Answer:
The probability is [tex]P(14 < X < 20 ) = 0.5354[/tex]
Step-by-step explanation:
From the question we are told that
The proportion that live with their parents is [tex]\r p = 0.142[/tex]
The sample size is n = 125
Given that there are two possible outcomes and that this outcomes are independent of each other then we can say the Recent census data follows a Binomial distribution
i.e
[tex]X \ \~ \ B( \mu , \sigma )[/tex]
Now the mean is evaluated as
[tex]\mu = n * \r p[/tex]
[tex]\mu = 125 * 0.142[/tex]
[tex]\mu = 17.75[/tex]
Generally the proportion that are not staying with parents is
[tex]\r q = 1 - \r p[/tex]
= > [tex]\r q = 0.858[/tex]
The standard deviation is mathematically evaluated as
[tex]\sigma = \sqrt{n * \r p * \r q }[/tex]
[tex]\sigma = \sqrt{ 125 * 0.142 * 0.858 }[/tex]
[tex]\sigma = 3.90[/tex]
Given the n is large then we can use normal approximation to evaluate the probability as follows
[tex]P(14 < X < 20 ) = P( \frac{ 14 - 17.75}{3.90} <\frac{ X - \mu }{\sigma } < \frac{ 20 - 17.75}{3.90} )[/tex]
Now applying continuity correction
[tex]P(14 < X < 20 ) = P( \frac{ 13.5 - 17.75}{3.90} < \frac{ X - \mu }{\sigma } < \frac{ 19.5 - 17.75}{3.90} )[/tex]
Generally
[tex]\frac{ X - \mu }{\sigma } = Z ( The \ standardized \ value \ of X )[/tex]
[tex]P(14 < X < 20 ) = P( \frac{ 13.5 - 17.75}{3.90} < Z< \frac{ 19.5 - 17.75}{3.90} )[/tex]
[tex]P(14 < X < 20 ) = P( -1.0897 < Z< 0.449 } )[/tex]
[tex]P(14 < X < 20 ) = P( Z< 0.449 ) - P(Z < -1.0897)[/tex]
So for the z - table
[tex]P( Z< 0.449 ) = 0.67328[/tex]
[tex]P(Z < -1.0897) = 0.13792[/tex]
[tex]P(14 < X < 20 ) = 0.67328 - 0.13792[/tex]
[tex]P(14 < X < 20 ) = 0.5354[/tex]
Josie ate 5/8 of a pie and Marge ate 6/10 of a pie. Who ate more and therefore burped louder?
Josie ate more and burped louder because 5/8 is greater than 6/10 and Josie ate 5/8 of the pie.
Given,
Josie ate 5/8 of a pie and Marge ate 6/10 of a pie.
We need to find who ate more and therefore burped louder.
We need to compare the given fraction and see which is greater.
We have,
Josie = 5/8 of a pie.
Marge = 6/10 of a pie.
Now,
We can compare the fraction in three ways:
Case 1. - In terms of %
5/8 x 100 = 62.5 %
6/10 x 100 = 60%
62.5 % > 60%
5/8 > 6/10
Case 2. - In terms of decimals
5/8 = 0.625
6/10 = 0.6
0.625 > 0.6
5/8 > 6/10
Case 3. -In terms of multiplying
5/8 = 6/10
5 x 10 = 6 x 8
50 = 48
50 > 48
5/8 > 6/10
5/8 is greater than 6/10 so the one who eats 5/8 of the pie ate more and burped louder.
Thus Josie ate more and burped louder.
Learn more about comparing fractions here:
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Use a t-test to test the claim about the population mean at the given level of significance using the given sample statistics. Assume the population is normally distributed. Claim: ; Sample statistics: , s, n What are the null and alternative hypotheses? Choose the correct answer below. A. H0: Ha: B. H0: Ha: C. H0: Ha: D. H0: Ha: What is the value of the standardized test statistic? The standardized test statistic is nothing. (Round to two decimal places as needed.) What is the P-value of the test statistic? P-value nothing (Round to three decimal places as needed.)
Complete question is;
Use a t-test to test the claim about the population mean μ at the given level of significance α using the given sample statistics. Assume the population is normally distributed.
Claim: μ ≥ 8300,α= 0.10
Sample statistics: ¯x = 8000, s = 440, n = 24
a. What are the null and alternative hypotheses?
b. What is the value of the standardized test statistic? (Round to 2 decimal places as needed.)
c. What is the p-value? (Round to three decimal places as needed.)
d. Decide whether to reject or fail to reject the null hypothesis.
Answer:
A) Null hypothesis:H0: μ ≥ 8300
Alternative Hypothesis:Ha:μ < 8300
B) t = -3.34
C) p-value = 0.001
D) we will reject the null hypothesis
Step-by-step explanation:
A) We are told that the claim is: μ ≥ 8300. Thus, the null hypothesis would be the claim. So;
Null hypothesis:H0: μ ≥ 8300
Also, alternative hypothesis would be;
Alternative Hypothesis:Ha:μ < 8300
B)Formula for standardized test statistic with a t-test is;
t = (¯x - μ)/√(s/n)
Plugging in the relevant values, we have;
t = (8000 - 8300)/√(440/24)
t = -3.34
C) From online p-value from t-score calculator attached using t = -3.34, n = 24, significance level = 0.01, DF = 24 - 1 = 23 and a one - tailed test, we have;
p-value = 0.001421 ≈ 0.001
D) The p-value of 0.001 is less than the significance value of 0.01,thus we will reject the null hypothesis
please hurry! solve this proof
Answer:
Step-by-step explanation:
Parallelogram has 2 parallel pairs of sides, and the parallel lines have to be opposite therefore they have to be parallel.
What is radical 3 divided by radical 3
Any number, except 0, divided by itself is always 1
x/x = 1 where x cannot be zero, but it can be any other number you want.
What is the zero of f(x)=-1.5x+60?
if point B is the midpoint of points A and C, find the value of x and AC. AB= 5x - 2, BC= 9x -10
Answer:
AC = 6 ÷ 7
x = 2
Step-by-step explanation:
Given that
AB = 5x - 2
BC = 9x - 10
So,
AC = AB + BC
= 5x - 2 + 9x - 10
14x -12 = 0
AC = 6 ÷ 7
As B is the mid point of point A and point C, so the value of x is determined by solving the given equations mentioned in the question
5x - 2 = 9x - 10
5x - 9x = -10 +2
-4x = -8
x = 2
Hence, the value of AC and the X is 6 ÷ 7 and 2 respectively
distance between these points.
R(-1,0), 5(8,6)
Answer:
Distance = 3√13
Step-by-step explanation:
[tex](-1 ,0)=(x_1 ,y_1)\\(8,6)=(x_2 , y_2)\\\\d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\ \\d = \sqrt{(8-(-1))^2+(6-0)^2}\\ \\d = \sqrt{(8+1)^2 +(6-0)^2}\\ \\d = \sqrt{(9)^2 +(6)^2}\\ \\d = \sqrt{81+36}\\ \\d = \sqrt{117} \\\\d= 3\sqrt{13}[/tex]
pls help!
If a and b are real numbers, then (a + b)^2 = a^2 + b^2
Provide a counterexample for the statement.
A)
a = 0 and b = 1
B)
a = 1 and b=0
C)
a = 1 and b = 2
D)
a = 0 and b = 0
Answer:
C ) a= 1 and b = 2
Step-by-step explanation:
(a + b)² = a² + 2ab + b²
It equals to
(a + b)² = a² + b²when ab = 0, in other words one of a or b or both should be zero
Looking through the answer options, only one of them:
C ) a= 1 and b = 2is the counterexample of the given statement, since none of a or be equals zero.
Please Help Brainlest
Answer:
A and C
I hope it helps ❤️
Answer: A and C
Step-by-step explanation:
Determine the answer by solving for x in each equation.
A. x + 4= 7 subtract 4 from both sides
-4 -4
x = 3
B. x/9 = 3 multiply both sides by 9
x=27
C. 5-x =2 subtract 5 from both sides
-5 -5
-1x = -3
x= 3
D. 8x = 32 divide both sides by 8
x = 4
E . x -10 = 7 Add 10 to both sides
+10 +10
x = 17
Consider this expression.
|m^2+n^2|
m = -5 and n = 3
Answer:
34
Step-by-step explanation:
To do this you would just plug in the values into the variables so you get [tex]|-5^{2} +3^{2} |[/tex] and when you simplify you get |25+9| which when you add together you get |34| and the absolute value is just 34 since it is not negative.
If m = -5 and n = 3, then the value of the expression |m² + n²| will be 34.
What is Algebra?Algebra is the study of graphic formulas, while logic is the interpretation among those signs.
The expression is given below.
⇒ |m² + n²|
Put m = -5 and n = 3, then the value of the expression will be
⇒ |(-5)² + 3²|
⇒ |25 + 9|
⇒ |34|
⇒ 34
More about the Algebra link is given below.
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how to find amount of ammonia gas in mole if the question gives
- ammonia gas is kept in a 10.0-L tank at 1 atm and 25°C
Answer:
0.409 mol
Step-by-step explanation:
Use ideal gas law:
PV = nRT
where P is absolute pressure,
V is volume,
n is number of moles,
R is universal gas constant,
and T is absolute temperature.
PV = nRT
(1 atm) (10.0 L) = n (0.0821 L·atm/mol/K) (25 + 273) K
n = 0.409 mol
How can you use the properties of operations to evaluate this expression? 18+4(28)
Step-by-step explanation:
open the brackets by multiplying 4 and 28 =112
18+112= 130
Answer:
Use the distributive property and expand 28, then distribute the 4 to 20 and the 4 to 8. Then you have 18 + 80 + 32. Use commutative property to reverse the order of 32 and 80 so that 18 and 32 are friendly numbers to add.
The town of Tola has a population of 45,000 and produces 6 tons of garbage each week. Express this information in terms of the function f
Complete question:
The amount of garbage, G produced by a city with population p is given by G = f(p). G is measured in tons per week, and p is measured in thousands of people. The town of Tola has a population of 45,000 and produces 6 tons of garbage each week. Express this information in terms of the function f
Answer:
The information of town Tola can be represented in function as 6 = f(45)
Step-by-step explanation:
Given;
population of Tola, p = 45,000
amount of garbage produced in tons per week, G = 6 tons = 6,000 kg
The function is given by;
G = f(p)
where;
G is the amount of garbage produced in tons per week
p is the population of Tola
Substitute in the given values into the function
6000 = f(45,000)
6 = f(45)
Therefore, the information of town Tola can be represented in function as 6 = f(45)
Un productor agricola tiene que envasar huevos en cajas de 12, de 6 o de 30. Si sabemos que tiene un numero parecido a 1000 huevos, pero no mas que eso, ¿Cuantos huevos tiene que envasar?
Answer:
El productor tiene que envasar 960 huevos.
Step-by-step explanation:
Es necesario determinar el mínimo común múltiplo de 6, 12 y 30. En primer lugar, se determina cada número como productos de números primos:
[tex]6 = 2\times 3[/tex]
[tex]12 = 2^{2}\times 3[/tex]
[tex]30 = 2\times 3\times 5[/tex]
El mínimo común múltiplo es:
[tex]M.C.M. = 2^{2}\times 3\times 5[/tex]
[tex]M.C.M. = 60[/tex]
El número total de huevos próximo a 1000 unidades es un múltiplo del mínimo común múltiplo:
[tex]n = 60\times 16[/tex]
[tex]n = 960[/tex]
El productor tiene que envasar 960 huevos.
Determine whether the relation is a function. {(−3,−6),(−2,−4),(−1,−2),(0,0),(1,2),(2,4),(3,6)}
Answer:
The relation is a function.
Step-by-step explanation:
In order for the relation to be a function, every input must only have one output. Basically, you can't have 2 outputs for 1 input but you can have 2 inputs for 1 output. Looking at all of the points in the relation, we see that no input has multiple outputs, so the answer is yes, the relation is a function.
solve for c: b/c =a
Answer:
c = b/a
Step-by-step explanation:
b/c = a
b = ac
b/a = c
Which expression is the exponential form of
Answer:
[tex](7x)^{\frac{3}{2} }[/tex]
2.
Select the correct answer.
What is a unit rate?
A.
a rate with one in the numerator
B.
a rate in which the numerator and the denominator are equal
a rate with one in the denominator
D.
a rate in
the denominator is greater than the numerator
sa ghich
Reset
Next
Answer:
a unit rate is a rate with one in the denominator
find the percentage increase from 150 to 210
Answer:
40%
Step-by-step explanation:
First you have to determine the increase as a number:
increase = new number - original number
That means you have an increase of 210 - 150 = 60
Then you will need to divide the increase by the original number and multiply the answer by 100:
% increase = increase ÷ original number × 100
That will give you: 60 ÷ 150 × 100 = 40
Mrs. diaz has 9 eggs. she cooks 5 eggs for breakfast. how many eggs are left? which model shows the problem?
Answer:
4
Step-by-step explanation:
9-4=5
hold up 9 fingers and take down 5
Rectangular Garden
A rectangular garden shown above is enclosed by
60
60
feet of fencing on three sides and by a wall on the fourth side. One of the sides of the garden that is perpendicular to the wall is
x
x
feet long. In terms of
x
,
x
,
what is the length, in feet, of the side of the garden that is against the wall?
Answer:
The length, in feet, of the side of the garden that is against the wall is(60 - x - CD) ft.
Step-by-step explanation:
Consider the diagram below.
The wall is labelled as AD, the side perpendicular to the wall is labelled as AB and the side against the wall is labelled as CB.
It is provided that the rectangular garden is enclosed by 60 feet of fencing on three sides.
That is,
AB + CB + CD = 60 ft.
⇒ x + CB + CD = 60 ft.
Then the length, in feet, of the side of the garden that is against the wall is:
x + CB + CD = 60 ft.
⇒ CB = (60 - x - CD) ft.
Answer: 60-2x
Step-by-step explanation:
10 points
Which of the following transformations were performed to make the
black figure become the blue figure? *
O Right 1
o Left 1
Ο ΟΟΟ
o Up 1
Down 1
Answer:
Left 1
Step-by-step explanation:
Its easy
Assume that any variable exponents represent whole numbers. Factor the greatest common factor from the polynomial.
Question:
Assume that any variable exponents represent whole numbers. Factor the greatest common factor from the polynomial.
[tex]9x^4 -6x^2[/tex]
Answer:
[tex]3x^2(3x^2 -2)[/tex]
Step-by-step explanation:
Given
[tex]9x^4 -6x^2[/tex]
Required
Factorize
[tex]9x^4 -6x^2[/tex]
Express 9 as 3 * 3 and 6 as 3 * 2
[tex]3 * 3x^4 -3 * 2x^2[/tex]
Factorize 3 from both terms
[tex]3(3x^4 -2x^2)[/tex]
Express x^4 as x^2 * x^2
[tex]3(3x^2 * x^2 -2x^2)[/tex]
Factorize x^2 from both terms
[tex]3x^2(3x^2 -2)[/tex]
Hence, the factors of [tex]9x^4 -6x^2[/tex] are
[tex]3x^2[/tex] and [tex]3x^2 - 2[/tex]
Simplify the following expression:
2x − 6y + 3x2 + 7y − 14x
Answer:
-12x+y+3x²
Step-by-step explanation:
2x-6y+3x²+7y-14x
2x-14x+3x²-6y+7y
-12x+3x²+y
If a = mg - kv²/ m find , correct to the nearest whole number the value of V when a= 2.8 ,m= 12 ,g = 9.8 and k= 8/3
Answer:
v = 22.59
Step-by-step explanation:
all you need is contained in this sheet
Answer:
Step-by-step explanation:
Suppose a company has a design maximum output of 280. Its actual output is 195 and its efficiency is 80%. Calculate its efficient output and its capacity utilization.
Answer:
Effective output = 224
Capacity Utilization = 80%
Step-by-step explanation:
Given the maximum output = 280
The actual output = 195
The efficiency = 80%
Below is the formula to calculate the efficiency.
Efficiency in percentage = (Effective output / Maximum output) x 100
Insert the given values in the formula.
80 =( Effective output / 280 ) x 100
Effective output = 280 x 0.8
Effective output = 224
Now the Capacity utilization ( %) = Actual output / Maximum output x 100
Capacity utilization in percentage = 224 / 280 x 100
Capacity Utilization = 80%
Can someone please help find the answer and explain how you got it please.
Answer:
5
Step-by-step explanation:
Hello!
We put in 2 for x and 6 for y
[tex]\frac{2(6)-2}{2}[/tex]
Now we can solve this
[tex]\frac{12 - 2}{2}[/tex]
[tex]\frac{10}{2} = 5[/tex]
The answer is 5
Hope this helps!
the product of a number and 5”. 4 the difference of a number and 7
Step-by-step explanation:
the product of a number and 5
n - number
the product - it's multiplication
n · 5 = 5 · n = 5nthe difference of a number and 7
n - number
the difference - it's subtraction
n - 7what is the distance between these two points? (0,0) (9,12)
Answer:
The distance between the two given points is 15 units.
Step-by-step explanation:
For this problem, we will use the distance formula.
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Now, let's plug in our coordinates.
[tex]d=\sqrt{(9-0)^2+(12-0)^2}[/tex]
Simplify the terms in the parentheses.
[tex]d=\sqrt{(9)^2+(12)^2}[/tex]
Simplify the exponents.
[tex]d=\sqrt{81 + 144}[/tex]
Add 81 to 144.
[tex]d=\sqrt{225}[/tex]
Solve the radical.
[tex]d = 15[/tex]
The distance between the two points is 15 units.
As you wake up to get your day started, you decide to make muffins for breakfast. The recipe you are using makes 2 dozen muffins and calls for 3 cups of flour and 1 cup of sugar. You decide to only make 18 muffins. How many cups of flour and sugar will you need for your recipe?
Answer:
1/4 cup of flour and 1/8 cup of sugar. (i am estimating)
Step-by-step explanation: