The scores of students on a standardized test are normally distributed with a mean of 300 and a standard deviation of 40. (a) what proportion of scores lie between 220 and 380 points?
0.9544 = 95.44% of scores lie between 220 and 380 points.
Normal distribution problems can be solved using the Z-score formula.
With a set of means and standard deviations, the Z-score for measure X is given by: After finding the Z-score, look at the Z-score table to find the p-value associated with that Z-score. This p-value is the probability that the value of the measure is less than X. H. Percentile of X. Subtract 1 from the p-value to get the probability that the value of the measure is greater than X.
[tex]z = \frac{x - \mu}{\sigma} \,[/tex]
We are given mean 300, standard deviation 40.
This means that µ= 300, σ = 40
What proportion of scores lie between 220 and 380 points?
This is the p-value of Z when X = 380 subtracted by the p-value of Z when X = 220.
X = 380
[tex]z = \frac{x - \mu}{\sigma} \,[/tex]
Z= (380-300)/40
Z= 2
Z=2 has a p-value of 0.9772.
X=300
[tex]z = \frac{x - \mu}{\sigma} \,[/tex]
Z= (220-380)/40
Z=-2
Z=-2 has a p-value of 0.9772.
0,9772 - 0,0228 = 0,9544
0.9544 = 95.44% of scores lie between 220 and 380 points.
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A rhombus with horizontal diagonal length 25 millimeters and vertical diagonal length 8 millimeters. what is the area of the rhombus? 25 mm2 33 mm2 50 mm2 100 mm2
The area of the rhombus is 100 mm². The correct answer is D.
What is a rhombus?A rhombus is one type of parallelogram and has 4 sides and 4 vertices.
Every side is equal in length and opposite angles are equal.
Given:
A rhombus with horizontal diagonal length 25 millimeters,
and vertical diagonal length 8 millimeters.
Let d₁ = 25 mm and, d₂ = 8 mm.
Let A be the area of rhombus.
To find the area of rhomus:
Using diagonals,
A = (1/2) × d₁× d₂.
Substituting the values of diagonals,
A = 1/2 x 25 x 8
A = 200/2
A = 100 mm².
Therefore, 100 mm² is the area of the rhombus.
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If AB = 55, and BC = 49, find the length of the radius to the nearest tenth. Assume BC is tangent to Circle A.
Answer:
25.0
Step-by-step explanation:
Notice that points A, B, and C form a right triangle. This allows us to use the Pythagorean theorem, a^2 + b^2 = c^2, to find the missing side. AB is the hypotenuse, so substitute 55 for c, and BC is the leg, so substitute 49 into either a or b in the formula.
a^2 + b^2 = c^2
49^2 + b^2 = 55^2
b^2 = 3025 - 2401
b^2 = 624
b = sqrt (624)
b = 24.9799919936
A circle is shown. Points Q, U, A, D are on the circle. Lines connect the points to form a quadrilateral. Angle Q U A is 111 degrees. Arc Q U is 88 degrees.
What is the measure of Arc A U?
44°
50°
64°
92°
The measure of Arc AU of the given Circle Geometry is; 50°
How to find the measure of arc angle?The circle theorem we will apply to solve for the arc measure states that “Measure of angles subtended to any point on the circumference of the circle from the same arc is equal to half of the angle subtended at the center by the same arc.”
We can express the above theorem as;
Angle at the center = 2 × Angle at the circumference
From the attached image below and from the given statement in the question, we are given that; ∠QUA = 111°
Therefore, applying the circle theorem earlier quoted, we can say that; m∠QDA = 2 × ∠QUA
m∠QDA = 2 × 111° = 222°
Which gives;
∠QOA = = 360° - 222° = 138°
∠QOA = ∠QOU + ∠UOA (by angle addition property)
Thus;
∠QOA = 138° = 88° + ∠UOA
∠UOA = 138° - 88° = 50°
Thus, the measure of Arc AU is;
Arc AU = ∠UOA = 50°
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Answer: b
Step-by-step explanation:
A. 2
B. 1/3
C. 5
D. -3
Answer: 2
Step-by-step explanation:
[tex]y=\frac{1}{3}x^2 +2x+5 \longrightarrow \frac{dy}{dx}=\frac{2}{3}x+2[/tex]
Setting this equal to 0 yields [tex]x=-3[/tex].
When [tex]x=-3[/tex], [tex]y=2[/tex]
Answer:
A. 2Step-by-step explanation:
Given quadratic equation:
y = (1/3)x² + 2x + 5Its leading coefficient is positive, so it has minimum value at vertex.
The x-coordinate of the vertex is:
x = -b/(2a)Substitute the coefficients:
x = - 2/(2*1/3) = - 3Find the value of y at vertex:
y = (1/3)(-3)² + 2(- 3) + 5 = 3 - 6 + 5 = 2The matching answer choice is A.
Explain why the surface area of a right prism can be found using the formula
A = ph + 2B
where p = the perimeter of the base, h = height and B = the area of the base.
Answer:
ph : perimeter = 4 sides of the base; p*h = the area of the sides of that prism
B : 2 areas of the base = top and bottom
A right prism consists of a rectangle and two undersides S night prism =
S rectangle + 2S base
the length of the rectangle is the circumference of the base which is P so A = ph + 2B
Select the correct answer. which exponential equation is equivalent to this logarithmic equation?
logarithmic equation log x = 4 is given by- [tex]10^{4}[/tex] = x
What is logarithmic equation?
A logarithmic equation is an equation that involves the logarithm of an expression containing a variable. To solve exponential equations, first see whether you can write both sides of the equation as powers of the same number.The given logarithmic equation is;
[tex]log x = 4[/tex]
Since, log with base 10 is written as [tex]log x[/tex] simply, therefore, we have:
[tex]log_{10} x[/tex] = 4
Using the definition of logarithm, we get;
[tex]x = 10^{4}[/tex]
Equivalently, [tex]10^{4} = x[/tex]
Thus, the exponential equation out of the specified options that is equivalent to this logarithmic equation log x = 4 is given by- [tex]10^{4}[/tex] = x
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The complete question is -
Which exponential equation is equivalent to this logarithmic equation?
log x = 4
Given u = ⟨3, 2⟩, v = ⟨1, 5⟩, and the angle between the vectors is 45°, what is u · v?
We need to use a technique called dot multiplication. In this technique, we multiply the magnitude of two given vectors by the value of the angle between them.
In the question, the value of the angle between two vectors [tex]cos(45^0)[/tex] and the coordinates of the two vectors are given. Let's multiply them by the dot product to get the result.
Formula: [tex]u.v=|u||v|cos(a)[/tex]
[tex]u=3i+2j[/tex]
[tex]v=i+5j[/tex]
[tex]cos(a)=\frac{1}{\sqrt{2}}[/tex]
To find the magnitude of a vector, we square the coordinates, add them up and take the square root of the result.
[tex]Magnitude=\sqrt{x^2+y^2+z^2+...}[/tex]Result: [tex]u.v=|\sqrt{(3^2)+(2^2)}||\sqrt{(1^2)+(5^2)}|.\frac{1}{\sqrt{2}}=(13\sqrt{2})\frac{\sqrt{2}}{2} =13[/tex]
Kelsey has a list of possible functions. pick one of the g(x) functions below and then describe to kelsey the key features of g(x), including the end behavior, y-intercept, and zeros. g(x) = (x 2)(x − 1)(x − 2) g(x) = (x 3)(x 2)(x − 3) g(x) = (x 2)(x − 2)(x − 3) g(x) = (x 5)(x 2)(x − 5) g(x) = (x 7)(x 1)(x − 1)
Answer: (x) = x^3 − x^2 − 4x + 4End behavior- Falls to the left rises to the righty intercept-(0, 4)Zeros- (1,-2,2)g(x) = x^3 + 2x^2 − 9x − 18
Step-by-step explanation:
What are the x- and y- coordinates of point p on the directed line segment from k to j such that p is three-fifths the length of the line segment from k to j? x = (startfraction m over m n endfraction) (x 2 minus x 1) x 1 y = (startfraction m over m n endfraction) (y 2 minus y 1) y 1 (40, 96) (85, 105) (80, 104) (96, 72)
The coordinate of P is (A) ( 40, 96).
What are coordinates?Coordinates are two integers (Cartesian coordinates) or a letter and a number that point to a specific place on a grid known as a coordinate plane. A coordinate plane has four quadrants and two axes: x (horizontal) and y (vertical) (vertical).To find What are the x- and y- coordinates of point p on the directed line segment from K to J:
It can be seen from the figure the coordinates of K and J:
K ( 160 ,120) and J (-40 , 80)The coordinates of P can be determined as:
[tex]x=\frac{m}{m+n} (x_{2}-x_{1})+x_{1} } \\y=\frac{m}{m+n} (y_{2}-y_{1})+y_{1} } \\[/tex]
So, as the P point divides the line into three-fifths of the length,
KP = (3/5)KJ JP = (2/5) KJWhich gives the ratio as 3: 2.
m:n = 3:2
x = (3/5) (-40 -160) + (160)x = 40y = ( 3/5)(-40) +120y = 96Therefore, the coordinate of P is (A) ( 40, 96).
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The complete question is shown below:
What are the x- and y- coordinates of point P on the directed line segment from K to J such that P is Three-fifths the length of the line segment from K to J?
x = (StartFraction m Over m + n EndFraction) (x 2 minus x 1) + x 1
y = (StartFraction m Over m + n EndFraction) (y 2 minus y 1) + y 1
(A) (40, 96)
(B) (85, 105)
(C) (80, 104)
(D) (96, 72)
On a zip-line course, you are harnessed to a
cable that travels through the treetops. You
start at platform A and zip to each of the other
platforms. How far do you travel from Platform
B to Platform C?
Using the distance between two points, it is found that you travel approximately 41 meters.
What is the distance between two points?Suppose that we have two points, [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The distance between them is given by:
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
In this problem, we have that:
The coordinates of B are (-25,-25).The coordinates of C are (-15,15).Hence the distance is:
D = sqrt[(-15 - (-25))² + (15 - (-25))²] = sqrt(10² + 40²) = 41 meters.
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Graph and label each cell phone plan as accurately as possible. You need a ruler or straight edge
See attachment for the graph of cell phone plan 1: y= 7.5x and cell phone plan 2: y= 5.5x + 10.1
What are linear equations?Linear equations are equations that have constant average rates of change, slope or gradient
How to graph and label each cell phone plan?The cell phone plans are given as:
Cell phone plan 1: y= 7.5x
Cell phone plan 2: y= 5.5x + 10.1
To plot the graph of both plans, we make use of the following domain for both cell phone plans
Domain: x >= 0
Next, we set x = 0, 1, 2, 3, 4 and 5 for both plans
So, we have:
Cell phone plan 1
y= 7.5x
When x = 0, y = 7.5 * 0 = 0
When x = 1, y = 7.5 * 1 = 7.5
When x = 2, y = 7.5 * 2 = 15
When x = 3, y = 7.5 * 3 = 22.5
When x = 4, y = 7.5 * 4 = 30
When x = 5, y = 7.5 * 5 = 37.5
Cell phone plan 2
y= 5.5x + 10.1
When x = 0, y = 5.5*0 + 10.1 = 10.1
When x = 1, y = 5.5 * 1 + 10.1 = 15.6
When x = 2, y = 5.5 * 2 + 10.1 = 21.1
When x = 3, y = 5.5 * 3 + 10.1 = 26.6
When x = 4, y = 5.5 * 4 + 10.1 = 32.1
When x = 5, y = 5.5 * 5 + 10.1= 37.6
Next, we plot both graphs on the domain x >= 0
See attachment for the graph of cell phone plan 1: y= 7.5x and cell phone plan 2: y= 5.5x + 10.1
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The graph shows two lines, A and B:
A graph is shown with x and y axes labeled from 0 to 6 at increments of 1. A straight line labeled A joins the ordered pair 2, 6 with the ordered pair 5, 0. Another straight line labeled B joins the ordered pair 0, 2 with the ordered pair 6, 6.
Based on the graph, which statement is correct about the solution to the system of equations for lines A and B?
(3, 4) is the solution to both lines A and B.
(3, 4) is the solution to line A but not to line B.
(0, 2) is the solution to both lines A and B.
(0, 2) is the solution to line A but not to line B.
Answer:
Part A) The system has one solution
Part B) The solution is the point (4,4)
i believe
what are the zeros of the function g(x)=x^2+3x-4
The zeroes of the function g(x) = x² +3x -4 as given in the task content is; x = -4 and x = 1.
What are the zeroes of the function given g(x) as represented in the task content?It follows from the task content that the function g(x) given in the task content is; g(x) = x² +3x -4.
On this note, it follows that the zeroes of the function can be determined by solving the quadratic function as follows;
x² +4x -x -4 = 0
(x+4) (x-1) = 0
Ultimately, it can be concluded that the values of x which represents the zeroes of the function are; x = -4 and x = 1.
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Write a series of instructions that will multiply eax by 18, using a combination of shift, mov, and add instructions
MOV EBX,EAX
SHL EAX,4
SHL EBX,1
ADD EAX,EBX these are the series of instructions that will multiply eax by 18, using a combination of shift, mov, and add instructions.
STEPS:
1. Copy EAX into another register, say EBX
2. We know that shift left by 'n' bits results in multiplication with 2^'n' , so perform shift left operation of EAX by 4 bits ( results in multiplication of EAX with 16) and perform shift left operation of EBX by 2 bits(results in multiplication of EBX with 2)
3. Now add EAX and EBX which is the required answer ( Since, i*16 + i*2 equals to i*18 )
INSTRUCTIONS:
mov ebx,eax ; make copy
shl eax,4 ; eax * 16
shl ebx,1 ; ebx * 2
add eax,ebx ; answer
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Question 1 (essay worth 4 points) (h2.02 mc) the cost of attending an amusement park is $15 for children and $40 for adults. on a particular day, the attendance at the amusement park is 5,000 attendees, and the total money earned by the park is $100,000. use the given matrix equation to solve for the number of children’s tickets sold. explain the steps that you took to solve this problem. a matrix with 2 rows and 2 columns, where row 1 is 1 and 1 and row 2 is 15 and 40, is multiplied by matrix with 2 rows and 1 column, where row 1 is c and row 2 is a, equals a matrix with 2 rows and 1 column, where row 1 is 5,000 and row 2 is 100,000.
Using a system of equations, it is found that there were 4,000 children tickets sold.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
For this problem, the variables are given by:
Variable x: Number of children tickets sold.Variable y: Number of adult tickets sold.The attendance at the amusement park is 5,000 attendees, hence:
x + y = 5000 -> y = 5000 - x.
Considering the cost of parking and that the total money earned by the park is $100,000, we have that:
15x + 40y = 100000
Applying the multiplication of the matrices, these equations are the same that the system gives. Replacing the second equation into the first:
15x + 40(5000 - x) = 100000
25x = 100000
x = 100000/25
x = 4000.
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10 Points !!!!!!!!!!!
Using proportions, the length of x is of 2.9.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
The triangles are similar, that is, they have the same angles, hence the corresponding sides are proportional, by the following rule of three:
x/7 = 5/12
Applying cross multiplication:
12x = 35
x = 35/12
x = 2.9.
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An Escalator Moves At The Rate Of 2 Feet Per Second. At What Rate Does The Escalator Move In Miles Per Hour?
A)0.02 mph
B)0.34 mph
C)0.68 mph
D)1.36 mph
Answer:
1.36mph
Step-by-step explanation:
The escalator is moving at 2ft/s, lets convert this to miles/second.
2ft/s = 0.000378788miles/s.
Now that we have the miles/second lets multiply this value by 3600 to get the miles/h, because there are 3600 seconds in an hour.
2ft/s=1.3636368miles/h
Or approximately 1.36miles/h.
Ken can run m miles at a
pace of 6.30 minutes per
mile. He ran slower for 10
minutes to warm up.
Write an equation that
represents the total time,
t, Ken spent running.
Equation that represents the total time t (in minutes) Ken spent running is = 10 + m/6.30.
In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign = The word equation and its cognates in other languages may have subtly different meanings; for example, in French an équation is defined as containing one or more variables, while in English, any well-formed formula consisting of two expressions related with an equals sign is an equation
How to solve such time related questions?
The key concept for solving such questions is the relationship between speed, distance and time.
The relationship between them is Distance = Speed x Time
Total time t (in minutes) =Initial Time + distance/speed
Given :-
Distance = mSpeed = 6.30 miles per hourInitial Time = 10 minThus,
t = 10 + m/6.30.
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Using the hsd test, if there are 16 df associated with mswithin, and α=0. 05 and the number of groups = 3, qcrit = _________
Using the hsd test qcrit = 3.65
HSD testis used to check differences among sample way for significance. The Tukey's HSD assessments all pairwise variations at the same time as controlling the probability of making one or greater type I errors.
A Tukey-Kramer test lets us check the null speculation of no distinction between the population approach for all pairs of businesses. The Tukey-Kramer check (also known as a Tukey sincere importance test, or Tukey HSD), is carried out in R inside the function.
solution
given;
using HSD test, the degree of freedom = 16
and α=0. 05
groups = 3
Hence, Qcrit = 3.65 {using HSD table}
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What is the volume of the pyramid
Answer:
Option A - 32 cm³
Step-by-step explanation:
Volume of a pyramid is given by the formula :
V = [tex]\frac{lwh}{3}[/tex]
Substituting values given gives us :
V = (4)(4)(6)/3
V = (16)(6)/3
V = 96/3
V = 32
Units will be cm³ as this is volume
Hope this helped and have a good day
Answer:
A. 32 cm³
Step-by-step explanation:
V = (1/3)(area of base)(height)
The base is a square of side 4 cm.
area of base = side × side
V = (1/3)(4 cm × 4 cm)(6 cm)
V = 32 cm³
pls help summer hw hurts my brain
Answer:
1) (3,1)
2) (4,1)
3) No solution
Step-by-step explanation:
The solution is point where the graphs cross. It is a little hard to see the pictures, but I think that I have the right ordered pairs. The ordered pairs are in the order (x,y). The x tells you how far (in these cases), the point is right of the origin (0,0 the middle of the whole graph). The y tells us (in these cases) how high the point is from the origin (0,0).
The last answer has no solution because the lines are parallel and they do not cross.
The number has over positive integer divisors. One of them is chosen at random. What is the probability that it is odd
The number has over positive integer divisors. One of them is chosen at random. If each divisor has the same probability, then the likelihood that a random one will be odd is precisely 1/19. This assumes that all divisors have the same probability. This is further explained below.
What is the probability that it is odd?Generally, The possibility of an occurrence may be quantified using the concept of probability. There are many occurrences that cannot be foreseen with complete accuracy.
In conclusion, The number may be divided into more than positive integers. A selection is made at random from among them. If each divisor has the same probability, then the chance that a random one would be odd is exactly 1/19. This assumes that each divisor has the same probability. This makes the assumption that the probability of each divisor is the same.
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NEED URGENT HELP: A random sample is taken of people who have bought tickets for a concert. In the sample, 21 out of 150 people say they will contribute $5.00 each towards a music scholarship for a local high school students. If 3,500 people bought concert tickets, predict how much will be raised for the scholarship.
Answer:
$2,450
Step-by-step explanation:
21:150 is the ratio of people who will donate $5.
21:150 / 3 = 7:50
7:50 x 2 = 14:100
14:100 = 21:50
14:100 x 35 = 490:3500
490 out of 3500 people will contribute $5.
490 x 5 = $2,450
I don’t understand why I got my answer wrong
The correct function that has been represented on the graph is,
f(x) = { 2 if -1 < x ≤ 2 as the values of f(x) for the other two parts, -6 ≤ x ≤ -1 and 2 ∠ x ≤ 6 are (2x+17)/5 and (16-7x)/2 respectively.
This can be broken into three parts :
-6 ≤ x ≤ -1-1 ∠ x ≤ 2 2 ∠ x ≤ 6In the first fragment two clearly visible points are (-1,3) and (-6,1). Thus the straight line can be easily drawn with equation [tex]\frac{y-3}{x+1} = \frac{3-1}{-1+6}[/tex]y-3/x+1 = 2/5
5y -15 = 2x +2
2x - 5y = -17
The second part is quite clear, the equation is y =2 (straight line parallel to x - axis)The third part two clearly visible points are (2,1) and (4,-6). Thus the straight line can be easily drawn with equation [tex]\frac{y-1}{x-2} = \frac{1+6}{2-4}[/tex]y-1/x-2 = -7/2
2y -2 = -7x + 14
2y + 7x = 16
Thus function becomes
2x - 5y = -17 for -6 ≤ x ≤ -1 y =2 for -1 ∠ x ≤ 2 2y + 7x = 16 for 2 ∠ x≤ 6Learn more about Straight lines here :
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-5/208 + 4/7 + -3/4. Please answer my question as soon as possible. Thanks!
Answer:
[tex] - 0.2026[/tex]
Step-by-step explanation:
I hope it is the right answer
Need help with my math please. 31-41.
Answer:
31: 98,765 x 9 + 3 = 888,888
32: 12.345 x 9 + 6 = 111,111
33: 3,367 x 15 = 50,505
34: 15,873 x 35 = 555,555
35: 33,334 x 33,334 = 1,111,155,556
36: 11,111 x 11,111 = 123,454,321
You skipped 37-39
40: 3 + 9 + 27 + 81 + 243 = 3(243-1)/2
41: 1/2 + 1/4 + 1/8 + 1/16 + 1/32 = 1 - 1/32
Step-by-step explanation:
It's just patterns bro
Howard buys 6 plants if same price from a flower shop for $640 including the shipping fee. If the shipping fee is $100, find the price of each plant.
3. What are the solutions to the system of equations graphed below?
Answer:
(-1, 5) and (3, -3)
Step-by-step explanation:
The solutions are all the points where the two functions intersect. Since the lines intersect at two different points, there are two solutions.
The two points at which the functions appear to intersect are (-1, 5) and (3, -3).
Pls answerrrrrrrrrrr