Probability that "sample-proportion" of "households-spending" more than $125 per-week is less than 0.29 is 0.8340.
In order to calculate the probability that the sample-proportion of households spending more than $125 a week is less than 0.29, we use the sampling-distribution of sample-proportions, assuming the sample was selected using simple random sampling.
The Population-proportion (p) is = 0.27
Sample-size (n) is = 467,
Sample-proportion (p') is = 0.29,
To calculate the probability, we find the z-score corresponding to the sample proportion and then find the probability,
The formula to calculate the z-score is:
z = (p' - p)/√((p × (1 - p))/n),
Substituting the values,
We get,
z = (0.29 - 0.27)/√((0.27 × (1 - 0.27))/467),
z = 0.02/√((0.27 × 0.73) / 467),
z ≈ 0.97
We know that the probability associated with a z-score of 0.97 is 0.8340.
Therefore, the required probability is 0.8340.
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11. Find the following GCD and LCM. (a) GCD (360, 4000) (c) GCD (627, 205143) (b) LCM (360, 4000) (d) LCM (627, 205143)
The required answers are:
(a) GCD = 40 (b) LCM = 36000 (c) GCD = 33 (d) LCM = 1032933
GCD and LCM of the given numbers are:
(a) Prime factors of 360: 2 x 2 x 2 x 3 x 3 x 5.Prime factors of 4000: 2 x 2 x 2 x 2 x 5 x 5 x 5.GCD = 2 x 2 x 2 x 5 = 40.
(b) LCM = 2 x 2 x 2 x 2 x 3 x 5 x 5 x 5 = 36000.
(c) Prime factors of 627: 3 x 11 x 19.Prime factors of 205143: 3 x 3 x 7 x 7 x 11.GCD = 3 x 11 = 33.
(d) LCM = 3 x 3 x 7 x 7 x 11 x 19 = 1032933.
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Jo records the number of text messages she receives each day she uses this information to draw this bar chart write 3 mistakes she has made
Answer:
X axis labels aren't evenly spaces
Y axis has no origin
Missing label
Step-by-step explanation:
Scale of a graph is important when displaying numerical data on a plot.
Based on the bar chart given, it could be seen that the x axis which is labeled days of the week is not adequately spaced. Data on both axis should he a recognizable.
2.)
Taking a look at the graph, it has no origin, the numbering of the vertical axis, number of text messages should start from 0
3.) Also, the x and y axis aren't labeled Hence charts should be well labeled to include x - axis and y-axis.
Answer:
X axis labels aren't evenly spaces
Missing label
there us no scale written starting at 0
Step-by-step explanation:
this will give u 3/3
A proton moves along the x-axis with u2 -1.0 x 10⁷ m/s.
As it passes the origin, what are the strength and direction of the magnetic field at the (1 cm, 0 cm, 0 cm) position? Give your answer using unit vectors Express your answer in terms of the unit vectors i, j, and k. Use the 'unit vector button to denote unit vectors in your answer.
The magnetic field using the unit vector notation B = Bx i= [(μ₀ / 4π) * (q * (-1.0 x 10⁷ m/s) / 10^-16 m²)] i.
To determine the strength and direction of the magnetic field at the (1 cm, 0 cm, 0 cm) position caused by a moving proton, we can use the formula for the magnetic field produced by a moving charge:
B = (μ₀ / 4π) * (qv × r / r³)
where B is the magnetic field, μ₀ is the permeability of free space (constant), q is the charge of the proton, v is its velocity, × denotes the cross product, r is the position vector, and r³ represents the magnitude cubed of the position vector.
Given information:
u = -1.0 x 10⁷ m/s (velocity of the proton)
Position vector r = 1 cm i
Let's calculate the magnetic field at the given position:
First, we convert the position vector from centimeters to meters:
r = (1 cm, 0 cm, 0 cm) = (0.01 m, 0 m, 0 m)
Next, we substitute the values into the formula and simplify:
B = (μ₀ / 4π) * (qv × r / r³)
= (μ₀ / 4π) * (q * (-1.0 x 10⁷ m/s) × (0.01 m i) / (0.01 m)³)
= (μ₀ / 4π) * (q * (-1.0 x 10⁷ m/s) × (0.01 m i) / 0.000001 m³)
= (μ₀ / 4π) * (q * (-1.0 x 10⁷ m/s) × (0.01 m i) / 10^-18 m³)
= (μ₀ / 4π) * (q * (-1.0 x 10⁷ m/s) / 10^-16 m²) i
Now, we can express the magnetic field using the unit vector notation:
B = Bx i
= [(μ₀ / 4π) * (q * (-1.0 x 10⁷ m/s) / 10^-16 m²)] i
where Bx represents the magnitude of the magnetic field in the x-direction.
Please note that the direction of the magnetic field will depend on the orientation of the velocity vector of the proton.
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1,3x + 3,9x = 0
Pls someone explain the steps for this. Like how do I find the x1 and x2.
Answer:
x=0
I used phone math!!!!!!!!
HELP NQNSJNDNXJJXnwnfnf
Answer:
C. 14 is the answerStep-by-step explanation:
1. Write the question.
17 - 2x = -11
2. Subtract 17 from both sides
-17 -17
- 2x = -28
3. Negatives cancel
2x = 28
4. Divide both sides by 2
/2 /2
x = 14
5. Check the answer, write the equation.
17 - 2x = -11
6. Substitute x with the value
17 - 2(14) = -11
17 - 28 = -11
-11 = -11
The answer is correct!
So, 14 is the answerHope this helped,
Kavitha
please help asap
which inequality is represented by this graph
Answer:
W is either less than or( less than or equal to)
Step-by-step explanation:
I do not know what shows if something is equal to so the best answer I can think if is less than -2 as it looks like W is everything lower or equal to -2
Rachel makes $38.25 in 3 hours.
How much money did she make
per hour?
4
HELPPPPP 10 points
I NEED IT NOW
Answer:
1 hour: $12.75
Step-by-step explanation:
Easy divide 38.25 by 3 which is 12.75
Can someone help me in proving theorems in square pleasee ASAP
Step-by-step explanation:
[tex]90 = 4x - 6 \\ 96 = 4x \\ x = 24[/tex]
[tex]2x - 8 = \\ = 48 - 8 = \\ = 40[/tex]
A certain college graduate borrows $6600 to buy a car. The lender charges interest at an annual rate of 10%. Assuming that interest is compounded continuously and that the borrower makes payments continuously at a constant annual rate k dollars per year, determine the payment rate k that is required to pay off the loan in 5 years. (Round your answer to two decimal places.) k = $ per yr
The borrower would need to make payments of approximately $943.57 per year to pay off the loan in 5 years.
To determine the payment rate required to pay off the loan in 5 years, we can use the continuous compound interest formula:
A = P * [tex]e^{(rt)[/tex],
where A is the final amount, P is the initial principal, e is the base of the natural logarithm (approximately 2.71828), r is the annual interest rate, and t is the time in years.
In this case, the initial principal is $6600, the annual interest rate is 10%, and the time is 5 years. We want to find the payment rate, so let's set A equal to zero, indicating that the loan is fully paid off:
0 = 6600 * [tex]e^{(0.10 * 5)[/tex]- k * 5,
Simplifying the equation, we have:
[tex]e^{(0.5)[/tex] = k / 6600.
Now, we can solve for k by multiplying both sides of the equation by 6600:
k = 6600 * [tex]e^{(0.5)[/tex],
Using a calculator or software, we find that k is approximately $943.57 per year.
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2x + 7 = 15
What does x equal?
Can someone help me with this. Need answer and explanation/work. Thank you. Will Mark brainliest.
Answer:
The hikers are 5 miles apart.
Step-by-step explanation:
East + West = 3 miles apart (x-axis)
North + South = 4 miles apart (y-axis)
Then use the pythagorean theorem to find the distance between them.
sqrt(distance) = sqrt(3^2+4^2)
distance = sqrt(25)
distance = 5 miles
what is the probability rule for deciding whether events a and b are independent
Events A and B are considered independent if and only if the probability of their intersection (P(A ∩ B)) is equal to the product of their individual probabilities (P(A) * P(B)).
Independence: Two events A and B are independent if the occurrence or non-occurrence of one event does not affect the probability of the other event.
Joint Probability: The joint probability P(A ∩ B) represents the probability of both events A and B occurring together.
Multiplication Rule: According to the multiplication rule for independent events, if events A and B are independent, the probability of their intersection is equal to the product of their individual probabilities.
P(A ∩ B) = P(A) * P(B)
Interpretation: If the equation holds true, events A and B are considered independent since the probability of their intersection can be determined solely by multiplying their individual probabilities.
Dependence: If the equation does not hold true, it implies that the occurrence of one event affects the probability of the other event, indicating dependence between the two events.
In summary, the multiplication rule for independent events states that events A and B are independent if and only if P(A ∩ B) = P(A) * P(B).
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Using Substitution, what is the point of intersection of the following
systems? *
3x – ly = 14
y = - 2x + 16
1) (6,4)
2) (-6,-4)
3) (-6, 4)
4) (6,-4)
Answer:
A
Step-by-step explanation:
(6,4)
3x-1y=14
-y= 3x-14
y=-2x+16
sub in first equation
3x-14 =-2x+16
3x+2x= 16 +14
5x = 30
x = 6
plug in x
y=-2x+16
y = -2(6)+16
y = 4
(6,4)
Let 2 = 3 + 6i and w = a + bi where a, b E R. Without using a calculator (a) determine z/w and hence, b in terms of a such that z/w is real; (b) determine arg{z - 9}; (c) determine =||w/w||
The correct answers for the given data are (a) b = 6, (b) arg(z - 9) = -π/4, and (c) ||w/w|| = 1.
(a) To determine z/w, we first need to express z and w in terms of their real and imaginary parts. Given 2 = 3 + 6i, we can rewrite it as z = 3 + 6i. Similarly, w = a + bi. Now, let's calculate z/w:
z/w = (3 + 6i)/(a + bi)
To make z/w real, the imaginary part of the denominator should cancel out the imaginary part of the numerator. This means 6/a = 6i/b. Simplifying further, we get ab = 6a + 6bi. Since a and b are real numbers, the only way for the equation to hold is if b = 6 and a = 1. Therefore, b = 6.
(b) To determine arg(z - 9), we need to subtract 9 from z = 3 + 6i:
z - 9 = (3 + 6i) - 9 = -6 + 6i
The argument (or angle) of -6 + 6i can be calculated as:
arg(-6 + 6i) = arctan(6/(-6)) = arctan(-1) = -π/4
(c) To determine ||w/w|| (the magnitude of w divided by the magnitude of w), we need to find the magnitude of w. Given w = a + bi, the magnitude of w is given by:
||w|| = √(a^2 + b^2)
Now, substituting a = 1 and b = 6 (from part a):
||w|| = √(1^2 + 6^2) = √37
Therefore, ||w/w|| = ||w||/||w|| = 1.
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What is the area of this
Answer:
area of trapezoid = 1/2×(a+b)×height
area of trapezoid =1/2×(15m+7m)×7m
area of trapezoid =1/2×22m×7
area of trapezoid =77m²
area of trapezoid =1/2×(a+b)×height
area of trapezoid =1/2×(9ft+12ft)×4ft
area of trapezoid =1/2×21ft×4ft
area of trapezoid =42ft²
Nicole wants to rent a boat and spend less than $33. The boat costs $6 per hour , and Nicole has a discount coupon for $9 off. What is the answer in inequality
Answer: Nicole can spend up to 7 hours in the boat.
Step-by-step explanation:
Based on the information given in the question, the possible number of hours that can be used will be calculated as thus:
(6 × t) - 9 ≤ 33
6t - 9 ≤ 33
Collect like terms
6t ≤ 33 + 9
6t ≤ 42
Divide both side by the coefficient of t
6t/6 ≤ 42/6
t ≤ 7
Nicole can spend up to 7 hours in the boat.
Need help with this question thank you!
Answer:
You asked this question like 4 times
Step-by-step explanation:
The answer is
(5,-1)
(-4,0)
This is my last question !
Answer:
x=50 degrees
Step-by-step explanation:
I'm not sure but hope this helps and have a wonderful day!!!!
Answer:
x = 48
Step-by-step explanation:
2x + 10 + x + 26 = 180
3x + 36 = 180
3x = 180 - 36
3x = 144
x = 48
Country Financial, a financial services company, uses surveys of adults age and older to determine if personal financial fitness is changing over time (USA Today, April 4, 2012). In February of 2012, a sample of adults showed indicating that their financial security was more than fair. In February of 2010, a sample of adults showed indicating that their financial security was more than fair. a. State the hypotheses that can be used to test for a significant difference between the population proportions for the two years. - Select your answer - - Select your answer - b. What is the sample proportion indicating that their financial security was more than fair in 2012
Complete question :
Country Financial, a financial services company, uses surveys of adults age 18 and older to determine if personal financial fitness is changing over time (USA Today, April 4, 2012). In February of 2012, a sample of 1000 adults showed 410 indicating that their financial security was more than fair. In February of 2010, a sample of 900 adults showed 315 indicating that their financial security was more than fair. a. State the hypotheses that can be used to test for a significant difference between the population proportions for the two years. H : Pi - P2 - Select your answer HA : P1 P2 - Select your answer - b. What is the sample proportion indicating that their financial security was more than fair in 2012? Round your answer to two decimal places. In 2010?
Answer:
H0 : p1 - p2 = 0
H1 : p1 - p2 ≠ 0
Phat 2010 = 0.35
Phat 2012 = 0.41
Step-by-step explanation:
The null and alternative hypothesis :
H0 : p1 - p2 = 0
H1 : p1 - p2 ≠ 0
The null means there is no difference in proportion for the two years while the alternative claims that there is difference in proportion for the two years.
Sample proportion for 2010:
Phat = x / n
x = 315 ; n = 900
Phat = 315 / 900
Phat = 0.35
Sample proportion for 2012 :
Phat = x / n
x = 410 ; n = 1000
Phat = 410 / 1000
Phat = 0.41
I will mark brainlyist! Can anyone answer and explain how to do these? Thank you!
Answer:
2) $1797
3) $152
4) $5,378
What does 5/9 + 1/3 equal to?
Answer:
= 5/9 + 1/3
=5/9 + 3/9
= 5+3/9
=8/9
16. Use the distributive property of multiplication to find the product of 2x5²
We have:
[tex]2x \cdot (5^2)[/tex]
[tex]= 2x \cdot 25[/tex]
[tex]= \boxed{50x}[/tex]
In a study of the accuracy of fast food? drive-through orders, Restaurant A had 239 accurate orders and 70 that were not accurate.
a. Construct a 95?% confidence interval estimate of the percentage of orders that are not accurate
The 95% confidence interval estimate of the percentage of orders that are not accurate is approximately (17.37%, 27.83%)
Let's denote p as the proportion of orders that are not accurate.
The sample proportion of orders that are not accurate is given by:
p(bar) = 70 / (239 + 70)
= 70 / 309
≈ 0.226
The standard error of the proportion is calculated as:
SE = √[(p(bar)(1 - p(bar))) / n]
= √[(0.226(1 - 0.226)) / 309]
≈ √(0.1785 / 309)
≈ 0.0267
To find the margin of error, we need to multiply the standard error by the critical value corresponding to a 95% confidence level. For a 95% confidence level, the critical value is approximately 1.96.
Margin of error = 1.96 × SE
≈ 1.96 × 0.0267
≈ 0.0523
Now we can construct the confidence interval:
Lower limit = p(bar) - Margin of error
= 0.226 - 0.0523
≈ 0.1737
Upper limit = p(bar) + Margin of error
= 0.226 + 0.0523
≈ 0.2783
Therefore, the 95% confidence interval estimate of the percentage of orders that are not accurate is approximately (17.37%, 27.83%).
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use base conversion method, convert the decimal expansion (25679),, to an Octal expansion.
The decimal number (25679)₁₀ is equivalent to the octal number (62117)₈. The base conversion method, also known as the radix conversion method, is a systematic approach to converting numbers from one base to another.
To convert the decimal expansion (25679)₁₀ to an octal expansion, we can use the base conversion method.
Step 1: Divide the decimal number by 8 and keep track of the remainders.
25679 ÷ 8 = 3209 remainder 7
3209 ÷ 8 = 401 remainder 1
401 ÷ 8 = 50 remainder 1
50 ÷ 8 = 6 remainder 2
6 ÷ 8 = 0 remainder 6
Step 2: The remainders from bottom to top form the octal expansion.
Therefore, (25679)₁₀ = (62117)₈.
Hence, the decimal number (25679)₁₀ is equivalent to the octal number (62117)₈.
The question should be:
Use base conversion method, convert the decimal expansion (25679)₁₀ to an Octal expansion.
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can somebody help me first answer gets brainiest pls help
P and Q are points on the line 4x+2y=8
b) Draw the line 4x+2y=8 for values of x from -2 to 3.
WINNER WILL GET BRAINLIEST
Please help me.
There is no picture but it would be great if you could help me.
Answer:
[tex]4 \sqrt{2 - 3 = 1[/tex]
Answer:
(-2,8), (-1,6), (0,4), (1,2), (2,0), (3,-2)
Step-by-step explanation:
Insert these points in graph and draw a line. You will get the answer. ^_^
sorry had to edit because of a blunder
[tex]\sqrt{x} 196
can someone help me
Answer:
14
Step-by-step explanation:
√196
Calculate the square root of 196 and get 14.
14
Find the volume of compostie figure
Step-by-step explanation:
The first composite shape is a combination of a rectangular prism and a pyramid. To find the volume of the entire shape you find the volume of each individual shape and add them together. The second figure consists of a cylinder and a hemisphere.
Hope that helps :)
Find the surface area of a cubical planter
measuring 30 inches on a side.
30 x 30 = 900
This is the surface area of one side
900 x 6
Multiply by 6 to get the surface area of all 6 sides of the cube
900 x 6 = 5400
(help asap) The steps to solving the expression the quantity of the sum of three squared plus four divided by the absolute value of negative 0.25 end quantity minus 10.4 ÷ 4 are listed below.
Part A: Explain what the missing expression should be in Step 3. (6 points)
Part B: Explain what the missing expression should be in Step 6. (6 points)
Step 1 the quantity of the sum of three squared plus four divided by the absolute value of negative 0.25 end quantity minus 10.4 ÷ 4
Step 2 the quantity of the sum of three squared plus four divided by 0.25 end quantity minus 10.4 ÷ 4
Step 3
Step 4 the quotient of quantity 13 divided by 0.25 end quantity minus 10.4 ÷ 4
Step 5 52 − 10.4 ÷ 4
Step 6
Step 7 49.4
The final result of the given expression is 49.4.
Part A: In the missing expression should be the result of squaring three and adding four.
This is because the expression in Step 2 states "the quantity of the sum of three squared plus four divided by 0.25.
" Therefore, to continue simplifying the expression, we need to evaluate the value of the sum of three squared plus four.
The quantity of [tex](3^2 + 4)[/tex] divided by 0.25
To solve Step 3, we first evaluate the expression inside the parentheses:
[tex]3^2 + 4 = 9 + 4 = 13[/tex]
So, Step 3 becomes:
The quantity of 13 divided by 0.25
Part B: In the missing expression should be the result of dividing 13 by 0.25.
This is because in Step 4, the expression is "the quotient of the quantity 13 divided by 0.25 end quantity minus 10.4 divided by 4."
To simplify further, we need to calculate the value of 13 divided by 0.25.
13 divided by 0.25
To solve Step 6, we perform the division:
13 ÷ 0.25 = 52
So, it becomes:
52 minus 10.4 ÷ 4
Following the remaining steps:
52 minus (10.4 ÷ 4) = 52 - 2.6 = 49.4
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