a. The percentage of students in the reference population scored above 775 is of: 16%.
b. The middle 95% of scores were between 400 and 900.
c. Approximately 160 students scored below 525.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.The mean and the standard deviation in this problem are given as follows:
[tex]\mu = 650, \sigma = 125[/tex]
Then the proportion of students who scored above 775 is one subtracted by the p-value of Z when X = 775, hence:
Z = (775 - 650)/125
Z = 1.
Z = 1 has a p-value of 0.84.
1 - 0.84 = 0.16, hence the percentage is of:
0.16 x 100% = 16%.
By the Empirical Rule, the middle 95% of scores are within 2 standard deviations of the mean, hence:
650 - 2 x 125 = 400.650 + 2 x 125 = 900.The proportion of students who scored below 525 is the p-value of Z when X = 525, hence:
Z = (525 - 650)/125
Z = -1.
Z = -1 has a p-value of 0.16.
Then the amount out of 1000 students is of:
0.16 x 1000 = 160 students.
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[tex]\sqrt{x} 48[/tex]
g in a school course, course x is related to course y if all the students who take course x are also in course y
This question is incomplete , I am answering this question in general as per my knowledge.
No, because you gave T a Boolean when T expected a student as its first argument and a course as its second parameter. This will be less formal if.
The expected,
T(‘‘user2012813",‘‘discrete math")=true
However, the function F(x) and A both yield either true or false (y). Thus, you are attempting to assess
T(F(‘‘user2012813"),A(‘‘discrete math"))=T(true, false)= NULL
Only the first formulation makes sense, but after relations are established, these kinds of structures can be used.
Null functions as both a value and a pointer in computer programming. A built-in constant called null has a value of zero. It is the same as how strings in C are terminated with the letter 0.
Null is another possible value for a pointer, and unless the CPU supports a unique bit pattern for a null pointer, it has the same value as zero.
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A rectangular auditorium seats 2100 people. The number of seats in each row exceeds the number of rows by 8. Find the number of seats in each row.
The number of seats in each row would be = 271 seats.
What is an auditorium?An auditorium is defined as the establishment that can be used for various events such as presentation, seminars and celebrations.
The total number of people seated in the auditorium= 2100 seats.
The total number of seats = 2100
The number of seats per row = 8x
That is,
2100 = 8x
make X the subject of formula;
X = 2100/8
X =263 +8
X = 271 seats per row.
Therefore, the number of seats per row would be = 271 seats per row.
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Find ED if AC=9x+1 and BD=13x-11 and ABCD is a rectangle.
Identify the equation of the function.
y= sqaure root x-1+3
The equation y= √(x-1) + 3 is a function of radical function.
What is a function?
A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
Type of function:
linear, power, quadratic, polynomial, rational, exponential, logarithmic, radical etc.
Given equation is
y= √(x-1) + 3
In the equation there is a term √(x-1).
A square root presents in the equation.
This means it is a radical function.
The given equation is of a radical function.
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USA Today reported that the state with the longest
mean life span is Hawaii, where the population mean life span is 77 years.
A random sample of 20 obituary notices in the Honolulu Advertizer gave the
following information about life span (in years) of Honolulu residents:
72 68 81 93 56 19 78 94 83 84
77 69 85 97 75 71 86 47 66 27
i. Use a calculator with mean and standard deviation keys to verify that
x 5 71.4 years and s < 20.65 years.
ii. Assuming that life span in Honolulu is approximately normally distributed, does this information indicate that the population mean life span for
Honolulu residents is less than 77 years? Use a 5% level of signifi cance.
There is not enough evidence to conclude that the population mean life span for Honolulu residents is less than 77 years.
What are the hypothesis tested?At the null hypothesis, it is tested if there is not enough evidence that the mean life span is less than 77 years, that is:
[tex]H_0: \mu \geq 77[/tex]
At the alternative hypothesis, it is tested if there is enough evidence that the mean life span is less than 77 years, that is:
[tex]H_1: \mu < 77[/tex]
We are testing if the mean is less than a value, hence we have a left-tailed test, with 20 - 1 = 19 df and a significance level of 0.05, thus the critical value is of:
t = -1.7291.
Thus the conclusion, considering the test statistic t, is given as follows:
t > -1.7291: not enough evidence to conclude that the mean life span is less than 77 years -> do not reject the null hypothesis.t < -1.7291: enough evidence to conclude that the mean life span is less than 77 years -> reject the null hypothesis.What is the test statistic?The equation to obtain the test statistic is presented as follows:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
The parameters are:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.s is the standard deviation of the sample.n is the sample size.In the context of this problem, the values of these parameters are given as follows:
[tex]\overline{x} = 71.4, \mu = 77, s = 20.65, n = 20[/tex]
Hence the test statistic is of:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{71.4 - 77}{\frac{20.65}{\sqrt{20}}}[/tex]
t = -1.21 -> not enough evidence to reject the null hypothesis.
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If the lines are perpendicular to each other and the slope of the one
line is 1/2 what is the slope of the other line?
Answer:2/1
Step-by-step explanation:
you just have to flip the slope if it is perpendicular.
A tree is 12 meters tall. What is its height in feet? Use the following conversion: 1 meter is 3.3 feet.
Answer:
The tree is 396 feets height
Step-by-step explanation:
1 m = 3.3 ft
then
12 meters to feet is:
(12)*(3.3) = 396
Write the domain as an inequality
x<-2
Write the range as an inequality
The domain of the given graph is -∞>x>-2
The range of the given graph is [0,-4]
What is the range and domain of a graph?
The range is the set of possible output values, which are shown on the y-axis.
The domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x -axis.
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The domain as an inequality x<-2 is { -∞>x>-2}.
The range as an inequality is [0,4]
What is the range and domain of a graph?
Functions in mathematics can be compared to the operations of a vending (soda) machine. When you put in a certain amount of money, you can select different types of sodas. Similarly, for functions, we input different numbers and we get new numbers as the result. Domain and range are the main aspects of functions. You can use quarters and one-dollar bills to buy a soda.
The machine will not give you any flavor of the soda if pennies are input. Hence, the domain represents the inputs we can have here, that is, quarters and one-dollar bills. No matter what amount you pay, you won't get a cheeseburger from a soda machine. Thus, the range is the possible outputs we can have here, that is, the flavors of soda in the machine.
The range is the set of possible output values, which are shown on the y-axis. The domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x -axis.
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3) Solve. Answer needs to remain as an improper
fraction.
3/4 - 3 1/2 + 6
Answer:
Exact form: 13/4
Decimal form: 3.25
Mixed form: 3 1/4
Step-by-step explanation:
16. Find the angle between 0 and 2π coterminal with the angle
23π/3
The angle between 0 and 2π coterminal with the angle 23π/3 will be equal to 17π/3.
What is trigonometry?The branch of mathematics that sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry. The trigonometric functions, also known as circular, angle, or goniometric functions in mathematics, are real functions that link the angle of a right-angled triangle to the ratios of its two side lengths.
Given that the angle between 0 and 2π coterminal with the angle 23π/3. The coterminal angle will be calculated as,
To calculate the coterminal angle subtract 2π from 23π/3. Solve mathematically,
Coternimal = ( 23π / 3 ) - 2π
Coterminal = 9 23π - 6π ) / 3
Coterminal = 17π / 3
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What is an equation of the line that passes through the point (−5,−2) and is parallel to the line x-y=5?
The required equation of the line is x - y + 3 = 0 which is parallel to line x-y=5.
What is the equation of the line?A straight line's general equation is y = MX + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis.
On the y-axis, this value c is referred to as the intercept.
The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.
So, the equation of the line will be:
The needed line will have the same slope as the parallel line.
The slope of the parallel line:
x - y = 5
y = x - 5
The parallel line's slope is 1.
Equation of a line with a slope of 1 through the point (-5,-2).
(y - y1) = m(x x1)
(y + 2) = 1(x + 5)
x - y + 3 = 0
Therefore, the required equation of the line is x - y + 3 = 0 which is parallel to line x-y=5.
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A baker has three canisters of flour in her supply room. Canister A can hold 30 pounds, canister B can hold 45 pounds, and canister C can hold 60 pounds.
Canister A contains 71% of its capacity.
Canister B is full.
Canister C has 8.8 pounds more than half its capacity.
The baker estimates that she does not have the 70 pounds of flour needed for this weekend's planned baking.
Use estimation strategies to determine which statements are true.
The true statement are
The baker's estimate is not reasonableThe baker has enough flour for the weekend's planned bakingHow to determine the true statementCanister A can hold 30 pounds and contains 71% of its capacity
= 0.71 * 30 pounds
canister B can hold 45 pounds and is 10/18 full
= 45 * 10/18 pounds
canister C can hold 60 pounds and it's 8.8 pounds more than half capacity
= 8.8 + 60 * 1/2 pounds
The total amount available
= 0.71 * 30 + 45 * 10/18 + 8.8 + 60 * 1/2
= 85.1 pounds
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Tamala’s school day is 7 1/2 hours. She has six classes that are 7/6 of an hour long each. How many hours is Tamala not in class while she is at school?
Answer:
The correct answer is [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
If she has 6 classes, then the total hours of classes are:
[tex]\frac{6}{1}[/tex] · [tex]\frac{7}{6}[/tex] = [tex]7[/tex]
[tex]7[/tex] · [tex]\frac{1}{2}[/tex] - [tex]7[/tex] = [tex]\frac{1}{2}[/tex]
On the Set of axes below graph the line whose equation is 2y=-3x-2
The linear equation contains point (2,k).State the value of k.
The value of k in the point (2, k) which lies on the line is -4.
How to find the value of k?
Every point lying on the curve of the line satisfies the equation of curve. Therefore, substitute the point in the given equation of line to find the value of k.
According to the given question:
The given equation is: 2y = - 3x - 2.
This is written as: 3x + 2y + 2 = 0.
Given the point (2, k) lies on the line given.
That means it should satisfy the given equation.
So, to find the value of 'k', simply substitute the point on the line.
So, it becomes: 3(2) + 2(k) + 2 = 0
⇒ 6 + 2k + 2 = 0
⇒ 2k = - 8
Dividing by 2 throughout, we get: k = - 4
Hence, (2, -4) lies on the line.
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Al, Bill, Dill, and Will ate some apples. Each of them ate a different
number of apples, and each of them ate at least two apples. However,
their father ate even more than they ate together; he ate 15. (Maybe
they were rather small apples!)
Could one of the boys have eaten more than five apples?
Answer:
Yes
Step-by-step explanation:
let x = one boy
let y = another boy
let z = a third boy
x + 2 + y + 2 + z + 2 = 15 Combine like terms
6 + x + y + z = 15 Subtract 6 apples from both sides
x + y + x = 9
When we subtract out the 2 apples each brother know that they ate at lease 2 apples each we are left with a total of 9 apples.
One boy could have eaten 4 additional apples? Yes.
4 + 1 + 1 < 9
If pentagon OPQRS is dilated by a scale factor of from the origin to create O′P′Q′R′S′, what is the ordered pair of point S′?
(8.75, 5.25)
(1.25, 0.75)
(1.75, 3.5)
(3.5, 8.75)
The correct answer is option A which is the ordered pair of point P’ will be (8.75, 5.25).
What is scale factor?The scale factor is defined as the proportion of the new image's size to that of the previous image. decision-making.
If pentagon OPQRS is dilated by a scale factor of 7/4 from the origin, to create O’P’Q’R’S’, what is the ordered pair of point P’
Multiply the coordinates of point P by the scale factor 7/4 to get the coordinates of P'.
Given : P(-5,3)
P' (x,y) = P (-5 x 7/4 , 3 x 7/4)
= P(-8.75, 5.25)
Therefore the correct answer is option A which is the ordered pair of point P’ will be (-8.75, 5.25).
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If the volume of a cone is 847picm³ and the height is 7 cm, what is the radius?
r≈10.75cm
Answer:
r≈10.75cm
V=πr^2h/3
3. Write the equation Passing through ( -5, 2) with a slope of 3
Answer:
y = 3x + 17
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here m = 3 , then
y = 3x + c ← is the partial equation
to find c substitute (- 5, 2) , that is x = - 5, y = 2 into the partial equation
2 = - 15 + c ⇒ c = 2 + 15 = 17
y = 3x + 17 ← equation of line
pelease help
7 1/4 x 0.55
Answer:
Step-by-step explanation:
3.9875
The 11 students in the Environmental Club represent 2% of the students in the seventh grade. How many students are in the seventh grade?
Answer:
The number of students in the seventh grade is 550.
Step-by-step explanation:
To find the number of students in the seventh grade, we need to use the information given in the problem: the number of students in the Environmental Club (11 students) and the percentage of students in the seventh grade that the Environmental Club represents (2%).
We can set up an equation to represent this information:
11 students / 2% = X students / 100%
The left side of the equation represents the number of students in the Environmental Club and the percentage of the seventh grade that they represent. The right side of the equation represents the total number of students in the seventh grade and the percentage that represents the whole.
Since percentages are just fractions with a denominator of 100, we can rewrite the equation as:
11 students / 0.02 = X students / 1
Then, we can use algebraic techniques to solve for X. One way to do this is to cross-multiply:
X = (11 students * 1) / 0.02
= 550 students
Therefore, there are 550 students in the seventh grade.
To order the right amount of flooring, you need to know the floor area of the living room
hown below. What is that area, in square feet?
Answer: Length (in feet) x width (in feet) = area in sq. ft.
Step-by-step explanation:
Question 4. Given that -4≤ x ≤6$ and 2≤ y ≤ 8, find:
(a) The smallest possible value of x-y. (1 mark)
(b) The largest possible value of {2x}/{y} (1 mark)
(c) The largest possible value of x²+y². (1 mark)
The smallest possible value of x - y will be -6 when x = -4 and y = 2. The largest possible value of {2x}/{y} will be 3/2 when x = 6 and y = 8. The largest possible value of x²+y² will be 100 when x = 6 and y = 8.
Given that -4 ≤ x ≤6 and 2≤ y ≤ 8,
The smallest possible value of x - y
⇒ (x - y)
As per the given, the smallest values of x and y are - 4 and 2
So, substitute the values of x = -4 and y = 2 in the expression (x - y)
⇒ - 4 - 2
⇒ - 6
The largest possible value of {2x}/{y}
⇒ {2x}/{y}
As per the given, the largest values of x and y are 6 and 8
So, substitute the values of x = 6 and y = 8 in the expression {2x}/{y}
⇒ 2(6)/8
⇒ 12/8
⇒ 3/2
The largest possible value of x²+y².
⇒ x²+y²
As per the given, the largest values of x and y are 6 and 8
So, substitute the values of x = 6 and y = 8 in the expression x²+y²
⇒ 6²+8²
⇒ 36 + 64
⇒ 100
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Write the standard form of the equation of the circle with radius 8 and center (10,−7).
The equations that represent the circle having a with radius 8 and center (10,−7) are; (x - 10)² + (y + 7)² = 8²
What is the standard form of the equation of a circle?The standard form of the equation of a circle is (x - h)² + (y - k)² = r², where (h, k) is the center of the circle, and r is its radius.
We have given that circle having radius of 8 units. Thus, r = 8.
Since we know that circle having the center (10,−7).
Thus, the equation of the circle, with a radius of 8 units is;
(x - h)² + (y - k)² = r²
(x - 10)² + (y + 7)² = 8²
Thus, the equations that represent the circle having a with radius 8 and center (10,−7) are; (x - 10)² + (y + 7)² = 8²
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Some please tell me how to do this please and thank you
Answer:84
Step-by-step explanation:21x4=84
Is the following correct?
All of the justifications used to demonstrate the following angles, including the alternate interior theorem justification, are valid.
What is the alternate interior theorem?When a transversal intersects two parallel lines, alternate interior angles are created that are equal to the alternate pairs of those pairs.
The angles formed on the opposing sides of the transversal are known as alternate internal angles.
Angles of the same size that are found on opposing sides of the transversal line are known as alternate angles.
Angles that alternate are equal: By creating a Z form, we can easily identify interior alternate angles: Alternate angles come in two varieties: alternate internal angles and alternate exterior angles.
All the reasons are given to prove the following angles are correct including the reason for the alternate interior theorem.
Therefore, all of the justifications used to demonstrate the following angles, including the alternate interior theorem justification, are valid.
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Write the polynomial as the product of linear factors.
h(x) = x3 − 6x2 + 13x − 10
Answer:
h(x) = (x -2)(x -2+i)(x -2-i)
Step-by-step explanation:
You want the linear factorization of h(x) = x³ -6x² +13x -10.
FactorsA graphing calculator (attachment 2) shows the one positive real root is x = 2. This means (x-2) is a factor.
When we factor that out, we have a quadratic with no real roots. The vertex of its graph at (2, 1) tells us the roots of it are 2±√-1 = 2±i.
Each root p gives rise to a linear factor (x -p), so the factorization is ...
h(x) = (x -2)(x -2+i)(x -2-i)
__
Additional comment
The first attachment shows these factors multiply out to give the polynomial h(x).
<95141404393>
Jen Butler has been pricing Speed-Pass train fares for a group trip to New York. Three adults and four children must pay $96Two adults and three children must pay $68 Find the price of the adult's ticket and the price of a child's ticket.
After solving the equations we can conclude that each ticket for an adult costs $24 whereas each ticket for a child costs $6.
What are equations?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.
For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
So, 2 equations can be formed:
Let a be adults and c be children.
3a + 4c = 96 ...(1)
2a + 3c = 68 ...(2)
Now, take equation (1):
3a + 4c = 96
3a = 96 - 4c
a = 96 - 4c/3
Now, substitute a = 96 - 4c/3 in equation (2):
2a + 3c = 68
2(96 - 4c/3) + 3c = 68
96 - 4c/3 + 3c = 68/2
96 - 4c + 3c = 34*3
-c = 102 - 96
c = $6
Now, substitute c = 6 in equation (1):
3a + 4c = 96
3a + 4(6) = 96
3a + 24 = 96
3a = 96 - 24
3a = 72
a = 72/3
a = $24
Therefore, after solving the equations we can conclude that each ticket for an adult costs $24 whereas each ticket for a child costs $6.
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please help with this it is very important its a final
The members of a small town’s local arts council are selling raffle tickets. The art council decides that the top three raffle ticket sellers will share a portion of the profits. The second-place seller will receive twice as much as the third-place seller. The first-place seller will receive $20 more than the second-place seller. The profit portion they will share is $200
If there were a 4th place prize and that 4th place winner received half of what 3rd place received. How much is the 4th place prize?
The prize of the 4th place is 18
How to determine the prize of the 4th place?
Given:
1. The second-place seller will receive twice as much as the third-place seller
2. The first-place seller will receive $20 more than the second-place seller
3. The profit portion they will share is $200
Let S, T, F and V represent the prize of the second, third, first and fourth place respectively
Statement 1 can be written as:
S = 2T --- (1)
Statement 2 can be written as:
F = S + 20 --- (2)
Statement 3 can be written as:
F + S + T = 200 --- (3)
Substitute (1) and (2) into (3):
F + S + T = 200
(S+20) + 2T + T= 200
(2T+20) +2T + T= 200 (Since S = 2T)
2T+20 +2T + T= 200
5T + 20 = 200
5T = 200-20
5T = 180
T = 180/5
T = 36
Thus, the third-place seller prize is 36
Since the 4th place winner received half of what the 3rd place received. Thus:
V = 1/2 × T
V = 1/2 × 36
V = 18
Therefore, the 4th place prize is 18
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