Using the normal distribution, there is a 0.7357 = 73.57% probability that the sample proportion of households spending more than $125 a week is less than 0.31.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.By the Central Limit Theorem, for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex], as long as [tex]np \geq 10[/tex] and [tex]n(1 - p) \geq 10[/tex].The estimate and the sample size are:
p = 0.29, n = 207.
Hence the mean and the standard error are given as follows:
[tex]\mu = p = 0.29[/tex].[tex]s = \sqrt{\frac{p(1 - p)}{n}} = \sqrt{\frac{0.29(0.71)}{207}} = 0.0315[/tex].The probability that the sample proportion of households spending more than $125 a week is less than 0.31 is the p-value of Z when X = 0.31, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.31 - 0.29}{0.0315}[/tex]
Z = 0.63
Z = 0.63 has a p-value of 0.7357.
0.7357 = 73.57% probability that the sample proportion of households spending more than $125 a week is less than 0.31.
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Which statement is NOT true about Euclidean geometry?
F. The shortest distance between two points is a straight line.
G. Basic geometric elements are points, lines, and planes.
H. Parallel lines may intersect.
J. The sum of the measures of any triangle always equals 180 degree.
Answer: H. Parallel lines may intersect.
Step-by-step explanation:
By definition, parallel lines never intersect.
Is (1, -1) a solution of y=3x-4?
Answer:
Yes because putting value of x and y as 1 and -1 in equation :
y=3x-4
-1 = 3 * 1 - 4
-1 = -1 (True)
A Submarine goes 23 000M deep into the sea
The pressure of the submarine at a depth of 23000 meters is 2.3575 * 10⁸ N/m²
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Pressure = density * acceleration due to gravity (g) * depth
g = 10 m/s², hence:
Pressure = 1025 * 10 * 23000 = 2.3575 * 10⁸ N/m²
The pressure of the submarine at a depth of 23000 meters is 2.3575 * 10⁸ N/m²
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Seven more than 4 times a number is 43 solve in algebraic equation?
Answer:
x = 9
Step-by-step explanation:
4x + 7 = 43
4x = 36
x = 9
giving brainliest !!!!!!!!!!!
The parabola vertex is (1,5), the focus of the parabola is (1,6), and the directrix y = 4.
What is the graph of a parabolic equation?The graph of a parabolic equation is a U-shape curve graph that is established from a quadratic equation.
From the given information:
[tex]\mathbf{y=\dfrac{1}{4}(x-1)^2+5}[/tex]
The vertex of an up-down facing parabolic equation takes the form:
y = ax² + bx + c is [tex]\mathbf{x_v = -\dfrac{b}{2a}}[/tex]
Rewriting the given equation:
[tex]\mathbf{y = \dfrac{x^2}{4}-\dfrac{x}{2}+\dfrac{21}{4}}[/tex]
[tex]\mathbf{x_v = -\dfrac{b}{2a}}[/tex]
[tex]\mathbf{x_v = -\dfrac{(-\dfrac{1}{2})}{2(\dfrac{1}{4})}}[/tex]
[tex]\mathbf{x_v =1}[/tex]
Replacing the value of x into the equation, y becomes:
[tex]\mathbf{y_v = 5}[/tex]
Thus, the parabola vertex is (1,5)
From the vertex, the focus of the parabola is (1,6), and the directrix y = 4.
The graphical representation of the parabola is seen in the image attached below.
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Solve the following
8903=e
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Equation:}[/tex]
[tex]\mathsf{8,903 = e^{5x}}}[/tex]
[tex]\huge\textbf{Simplify:}[/tex]
[tex]\mathsf{8,903 = e^{5x}}}[/tex]
[tex]\mathsf{e^{5x} = 8,903}}[/tex]
[tex]\huge\textbf{Solve for the exponent:}[/tex]
[tex]\large\textsf{We get: }\downarrow\\\\\mathsf{2.718282^{5x}=8903}[/tex]
[tex]\huge\textbf{Take the logarithm from both sides:}[/tex]
[tex]\mathsf{log(2.718282^{5x}) = log(8,903x)}[/tex]
[tex]\large\textsf{We get:}\\\\\mathsf{5x \times log(2.718282)=log(8903)}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\mathsf{5x = \dfrac{log(8903)}{log(2.718282)}}[/tex]
[tex]\large\textsf{We get: }\\\\\mathsf{5x = 9.094143}[/tex]
[tex]\huge\textbf{Divide 5 to both sides:}[/tex]
[tex]\mathsf{\dfrac{5x}{5} = \dfrac{9.094143}{5}}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\mathsf{x= \dfrac{9.094143}{5}}[/tex]
[tex]\mathsf{x = 1.818829}[/tex]
[tex]\mathsf{x \approx 2}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{x =}\frak{\ 1.818829}}\huge\checkmark[/tex]
[tex]\large\textbf{Or if you're estimating your answer}\downarrow[/tex]
[tex]\huge\boxed{\mathsf{x \approx }\frak{\ 2}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Place value in the thousands for the 0 in 10000
The place value in the thousands for the 0 in 10,000 is three (3).
What is a place value?A place value refers to a numerical value which denotes a digit based on its position in a given number and it includes:
TenthsHundredthsThousandthsUnitTensHundredsThousandsIn this scenario, the place value in the thousands for the 0 in 10,000 is three (3).
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Consider the dot plot below. Of the following statements, which two characteristics of this dot plot make the median a better choice than the mean to summarize the center of the distribution?
A dot plot with an axis marked from 0 to 10 at increments of 1 is shown. Plot shows 8 dots at 10, 7 dots at 9, 6 dots at 8, 3 dots at 7, 2 dots at 0 and 6, and 1 dot at 5.
The mean is equal to the median and the data are symmetric.
The peak is equal to the median and the data are skewed.
The data are symmetric and there are outliers.
The data are skewed and there are outliers.
The two characteristics that makes the median a better choice are: A. The data are skewed and there are outliers.
What Characteristics of a Dot Plot Makes Median a Better Choice?In a data distribution, the median is a better choice to use to describe the data over the mean when an outlier exist and the data is skewed.
IN the dot plot given below, the data has an outlier of 10 while the data distribution is also screwed, this makes the median a better choice.
Therefore, the answer is: A. The data are skewed and there are outliers.
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if x+4/4= y+3/3 then y/3=
The value of y / 3 in the equation is x / 4.
How to use equation to find y / 3 ?Therefore,
x + 4 / 4 = y + 3 / 3
then y / 3 can be found as follows,
x + 4 / 4 = x / 4 + 4 / 4 = x / 4 + 1
y + 3 / 3 = y / 3 + 3 / 3 = y / 3 + 1
x / 4 + 1 = y / 3 + 1
subtract 1 from both sides of the equation
x / 4 + 1 - 1 = y / 3 + 1 - 1
x / 4 = y / 3
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For f(x) = 4x+1 and g(x)=x²-5, find (f-g)(x).
Answer: -x² + 4x + 6
Given:
f(x) = 4x + 1
g(x) = x² - 5
Solve:
= (f - g)(x)
= f(x) - g(x)
= 4x + 1 - (x² - 5)
= 4x + 1 - x² + 5
= -x² + 4x + 6
Answer:
(f-g) (x) = 4x+1 - x² + 5 = -x² + 4x + 6
Step-by-step explanation:
Explanation can be given if needed in the comments (ㅅ´ ˘ `)
If 70 mL of solution contains 280 mg of drug, how many milligrams of drug are in 50 mL of solution?
A sample of 40 observations is selected from one population with a population standard deviation of 5. The sample mean is 102. A sample of 50 observations is selected from a second population with a population standard deviation of 6. The sample mean is 99. Conduct the following test of hypothesis using the .04 significance level.
Is this a one-tailed or a two-tailed test?
State the decision rule.
Compute the value of the test statistic.
What is your decision regarding H0?
What is the p-value?
1) This is a Two tailed Test.
2) Decision rule is; If the p-value is greater than 4% fail to reject H₀.
3) P-value = 0.00968764 and so we reject H₀
How to state the decision rule in hypothesis testing?We are given the hypothesis as;
Null Hypothesis; H₀: m₁ = m₂
Alternative Hypothesis; H₁: m₁ ≠ m₂
1) Since the alternative hypothesis has "not equal to sign", then it is a two tailed test.
2) Since we are told to use significance level as 0.04, then we can say that the decision rule is;
If the p-value is greater than 4% fail to reject H₀.
3) Using a 2-Sample Z-Test online TI calculator gives the test statistic as;
z = 2.5868
4) From z-score calculator, p-value equals 0.00968764. This is less than 0.04 and as such the decision regarding H₀ is to reject H₀.
5) P-value = 0.00968764
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Without exponents
logc (xy^6z^-4) what is the equivalent expression
By eliminating exponents, the logarithmic expression [tex]\log_{c} x\cdot y^{6}\cdot z^{-4}[/tex] is equivalent to the logarithmic expression [tex]\log_{c} x + 6\cdot \log_{c} y - 4\cdot \log_{c} z[/tex].
How to simplify logarithmic functions
In this problem we are supposed to eliminate all exponents of a logarithmic function by applying any of the following properties:
㏒ x · y = ㏒ x + ㏒ y㏒ x/y = ㏒ x - ㏒ y㏒ yˣ = x · ㏒ yNow, we proceed to simplify the function:
[tex]\log_{c} x\cdot y^{6}\cdot z^{-4}[/tex]
[tex]\log_{c} x + \log_{c} y^{6} + \log_{c} z^{-4}[/tex]
[tex]\log_{c} x + 6\cdot \log_{c} y - 4\cdot \log_{c} z[/tex]
By eliminating exponents, the logarithmic expression [tex]\log_{c} x\cdot y^{6}\cdot z^{-4}[/tex] is equivalent to the logarithmic expression [tex]\log_{c} x + 6\cdot \log_{c} y - 4\cdot \log_{c} z[/tex].
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Find the slope-intercept form of the line that
passes through the point (-7, 3) and is
parallel to the line 2x+5y = 3.
47 POINTS !,!!!!!!!!!!!!!!
If no less than 100000 packets must be packed each week, the minimum number of packets needed to be packed each day for the remaining days is 21250.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
There are 6 days from Monday to Saturday. The factory is closed on Tuesday and 15000 packets were packed on Monday. If no less than 100000 packet must be packed, hence:
4x + 15000 ≥ 100000
x ≥ 21250
If no less than 100000 packets must be packed each week, the minimum number of packets needed to be packed each day for the remaining days is 21250.
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30 feet below the surface of the water. You are ascending towards the
surface of the water. The graph models this situation. What is the slope of the line?
Answer is slope of 5
Step by step
You can graph the slope as seen on the attached picture. You go up 30, you go right +6. Slope is y/x, so 30/6, equals 5
You can also use the slope formula
(y2-y1) over (x2-x1)
Using points on the graph
(6,0) and (0,-30)
(-30-0 ) over (0-6)
-30 over -6
-30/-6
= 5
(x-1)^2 + (y-2)^2 = 6.25
Answer: The center of the circle will be (1,2) and the radius will be 2.5
Step-by-step explanation: Basically since its (x-1) it would become x=1 so that's ur first value same thign with y but that would be ur second value. And since in your equation it is 6.25 that would be 2.5 because 6.25 is r^2 and you are looking for r.
If B is the midpoint of AC, which of the following equations is correct?
AB + AC = B
OBA + BC = AC
O None of these choices are correct.
O
AB = AC
Answer:
BA + BC = AC
Step-by-step explanation:
B is the midpoint of AC
Then
BA = AC/2 and BC = AC/2
Then
BA + BC = AC/2 + AC/2 = AC
Answer:a
Step-by-step explanation:
Given quadrialateral PQRS is similar to TUVW, find side PS.
The length of side PS according to the quadrilateral descriptions is; 21.
What is the length of side PS?Since, it follows from the task content that the two quadrilaterals given are congruent, hence, the corresponding sides are congruent and are in proportion to each other.
On this note, we have;
x/35 = 15/25
x = (35×15)/25
x = 21.
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(x-2)(x+3)=(x-2)(4-x)
The value of x is 0.5
How to evaluate the equation?The equation is given as:
(x -2)(x + 3) = (x - 2)(4 - x)
Divide both sides by x - 2
x + 3 = 4 - x
Evaluate the like terms
2x = 1
Divide by 2
x = 0.5
Hence, the value of x is 0.5
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A cube has it's one edge 5 cm and a cuboid measures 4m multiple 3m multiple 2m which has a greate surface area and how much ?
Answer:
Gievn that l=3m,b=5m,h=4m
L.S.A=2(l+b)h
=2×(3.5)×4
=2×8×4
=64sq.m
Step-by-step explanation:
please answer every question here
If the company sells 0 computers, they will not make a profit. They will lose $10780
How to interpret the slope?The function is given as:
P = 490n - 10780
A linear equation is represented as:
P = mn + c
Where
m represents the slope
By comparison, we have:
m = 490
This means that the slope is 490
Hence, the interpretation is
Slope; 490
The company earns $490 per computer sold
How to interpret the vertical intercept?The function is given as:
P = 490n - 10780
A linear equation is represented as:
P = mn + c
Where
c represents the vertical intercept
By comparison, we have:
c = -10780
This means that the vertical intercept is -10780
Hence, the interpretation is
Vertical intercept; -10780
If the company sells 0 computers, they will not make a profit. They will lose $10780
How to interpret the horizontal intercept?The function is given as:
P = 490n - 10780
A linear equation is represented as:
P = mn + c
Where
-c/m represents the horizontal intercept
By comparison, we have:
-c/m = 10780/490
-c/m = 22
This means that the horizontal intercept is 22
Hence, the interpretation is
Horizontal intercept; 22
If the company sells 22 computers, they will break even. They will earn $0
How to evaluate P when n = 46We have:
P = 490n - 10780
This gives
P = 490* 46 - 10780
P = 11760
If the company sells 46 computers, they will earn $11760
How to evaluate n when P = 15190We have:
P = 490n - 10780
This gives
15190 = 490n - 10780
490n = 15190+10780
490n = 25970
n = 53
The company will earn $15190, if they sell 53 computers
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Six men, A, B, C, D, E, and F of negligible honesty, met on a perfectly rough day, each carrying a light inextensible umbrella. Each man brought his own umbrella and took away let us say 'borrowed' _ - another's. The umbrella borrowed by A belonged to borrower of B's umbrella. The owner of the umbrella borrowed by C borrowed the umbrella belonging to the borrower of D's umbrella. If the borrower of E's umbrella was not the owner of that borrowed by F, who borrowed A's umbrella?
Answer:
Six Serving Men is a team exercise that examines an issue from twelve different viewpoints. It is based on the words of the poem by Rudyard Kipling: I keep six honest serving men, they taught me all I knew. Their names are What and Why and When and How and Where and Who. To use this technique in a meeting, provide 12 areas for answering questions related to the central topic
Step-by-step explanation:
A city currently has 2.16 thousand residents. Each year the city's population grows by around 220 persons.
After 15 years what will the approximate population of the city be? Round to three significant digits.
hi
I cannot figure the number 2.16 thousand has it does not mean anything to me.
But the only thing you need to do is to add 15 times 220
so = 3300
Answer:
5,460 people
Step-by-step explanation:
2,160 + 220x is the expression. Now, we plug in 15 for x.
2,160 + 220(15)
2,160 + 3,300 = 5,460
Brainliest, please :)
A store is having a sale on chocolate chips and walnuts. For 5 pounds of chocolate chips and 3 pounds of walnuts, the total cost is $25 . For 7 pounds of chocolate chips and 9 pounds of walnuts, the total cost is $53 . Find the cost for each pound of chocolate chips and each pound of walnuts.
Answer:
one pound of chocolate chips = $2.75
one pound of walnuts = $3.75
Step-by-step explanation:
we can solve this by first making an equation
let's write the number of chocolate chips in c
and the number of walnuts in w
5c + 3w = 25
7c + 9w = 53
let's first solve for c by multiplying the top equation by 3 and subtracting the bottom equation from it
(15c + 9w = 75) - (7c + 9w = 53)
8c = 22
c = $2.75
Let's now start to solve for w by inputting c into one of the equations.
(2.75)7 + 9w = 53
19.25 + 9w = 53
9w = 53 - 19.25
9w = 33.75
w = $3.75
a pound of chocolate chips = 2.75
a pound of walnuts = 3.75
give me brainliest, please!
Hope this helps :)
Answer:
each pound of chocolate chips costs $2.75
each pound of walnuts costs $3.75
Step-by-step explanation:
let c be the cost of a pound of chocolate chips
and w be the cost of a pound of chocolate chips
For 5 pounds of chocolate chips and 3 pounds of walnuts,
the total cost is $25 means 5c + 3w = 25
For 7 pounds of chocolate chips and 9 pounds of walnuts,
the total cost is $53 means 7c + 9w = 53
Now we have to solve the system:
[tex]\begin{cases}5c+3w=25&\\ 7c+9w=53&\end{cases}[/tex]
[tex]\Longleftrightarrow \begin{cases}15c+9w=75&\\ 7c+9w=53&\end{cases}[/tex]
[tex]\Longleftrightarrow \begin{cases}15c+9w=75&\\ 8c=22&\end{cases}[/tex]
[tex]\Longleftrightarrow \begin{cases}15c+9w=75&\\ c=\frac{11}{4} &\end{cases}[/tex]
[tex]\Longleftrightarrow \begin{cases}9w=75-15 \times \frac{11}{4} &\\ c=\frac{11}{4} &\end{cases}[/tex]
[tex]\Longleftrightarrow \begin{cases}9w=\frac{135}{4} &\\ c=\frac{11}{4} &\end{cases}[/tex]
[tex]\Longleftrightarrow \begin{cases}w= \frac{15}{4} &\\ c=\frac{11}{4} &\end{cases}[/tex]
HELP!!!!!!!!!!!!!!!!!!!!!!!!
The recursive formula for f(n) is f(n) = 4.25 + f(n - 1), f(0) = 2.25.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let f(n) represent the total cost of shoe rentals for n games, hence:
The recursive formula for f(n) is f(n) = 4.25 + f(n - 1), f(0) = 2.25.
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A. Reflection around the x-axis:
1. A (5, 1)→ A'
2. B (1, 3) B¹.
3. C (-2, 2)→ C'.
4. D (-5, 4) D'
B. Reflection around the y-axis:
1. A (5, 1)→ A'
2. B (1, 3) B¹.
3. C (-2, 2)→ C'_
4. D (-5, 4) D'
Part A
1) (5, -1)
2) (1, -3)
3) (-2, -2)
4) (-5, -4)
Part B
1) (-5, 1)
2) (-1, 3)
3) (2, 2)
4) (5, 4)
12480 es divisible de 6
Doy 50
12,480 es par y la suma de sus digitos da un multiplo de 3, por ello concluimos que es divisible por 6.
¿Como saber si un número es divisible por 6?Para que un número sea divisible por 6 debe cumplir dos condiciones.
Ser par.La suma de sus digitos debe ser multiplo de 3.En este caso tenemos 12,480, que sabemos que es par.
La suma de sus digitos da:
1 + 2 + 4 + 8 + 0 = 15
15 es multiplo de 3.
Entonces este número cumple ambas condiciones, por lo que concluimos que 12,480 es divisible por 6.
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19
Select the correct answer.
Which exponential function has the greatest average rate of change over the interval [0, 2]?
OA j(x) = 3(1.6)²
OB. An exponential function, f, with a y-intercept of 1.5 and a common ratio of 2.
OC.
OD.
g(x)
k(x)
The function with the greatest average rate of change is the function k(x)
How to determine the function?The average rate of change is calculated as
[tex]m = \frac{y_2 - y_1}{x_2 -x_1}[/tex]
The interval is [0,2].
So, we have
[tex]m = \frac{y_2 - y_1}{2 -0}[/tex]
[tex]m = \frac{y_2 - y_1}{2}[/tex]
For function j(x), we have
j(2) = 3 * 1.6^2 = 7.68
j(2) = 3 * 1.6^0 = 3
So, we have
[tex]m_j = \frac{7.68 - 3}{2}[/tex]
[tex]m_j = 2.34[/tex]
For function g(x), we have
g(2) = 25/2
g(0) = 8
So, we have
[tex]m_g = \frac{25/2 - 8}{2}[/tex]
[tex]m_g = 2.25[/tex]
For function k(x), we have
k(2) = 9
k(0) = 4
So, we have
[tex]m_k = \frac{9 - 4}{2}[/tex]
[tex]m_k = 2.5[/tex]
For function f(x), we have
f(2) = 1.5 * 2^2 = 6
f(0) = 1.5
So, we have
[tex]m_f = \frac{6 - 1.5}{2}[/tex]
[tex]m_f = 2.25[/tex]
The function with the greatest average rate of change is the function k(x) with a rate of 2.5
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who knows ow to solve this triangle?
The measure of x in the right angled triangle shown is 4.09
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Trigonometric ratio is used to show the relationship between the sides and angles of a right angled triangle.
From the diagram shown:
sin(17) = x / 14
x = 4.09
The measure of x in the right angled triangle shown is 4.09
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