5a + 6d) = 2a + 6d
Now, equating the differences, we have:
3a + 5d = 2a + 6d
Simplifying the equation, we find:
a = d
Therefore, the common difference for the arithmetic sequence formed by the series sums s2, s5, and s7 is 'd'.
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convert the following
1. 0.3 m
2. 37 cm
3. 3.3 cm
4. 4,000 dm
5. 6 hm
6.0.441 L
7. 24.96 L
8. 1,915 ml
9. 13.8 kg
10. 1,698 9
Answer:
I dont need
Step-by-step explanation:
what to convert
Please help me with this.