Based on the given information and conducting a hypothesis test, we can conclude that there is evidence to suggest that the percentage of home sales to first-time buyers has changed from what it was two years ago at a significance level of 10%.
1. Hypotheses:
The null hypothesis (H0) assumes that the percentage of home sales to first-time buyers is the same as it was two years ago, while the alternative hypothesis (H1) suggests that the percentage has changed.
H0: The percentage of home sales to first-time buyers is the same as it was two years ago (p = 1/5 = 0.20)
H1: The percentage of home sales to first-time buyers has changed (p ≠ 0.20)
2. Test statistic and significance level:
We need to conduct a one-sample proportion test using the z-test. With a significance level of 10% (a = 0.10), we will compare the test statistic (z-score) to the critical values.
3. Calculation of the test statistic:
The test statistic for the one-sample proportion test is calculated using the formula:
z = (p' - p) / √(p * (1 - p) / n)
where p' is the sample proportion, p is the population proportion under the null hypothesis, and n is the sample size.
In this case, p' = 39/250 = 0.156, p = 0.20, and n = 250.
Substituting these values into the formula, we can calculate the test statistic (z).
4. Comparison with the critical values:
For a two-tailed test and a significance level of 10%, the critical values are approximately -1.645 and 1.645 (from the standard normal distribution).
5. Conclusion:
If the test statistic (z) falls outside the range between -1.645 and 1.645, we reject the null hypothesis and conclude that the percentage of home sales to first-time buyers has changed from what it was two years ago. If the test statistic falls within this range, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest a significant change in the percentage.
Remember to calculate the test statistic (z) and compare it to the critical values to draw a conclusion based on the provided sample data.
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Replace variables with values and
evaluate using order of operations:
V=Lwh
L = 4
W= 10
h = 12
I need help please
Answer:
480
Step-by-step explanation:
Substitute in the numbers for your letters, the length being 4, width being 10 and height being 12. To make things easier, multiply 10 by 12 which gets you 120. Then multiply 120 by 4 and you get 480.
Determine the value of x in the equation below.
16 - (x + 5) = 5
Answer:
x=6
Explanation:
16-(x+5)=15
open the bracket using 1 as an invisible number after the minus sign16-x+5=15You move -x to cross the equality sign and it change to + 16+5-15 =x+15 change to -15 because of the equality sign 21-15=6x=6A water tank in Stewart's
home had a small, steady
leak.
Loss of 1 3/5 mL in 10 min.
a. Use a complex fraction to
represent the change in the
volume of water in 1 minute.
___ milliliters
10 minutes
b. Simplify the complex fraction to find the change in the volume of water in the tank in 1 minute.
The change in the volume of water in 1 minute is a decrease of 0.16 milliliters.
Since a water tank in Stewart's home had a small, steady leak loss of 1 3/5 mL in 10 min, to find the change in the volume of water in 1 minute, the following calculation must be performed:
The total leak must be calculated and divided by the 10 minutes duration. 3/5 = 0.6 1 + 0.6 = 1.6 1.6 / 10 = 0.16
Therefore, the change in the volume of water in 1 minute is a decrease of 0.16 milliliters.
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The table shown below represents a function. Which of the following values cannot be used to complete the table?
X Y
-10 5
-25 10
-5 15
__ 20
1. -20
2. -15
3. -5
Answer:
3.-5 is correct
Step-by-step explanation:
We are given,
The table which represents a function.
Now, 'A function is a relation in which every element of the domain has a unique image'.
So, from the table, we see that,
-5 has the image 15.
So, it cannot have another image.
Thus, the number which cannot be used to complete the table is -5.
Hence, option C is correct.
Abby found that the radius of her bike tire was 14 inches what is the circumstances of the tire
Answer:
28
Step-by-step explanation:
radius= 14
circumstances of tire=?
Based on given conditions, formulate
circumstances= 2 multiply radius
= 2 multiply by 14
= 28
One-half of a number added to seven is eleven. What is the number?
What is the slope of this graph?
Rise
Run
Rise = 3
Run = 6
1
2
In a run chart, the variable being measured is typically placed on what axis?
(A) X axis
(B) Y axis
(C) Either axis
(D) Neither axis;
What are the 3 linear functions?.
Answer:
point-slope form, standard form, and slope-intercept form
Step-by-step explanation:
The three main types of linear functions are: point-slope form, standard form, and slope-intercept form.
Here is an image with each form
11/14+(-1/4)
pls help me.
give the anwser as a reduced,proper or improper fraction.
Answer:
15/28 or 0.53 decimal form
Step-by-step explanation:
11/14 + (-1/4)
11/14 + -1/4
= 15/28 or 0.53 decimal form
Answer:
11/14 + (-1/4) = 15/28
i am not sure
What is 1.75 - 1/6
Thanks!
Answer:
19/12
Step-by-step explanation:
1.75=7/4
7/4-1/6
21/12-2/12
19/12
Answer:
19/12
Step-by-step explanation:
1.75=7/4
7/4-1/6
21/12-2/12
19/12
If the model improves after adding an interaction, what should happen to the R2 and the standard deviation:
a. Both should increase
b. Both should decrease
c. R2 should increase, standard deviation should decrease
d. Standard deviation should increase, R2 should decrease
The correct answer is option C.
If the model improves after adding an interaction, R² should increase and the standard deviation should decrease. Option C is the right answer.
R², also known as the coefficient of determination, is a statistical measure of how well the regression line fits the data points. It indicates the proportion of variance in the dependent variable that can be explained by the independent variables.
The standard deviation is a measure of how spread out the data is in relation to the mean. If the data points are more concentrated around the mean, the standard deviation will be smaller. If the data is more dispersed, the standard deviation will be larger. Interaction terms in regression models explain how the relationship between two independent variables influences the dependent variable.
The inclusion of interaction terms can enhance the model's explanatory power by providing a more accurate depiction of the relationship between the independent and dependent variables. This can result in an increase in R² and a decrease in standard deviation.
So, we can say that if the model improves after adding an interaction, R² should increase and the standard deviation should decrease. Option C is the correct answer.
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Multiply the first equation by 2 . Give the abbreviation of the indicated operation. { 2
1
x−2y=4
3x+4y=8
The transformed system is { 1⋅x+−4⋅y=
3x+4y=8.
(Simplify your answers.) The abbreviation of the indicated operation is Change the third equation by adding to it (−5) times the first equation. Give the abbreviation of the indicated operation. ⎩
⎨
⎧
x+2y+4z=1
4x−4y−5z=2
5x+5y+5z=2
The transformed system is ⎩
⎨
⎧
x+2y+4z=1
4x−4y−5z=2. (Simplify your answers.) □x+0y+1z=
x+2y+4z
4x−4y−5z
5x+5y+5z
=1
=2
=2
The transformed system are:
Equation 1: x + 2y + 4z = 1
Equation 2: 4x - 4y - 5z = 2
The abbreviation of the indicated operation "Multiply the first equation by 2" is "M1→2M".
After multiplying the first equation by 2, the system becomes:
{ 2x - 4y = 8
3x + 4y = 8
The abbreviation of the indicated operation "Change the third equation by adding to it (-5) times the first equation" is "C3+(-5)×1C".
After performing this operation, the system becomes:
{ x + 2y + 4z = 1
4x - 4y - 5z = 2
The simplified answers for the transformed system are:
Equation 1: x + 2y + 4z = 1
Equation 2: 4x - 4y - 5z = 2
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An object occupies the region between the unit sphere at the origin and a sphere of radius 2 with center at the origin, and has density equal to the distance from the origin. Find the mass.
The mass of the solid is 7π/2 units.
The task is to calculate the mass of the solid.
Step-by-step solution: The solid occupies the region between the unit sphere at the origin and a sphere of radius 2 with the center at the origin. The spherical coordinates in 3D space are (r,θ,φ), where:r = radius, θ = polar angle, φ = azimuthal angle.
The equations of the given sphere are r=1 for the unit sphere and r=2 for the second sphere.
Using spherical coordinates, the solid can be defined as 1≤r≤2, 0≤θ≤2π, 0≤φ≤π.
The density is equal to the distance from the origin, i.e. ρ = r.
The mass of the solid is given by the triple integral ρ dV taken over the solid, where dV is the volume element in spherical coordinates.dV = r²sin φ dφdθdr
The limits for the triple integral are: 0 ≤ θ ≤ 2π, 0 ≤ φ ≤ π, and 1 ≤ r ≤ 2.M = ∭ρ dV = ∭r(r²sin φ) dφdθdr= ∫[0,2π]∫[0,π]∫[1,2] r³sin φ drdφdθ= ∫[0,2π]∫[0,π] -cos φ [r⁴/4]₁ ₂ drdφdθ= ∫[0,2π]∫[0,π] 7/4 cos φ dφdθ= ∫[0,2π] 7sin φ/4 ]₀ π dθ= 14π/4= 7π/2 units.
The mass of the solid is 7π/2 units.
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The mean age of the students in this class is 15.75. The standard deviation is 1.55. Determine the number of standard deviations from the mean required to include
of the ages listed.
13, 17, 18, 15, 16, 14, 15, 18, 17, 16, 15, 16, 13, 15, 17, 17
Answer:
1.774 standard deviations
Step-by-step explanation:
From the data, the minimum value is x = 13 and the maximum value is x' = 18. The mean X = 15.75 and the standard deviation, σ = 1.55.
The difference between the mean and the minimum value is the deviation from the mean. So, X - x = 15.75 - 13 = 2.75. To find the number of standard deviations this is, we divide it by the standard deviation, σ = 1.55.
So, 2.75/1.55 = 1.774.
So, the number of standard deviations to contain the value 13 is 1.774σ
Also, the difference between the maximum value and the mean is the deviation from the mean. So, x' - X = 18 - 15.75 = 2.25. To find the number of standard deviations this is, we divide it by the standard deviation, σ = 1.55.
So, 2.25/1.55 = 1.452.
So, the number of standard deviations to contain the value 18 is 1.452σ
Since 1.774σ > 1.452σ and 1.774σ would contain both the values of 13 and 18, the number of standard deviations from the mean required to contain the values is 1.774 standard deviations.
A number is called "bright" if it is 34 times larger than the sum of its digits. How many "bright" three-digit numbers are there?
A : 0
B : 1
C : 2
D : 3
E : 4
Step-by-step explanation:
Let the number be \(\overline{abc}=100a+10b+c\).
\(100a+10b+c=34a+34b+34c \\ \\ 66a-24b-33c=0 \\ \\ 22a-8b-11c=0\)
Taking the equation mod \(11\) yields \(-8b \equiv \pmod{11}\), meaning \(b=0\).
So, \(22a-11c=0 \implies c=2a\).
So, the only possibilites are \((a,c)=(1,2), (2,4),(3,6), (4,8)\).
Therefore, there are \(4\) such numbers.
Jordan drove for 6 hours at 55 miles per hour, while Matt drove for 3 hours at 60 miles per hour. If Isaac drove 82 miles longer than Jordan and Matt drove combined, for how many miles did Isaac drive.
Answer:
592 miles
Step-by-step explanation:
Answer:
592 miles
Step-by-step explanation:
1. To figure out how many miles Jordan drove, multiply 6 by 55. 6 x 55 = 330.
2. To figure out how many miles Matt drove, multiply 3 by 60. 3 x 60 = 180.
3. Add 330 and 180 together to find out how many miles they drove in total. 330 + 180 = 510 miles.
4. Add Isaac's 82 miles to 510 miles to get the answer of 592 miles.
the angles of traingle are in the ratio 3:7:8 find them in degrees as well as in radians
Graph the following quadratic equation y=5x^2
Given:
\(y=5x^2\)We have the graph below:
HELPPPPPPP ! LOOK AT ATTACHMENT Where does the horizontal asymptote lie for ?
A.
B.
C.
D.
Answer:
D
Step-by-step explanation:
The right part of a figure is shown. The left part of this figure is missing. Line j is a line of symmetry. Which choice shows the left part of the figure?
Answer: The one on the bottom right.
Step-by-step explanation:
Symmetry is basically like a mirror. The line of symmetry is the exact point where it starts to reflect.
A symmetrical shape can also be folded onto itself equally.
Looking at the photo, the picture on the bottom right is the left part of the figure.
What is greater 4.5 or 3.75
Answer:
4.5
Step-by-step explanation:
4.5>3.75
If we forgot about the decimals, we would have 4 and 3, and 4 is automatically larger; even with the decimals.
Hope this helps!
-AxekickNebulite
Find the measure of the line segment CD. Assume that lines which appear tangent are tangent.
The value of the measure of the line segment CD is,
⇒ CD = 10
We have to given that;
In circle,
CD = 2 + x
BC = 8
AB = 12
Hence, We can formulate;
AB² = BD × CD
12² = (8 + 2 + x) × 8
144 = 8 (10 + x)
18 = 10 + x
x = 18 - 10
x = 8
Thus, The value of the measure of the line segment CD is,
⇒ CD = 2 + x = 2 + 8 = 10
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Find the percent equivalent to 96 over 160.
Step-by-step explanation:
96/160 X 100% = 60 %
Suppose a city with population 400,000 has been growing at a rate of 8% per year. If this rate continues, find the population of this city in 19 years.
The population in 19 years will be approximately (Round to the nearest whole number as needed.)
Answer:
1726280
Step-by-step explanation:
find the terminal point p(x, y) on the unit circle determined by the given value of t. t = 11 6
The terminal point on the unit circle determined by t = 11/6 is approximately:
p(-0.866, 0.5)
For the terminal point on the unit circle determined by t = 11/6, we use the fact that the angle t (in radians) measured counterclockwise from the positive x-axis to the terminal point is given by:
t = arctan(y/x)
where (x, y) is the point on the unit circle.
Since we know that the point lies on the unit circle, we have:
x^2 + y^2 = 1
Solving for y, we get:
y = ±sqrt(1 - x^2)
Substituting this into the equation for t, we get:
t = arctan(±sqrt(1 - x^2)/x)
To determine the correct sign, we note that t = 11/6 is in the second quadrant, where x is negative and y is positive.
Therefore, we need to take the positive square root:
t = arctan(sqrt(1 - x^2)/(-x))
Multiplying both sides by -x and taking the tangent of both sides, we get:
tan(t) = sqrt(1 - x^2)/x
Squaring both sides and using the identity tan^2(t) + 1 = sec^2(t), we get:
x^2 = 1/(1 + tan^2(t)) = 1/(1 + (tan(11/6))^2)
Solving for x, we get:
x = -sqrt(1/(1 + (tan(11/6))^2)) ≈ -0.866
Substituting this value of x into the equation for y, we get:
y = sqrt(1 - x^2) ≈ 0.5
Therefore, the terminal point on the unit circle determined by t = 11/6 is approximately:
p(-0.866, 0.5)
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A forecasting method has produced the following over the past five months. What is the mean absolute deviation?.
List of four quantitative forecasting methods.
Moving averages, exponential smoothing, trend projection, and linear regression are all in the list. (Forecasting strategies, medium)
The average distance between observations and their mean is indicated by the variability metric known as mean absolute deviation . It uses the data original units to facilitate interpretation. Greater values imply a bigger divergence from the mean. Lower values, on the other hand, are related to the data surrounding it clustering. The average absolute deviation and the mean deviation are other names for the mean absolute deviation.
The next three procedures are necessary to calculate the mean absolute deviation.
1.By adding up all the observations and dividing by the sample size,
you can determine the sample average.
2.Discover the total deviation from the mean of each data point. When
negative signals appear, ignore them and instead deduct the
observed values from the mean
3.Divided the total value of above step
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what is the sum of. -6n + 3 and 4n -9 please help
Answer:
-2n-6
Step-by-step explanation:
Answer: -2n+7
Step-by-step explanation:
-6n+4 equals 2n
3+4 equals 7
-2n+7
The function y=0.75x + 2 represents the cost y (in dollars) of an ice cream sundae with x toppings. A sundae comes with 1, 2, 3, or 4 toppings. Identify the independent and dependent variables, the domain, and the range.
Answer:
Please check answer for explanation
Step-by-step explanation:
The independent variable is x
The dependent variable is y
The domain is the range of values of x
That will be 1-4
Now let’s get the range, the range just represent the y-values of the terms in the domain
at x = 1
y = 0.75(1) + 2 = 2.75
at x = 4
y = 0.75(4) + 2 = 3 + 2 = 5
The range is 2.75 to 5
Rational and Irrational Sums
Rational
Irrational
-4 +23
2/3 + 1/2
-1/4 + 12
2/5 + 15
-3/5 + 6/7
TL + 4
-V3+ 5/8
3.25 +4.17
Answer:
Rational
Rational
Rational
Rational
Rational
Irrational
Irrational
Rational
Step-by-step explanation:
First we need to establish what a rational, and a irrational numbers are. A rational number are basically integers that can be written as fractions which means any of the options that are integers or fractions are in fact rational numbers. A irrational number are basically numbers that cannot be written as a fraction which means things like repeating decimals or just numbers that cannot be expressed as a fraction of two other whole numbers.
First option:
\(-4+23\)
\(-4 + 23=19\)
19 is a rational number because it can be expressed as two integers which are 1 and 19
Second option:
\(\frac{2}{3} +\frac{1}{2}\)
Both are fractions which means the sum will be a fraction which also means it is a rational number since we previously established that every fraction is a rational number.
Third option:
\(-\frac{1}{2} + 12\)
You can write 12 as a fraction which is 12/1 and then solve which the sum will also be a fraction which means it will also be a rational number.
Fourth Option:
\(\frac{2}{5} +15\)
15 can be written as 15/1 which means it is a rational number which also means the sum of the two fractions will also be a rational number.
Fifth option:
Adding fractions, fractions are rational numbers which means the sum will also be a rational number
Sixth option:
Pie is a infinite decimal number which means it is irrational because it cannot be written as a fraction.
Seventh option:
\(\sqrt[]{3} +\frac{5}{8}\)
/3 cannot be written as a fraction which means the entire equation is irrational because a rational plus a irrational number will always equal a irrational number.
Eighth option:
\(3.25+4.17\)
Since how these decimals are not repeating they are both rational numbers.
Hope this helps.