The probability that the mean GPA of a random sample of 20 students selected from this university is 3.10 or higher is 10.93%
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution:Problems of normally distributed samples are solved using the z-score methods.
We know that, in a set with mean and standard deviation , the z-score of a measure X is given by:
Z = X - μ/σ
After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem:The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean and standard deviation , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean and standard deviation .
For a Skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this problem, we have that:
μ = 3.02 , σ = 0.29 , n = 20 and s = 0.29/√ 20 = 0.0648
Find the probability that the mean GPA of a random sample of 20 students selected from this university is 3.10 or higher.
This is 1 subtracted by the p- value of Z when X = 3.10. So
By the Central Limit Theorem:
Z = X - μ / s
⇒ Z = 3.1 - 3.02/ 0.0648
⇒ Z = 1.23
The Z = 1.23 has a P- value of 0.8907
∴ 1 - 0.8907 = 0.1093
Now, for getting the percentage,
0.1093 × 100% = 10.93%
10.93% probability that the mean GPA of a random sample of 20 students selected from this university is 3.10 or higher.
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What translation is made from f(x) → f(x) + 6? sliding it up reflection across the y-axis rotation around the origin reflection across the x-axis
The translation made from f(x) → f(x) + 6 is sliding it up
what is translation in geometry?A translation is a geometric change in Euclidean geometry that involves moving each point in a figure, shape, or space by the same amount in one direction.
A translation can also be thought of as moving the origin of the coordinate system or as adding a constant vector to each point.
Any translation in a Euclidean space is an isometry.
the translation made from f(x) → f(x) + 6 involves moving the graph up 6 units
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Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options. The radius of the circle is 3 units. The center of the circle lies on the x-axis. The center of the circle lies on the y-axis. The standard form of the equation is (x – 1)² + y² = 3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
Answer:
A, B, E
Step-by-step explanation:
You want three true statements describing the circle whose equation is ...
x² + y² – 2x – 8 = 0
GraphA graphing calculator can plot this equation for you. The result is attached.
We see that ...
The radius of the circle is 3 units.The center of the circle lies on the x-axis.The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.__
Additional comment
The standard form equation of a circle is ...
(x -h)² +(y -k)² = r² . . . . . center (h, k), radius r
Rearranging the given equation to this form, we have ...
(x -1)² +y² = 8 +1 = 9 . . . . . . . . r²=9 ⇒ r=3
This means the center is (1, 0), and the radius is 3. The point (1, 0) is on the x-axis.
The circle with equation x² + y² = 9 is centered at the origin and has radius 3.
10 is the geometric mean between 23 and what other value? Round your answer to the tenths' place.
10 is the geometric mean between 23 and 4.35.
What is geometric mean?The geometric mean is a type of average, generally used for growth rates. Let c is the geometric mean of a and b, then c=[tex]\sqrt{ab}[/tex].
Given that,
The geometric mean of 23 and other value is 10.
Let the other value is x.
Use the geometric mean property,
G.M.=[tex]\sqrt{ab}[/tex] (1)
Substitute the given values in equation (1)
10=[tex]\sqrt{23x}[/tex]
⇒x=100/23
⇒x=4.347
The geometric mean of 23 and 4.35 is 10.
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Gary and Kathy's restaurant bill comes to $35.50. They are planning to tip the waiter 20%. How much money will they pay including the tip?
Answer: $42.60
Step-by-step explanation:
divide $35.50 by 5 and then add the quotient ---> $7.10, to $35.50, which equals $42.60.
What did the king krum call the royal math and science teacher
Answer: HISFAVORITESUBJECTS
Step-by-step explanation:
Use a quadratic equation to find two real numbers with a sum of 31 and a product of 210?
The quadratic equation whose sum of two real roots is 31 and product is 210 will be [tex]x^{2} -31x+210 = 0[/tex].
According to the question,
We have the following information:
The sum of roots of a quadratic equation = 31
The product of roots of a quadratic equation = 210
We know that the standard form of the quadratic equation is given as follows:
[tex]ax^{2} +bx+c = 0[/tex]
Now, the sum of roots is -b/a and the product of roots is c/a.
So, we have the following expressions:
-b/a = 31
b = -31 and a = 1
c/a = 210
c = 210 and a = 1
So, the equation will be:
[tex]x^{2} -31x+210 = 0[/tex]
Hence, the quadratic equation whose sum of two real roots is 31 and product is 210 will be [tex]x^{2} -31x+210 = 0[/tex].
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9. If XYZ LMN, what is the length of XZ?
The two triangles are congruent.
So, their corresponding sides will be equal.
So, 2x+5 = 5x-19
3x = 24
x = 8 cm.
So, XZ = 2*8+5 = 21 cm
−2 1/4×(−1 1/3)[tex]−2 1/4×(−1 1/3)[/tex]
The value after multiplying the given mixed fractions is 7/6 .
In the question ,
it is given that ,
the two mixed fraction are given as [tex]-2\frac{1}{4}[/tex] and [tex]-1\frac{1}{3}[/tex] ,
we need to find their value after multiplication .
we first convert the mixed fractions into improper fraction ,
So ,
[tex]-2\frac{1}{4}[/tex] = (-2×4+1)/4 = (-8+1)/4 = -7/4
and
[tex]-1\frac{1}{3}[/tex] = (-1×3+1)/3 = (-3+1)/3 = -2/3
So , the product of -7/4 and -2/3 is written as
= -7/4 × -2/3
= (-7 × -2)/(4 × 3)
= 14/12
after simplifying ,
= 7/6
Therefore , The value after multiplying the given mixed fractions is 7/6 .
The given question is incomplete , the complete question is
Find the value after multiplying the given mixed fraction [tex]-2\frac{1}{4} \times -1\frac{1}{3}[/tex] .
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Select all triangles congruent to triangle 4.
Answer:
1, 2, 4, 5
Step-by-step explanation:
You want triangles congruent to triangle 4.
CongruenceIn this exercise, we can determine congruence using SSS congruence: the lengths of the sides in congruent triangles will match. (The order of appearance of the side lengths as you go around the triangle is irrelevant.)
Triangle 4The lengths of the sides are ...
diagonal of 4×2 rectangle5 grid squaresdiagonal of 4×3 rectangleLooking at the other triangles, we see side lengths of ...
Triangle 1All side lengths match: congruent to 4.
Triangle 2All side lengths match: congruent to 4.
Triangle 3One side is 6 grid squares: not congruent.
Triangle 5All side lengths match: congruent to 4.
Triangle 6One side is 6 grid squares: not congruent.
Triangle 7One side is the diagonal of a 3×2 rectangle: not congruent.
Triangle 8One side is the diagonal of a 4×1 rectangle: not congruent.
__
Additional comment
Triangles 3 and 6 are congruent to each other, but not to triangle 4.
A group consisting of 42 aggressive zombies triples in size every hour. Which equation matches the number of zombies after 2 hours?
The equation that matches the number of zombies after 2 hours is z = 42 × 3².
What is an equation?An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
In this case, a group consisting of 42 aggressive zombies triples in size every hour.
Let the number of zombies be z.
Therefore, the equation that matches the number of zombies after 2 hours will be:
= 42 × 3^n
= 42 × 3²
= 42 × 9
= 378 zombies
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find the salary of a person who is paid $3,800.00 per month
Answer:45600
Step-by-step explanation: 3800x12
Trace metals in drinking water affect the flavor and an unusually high concentration can pose a health hazard. Ten pairs ...
a) The hypothesis are given as follows:
Null: [tex]H_0: \mu_d \leq 0[/tex]Alternative: [tex]H_1: \mu_d > 0[/tex]b) The significance level is of α = 0.1.
c) The test statistic is of: t = 4.86.
d) The p-value is of: 0.
What are the hypothesis tested?At the null hypothesis, it is tested if there is not enough evidence that the mean level is greater at the bottom of the surface, that is, if the mean is not positive, hence:
[tex]H_0: \mu_d \leq 0[/tex]
At the alternative hypothesis, it is tested if there is enough evidence that the mean level is greater at the bottom of the surface, that is, if the mean is positive, hence:
[tex]H_1: \mu_d > 0[/tex]
As stated in the problem, the significance level is of:
α = 0.1.
How to calculate the test statistic?
The test statistic is calculated by the formula presented as follows:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
The variables of this formula are listed as follows:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null and at the alternative hypothesis.s is the standard deviation of the sample.n is the sample size.From the table, the sample is composed by the differences and given as follows:
0.015, 0.028, 0.177, 0.121, 0.102, 0.107, 0.019, 0.066, 0.058, 0.121.
The above sample is inserted into a calculator, to obtain the parameter values given as follows:
[tex]\overline{x} = 0.0814, \mu = 0, s = 0.053, n = 10[/tex]
Hence the numeric value of the test statistic is given as follows:
t = (0.0814 - 0)/(0.053/sqrt(10))
t = 4.86.
What is the p-value?Using a t-distribution calculator, considering a right-tailed test, as we are testing if the mean is greater than a value, with 10 - 1 = 9 df and t = 4.86, the p-value is of 0.
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The amount of chlorine needed to treat a wimming
pool i directly proportional to the volume of the pool
The constant of proportionality for the relationship is 0.002.
We are provided that amount of chlorine needed is directly proportional to the volume of the pool .
So we can formulate the relation as
C = kV ... (1) ( where C = amount of chlorine ,
k = constant of proportionality
V = volume of the pool )
the sample ratio of chlorine to the the volume of pool , we have :
5 : 2500
10 : 5000
15 : 7500
So taking the first sample value and putting it in eqn (1)
we get
5 = k (2500)
therefore,
k = 5/ 2500
k = 0.002
So the constant of proportionality will be 0.002
Similarly if we take the other values also the constant of proportionality will remain the same.
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What is the slope of the line
Answer:
The answer to this question is undefined or c
Step-by-step explanation:
A horizontal line has a slope of 0 because it does not go vertically and a vertical line has a slope of undefined because it does not go horizontally
Sarah used 2. 5 cups of cheese in a dish that serves 10 people. Amyn used 1. 6 cups of cheese in a dish that serves 8 people. How much more cheese is in one serving of sarah’s dish?.
Answer: In one serving of Sarah's dish 0.05 more cheese than in one serving of Amyn's dish.
Given: Sarah used cups of cheese in a dish that serves people and Amyn used cups of cheese in a dish that serves people.
Now, the amount of cheese served by Sarah for a people is.
And the amount of cheese served by Amyn for a people is
Therefore, the difference between the amount of cheese served by Sarah and Amyn is calculated as
Cheese served by Sarah's in one serving cheese served by Amyn's in one serving
Hence, 0.05 more cheese is in one serving of Sarah's dish.
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Step-by-step explanation:
The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes was 7 to 4. If there were 8085 total votes, how many no
votes were there?
There are 2940 no votes.
From the question, we have
there were 8085 total votes
ratio= 7 :4
No votes = 4/11*8085
=2940
Divide:
Divide, in its simplest form, means to divide into two or more equivalent portions, spaces, groups, or divisions. Divide, in plain English, means to provide the entire thing to a group in equal portions or to divide it into equal pieces. Let's say a square is divided into two triangles with equal areas by a diagonal. A division operation may or may not provide an integer as the outcome. The outcome may occasionally take the form of decimal numbers.
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Identify the vertical asymptotes and horizontal asymptote of each.
Vertical asymptotes is x = -4 and horizontal asymptote is y = 1
What is an Asymptote?
An asymptote is a line that a curve approaches but never touches. A line where the graph of a function converges is known as an asymptote.
There are 3 types of asymptotes.
Horizontal asymptote (HA) - It is a horizontal line and hence its equation is of the form y = k.Vertical asymptote (VA) - It is a vertical line and hence its equation is of the form x = k.Slanting asymptote (Oblique asymptote) - It is a slanting line and hence its equation is of the form y = mx + b.The given expression,
f(x) = (x² - 3x) / (x² + x - 12)
First, find Horizontal asymptote
so,
Horizontal asymptote (y) = (leading coefficient of numerator) / (leading coefficient of denominator)
leading coefficient of numerator = 1
leading coefficient of denominator = 1
y = 1/1
y =1 (Horizontal asymptote)
Now, find Vertical asymptote
so, let's simplify the expression f(x) = (x² - 3x) / (x + x - 12)
f(x) = (x(x - 3) ) / (x² + 4x - 3x - 12)
f(x) = (x(x - 3) ) / (x(x + 4) - 3 (x + 4) )
f(x) = (x(x - 3) ) / ( (x -3) (x + 4) )
f(x) = x / (x + 4)
Now, put the denominator = 0
x + 4 = 0
x = -4 ( Vertical asymptote )
Hence, Vertical asymptotes is x = -4 and horizontal asymptote is y = 1
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help please and thankyou 3
The trigonometric function use to solve the angle x in the right triangles are as follows:
sin x = 6 / 10cos x = 5 / 10tan x = 4 / 6How to find the angles of a right triangle?A right angle triangle is a triangle that has one of its angles as 90 degrees. The side and angles of a right angle triangle can be found using trigonometric ratios.
Therefore, the trigonometric function that can be use to find the angle x in the triangles are as follows:
Triangle PNM
sin x = opposite / hypotenuse
sin x = 6 / 10
sin x = 3 / 5
Triangle ABC
cos x = adjacent / hypotenuse
cos x = 5 / 10
cos x = 1 / 2
Triangle DEF
tan x = opposite / adjacent
tan x = 4 / 6
tan x = 2 / 3
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An Olympic sized swimming pool consists of 660,000 gallons of water. It is currently be drained at a rate of 2,000 gallons a second. Write an equation in slope-intercept form to model this relationship.
The equation in slope intercept form to model the relationship is:
y = 660,000x+2000
Given,
An Olympic sized swimming pool consists of 660,000 gallons of water.
It is currently be drained at a rate of 2,000 gallons a second.
we are asked to determine the equation in slope intercept form = ?
we know the slope intercept form is:
y = mx+c
based on the given conditions, we formulate:
y = 660,000x + 2000
Hence we get the required answer.
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Which expression is equal to 14y−17+512y+6 , expressed in simplest form?
Answer:
526y-11
Step-by-step explanation:
14y-17+512y+6=526y-11
Answer:
Option (C)
Step-by-step explanation:
To simplify an expression, we can combine like terms. For this expression, there are two pairs of like terms, one-fourth y and five-twelfths y, and the constants negative seventeen and six.
To combine the fractions, we can find the least common denominator, twelve, so we can rewrite the fraction as three-twelfths.
Now combine the like terms to get eight-twelfths y minus eleven, which simplifies to two-thirds y minus eleven.
What is the constant rate of change in this equation? Write only the number as your answer y=5x + 12
Answer:
The slope (constant rate of change) is 5.
Jerry has 4 1/2 cup of strawberry he use 3/4 cup of a strawberry to make a breakfast smoothie he wants to use the remaining strawberry to make pancakes if he takes 1 1/4 cup of strawberries to make one pancake how many pancake can he make.
Jerry will able to make 3 pancakes if he has 4 1/2 cup of strawberry from which he make use of 3/4 strawberry to make breakfast smoothie and he need 1 1/4 cup of strawberries to make one pancake.
Total strawberry Jerry has = 4 1/2 cup = 9/2 cups
Strawberry used to make smoothies = 3/4 cup
Remaining strawberries
= 9/2 - 3/4
= (18-3)/4 = 15/4
To make one pancake, Jerry needs = 1 1/4 cup = 5/4 cup
Number of pancakes Jerry can make = 15/4/5/4 = 3 pancakes
Hence, the number of pancakes, Jerry can make is 3
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I need help please!!
the slope of the given point is m=2/17
An arts and crafts store sells sheets of stickers. Use the table to write an equation you can use to find the total cost y in dollars for x sheets of stickers.
The equation that can be use to find the total cost y in dollars for x sheets of sticker is y = 2.55x.
What is an equation?An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
In this case, it should be noted that a proportional relationship exist between the figures that are given.
Therefore, the constant will be:
= Cost / Number of sheet
= 12.75 / 5
= 2.55
Therefore, the equation is y = 2.55x
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The pharmacists milkweed concoction didn’t work. It only gave the queen split ends. However, the queen, in a rare kind hearted moment, agreed to let the pharmacist try again. This time he has decided to combine a mixture 50% sorghum with a mixture containing 75% sorghum to create a 10 ounce mixture containing 60% sorghum. How many ounces of the 50% mixture should the pharmacist use?
The ounces of the 50% mixture that the pharmacist should use is 6 ounce.
How to calculate the ounces?From the information, we need two equations to solve this problem.
equation 1:
x + y = 10
equation 2:
.5x + .75y = 10(.6)
set y = 10 - x
.5x + .75(10-x) = 6
.5x + 7.5 - .75x = 6
.5x -.75x = 6 - 7.5
-.25x = -1.5
Divide
x = -1.5/-.25
x = 6
Therefore, 6 ounce of the 50% sorghum are required.
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Please help me out don’t answer if you don’t know I would really appreciate it ;)
What is the simplified version of each expression? Assume all variables are positive
Answer:
A) 3
B) 2[tex]\sqrt{6}[/tex]
C) 3[tex]\sqrt{2}[/tex]
Step-by-step explanation:
A
3x3 = 9
B
24 = 2x2x2x3 We can pull out a pair of 2 and are left with 6
C
18 = 2x3x3 We can pull out a pair of 3 and are left with 2
Write each as an algebraic expression.
10) the product of 10 and a number n
12) the difference of 19 and a number n
14) The product of 7 and the sum of × and 2
15) The difference of 11 and the quotient of x and 3
11) the sum of a number n and 5
13) a number n squared
Answer:
10) 10n
12) 19-n
14) 7(x+2)
15) x/3 -11
11) n+5
13) n^2
Step-by-step explanation:
product = multiply
difference= subtract
sum = add
quotient = divide
Answer:
lo siento soy nuevo en este aplicación ay mis sierras disculpas
For each of the six plots, identify the strength of the relationship (e.g. weak, moderate, or strong) in the data and whether fitting a linear model would be reasonable. a. strong relationship, a linear model would NOT be reasonable b. strong relationship, a linear model would NOT be reasonable c. strong relationship, a linear model would be reasonable d. weak relationship, a linear model would be reasonable e. weak relationship, a linear model would NOT be reasonablelX f. moderate relationship, a linear model would be reasonable
The strength and relationships of the given data is verified as reasonable.
Given,
Determine the degree of the link (weak, moderate, or strong) in each of the six plots and if it is reasonable to fit a linear model to the data.
(a) There is a moderate relationship in the data. A linear model should not be reasonable.
→ From the plot here, it is clear that the data is following a quadratic trend, so a linear model should not be reasonable. On the other hand, it is also clear that the data is scattered more than a little around the approximate quadratic trend line, so there is a moderate relationship in the data.
(b) There is a strong relationship in the data. A linear model should be reasonable.
→ From the plot here, it is clear that the data is following a linear trend, so a linear model should be reasonable. On the other hand, it is also clear that the data is scattered almost a little around the approximate linear trend line, so there is a strong relationship in the data.
(c) There is a weak relationship in the data. A linear model should not be reasonable.
→ From the plot here, it is clear that the data is not following any trend, so a linear model should not be reasonable. On the other hand, it is also clear that the data is scattered everywhere, so there is a weak relationship in the data.
(d) There is a moderate relationship in the data. A linear model should not be reasonable.
→ From the plot here, it is clear that the data is following a quadratic trend, so a linear model should not be reasonable. On the other hand, it is also clear that the data is scattered more than a little around the approximate quadratic trend line, so there is a moderate relationship in the data.
(e) There is a strong relationship in the data. A linear model should be reasonable.
→ From the plot here, it is clear that the data is following a linear trend, so a linear model should be reasonable. On the other hand, it is also clear that the data is scattered almost a little around the approximate linear trend line, so there is a strong relationship in the data.
(f) There is a weak relationship in the data. A linear model should not be reasonable.
→ From the plot here, it is clear that the data is not following any trend, so a linear model should not be reasonable. On the other hand, it is also clear that the data is scattered everywhere, so there is a weak relationship in the data.
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if f(x)=-3x+9, find the value of 3f (2)-2f(0)
im gonna cry some1 pls help me
Jada has 12 library books checked out and Han has 13less than that. How many books does Han have checked out?
Answer:
-1
Step-by-step explanation:
Jada = 12 books
Han = 13 less books than Jada
12-13= -1
Han would have negative 1 books but in this situation it would not be possible.