The mean of the exam score is 65.56
The given exam data is as follows;
Possible Score range ----------- frequency (f) -------- score (x) -----------(fx)
40 - 50 ------------------------- 21 ------------------- -----45 -------------- 945
50 - 60 --------------------------- 39------------------------55 ---------------2145
60 - 70 ----------------------------- 40---------------------- 65 ---------------- 2600
70 - 80 ------------------------------ 34 --------------------- 75 ----------------- 2550
80 - 90 ------------------------------ 28 --------------------- 85 ---------------- 2380
Note:[tex]score (x) = \frac{sum \ of \ the \ range }{2} , \ example \ \frac{40+49.99}{2} \approx 45[/tex]
The sum of the frequency (f) = 162
The sum of fx, ∑fx = 10620
The mean of the exam score:
[tex]\bar x = \frac{\Sigma fx }{\Sigma f} = \frac{10620}{162} = 65.56[/tex]
Therefore, the mean of the exam score is 65.56
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You are dealt one card from a standard 52-card deck. Find the probability of being dealt a diamond
The probability would be 1/52, since there are only 1 two of diamonds in all 52 cards.
Final answer. 1/52 or 1.92%
Answer:
13/52
Step-by-step explanation:
a standard 52-card deck has 13 diamond cards (1,2,3,4,5,6,7,8,9,10,J,Q,K)
P(diamond) = number of diamonds/number of cards in a deck = 13/52
Evaluate f(x) when x= 6.
f(x)= {6x^2 +2 if 6 < x <9
12 if 9
6
12
74
218
Answer:
If i am not wrong the answer is 12
how many terms are there in the series. 201.208.215......319
Answer:
222
Step-by-step explanation:
add 7 no. to each of like 201+7 = 208, 208+7=215 ,215+7=222
52 POINTS I need help!
Question 1
The vertex form of the equation of a vertical parabola is given by
, where (h, k) is the vertex of the parabola and the absolute value of p is the distance from the vertex to the focus, which is also the distance from the vertex to the directrix. You will use the GeoGebra geometry tool to create a vertical parabola and write the vertex form of its equation. Open GeoGebra, and complete each step below. If you need help, follow these instructions for using GeoGebra.
Part A
Mark the focus of the parabola you are going to create at F(6, 4). Draw a horizontal line that is 6 units below the focus. This line will be the directrix of your parabola. What is the equation of the line?
Part B
Construct the line that is perpendicular to the directrix and passes through the focus. This line will be the axis of symmetry of the parabola. What are the coordinates of the point of intersection, A, of the axis of symmetry and the directrix of the parabola?
Part C
Explain how you can locate the vertex, V, of the parabola with the given focus and directrix. Write the coordinates of the vertex.
Part D
Which way will the parabola open? Explain.
Part E
How can you find the value of p? Is the value of p for your parabola positive or negative? Explain.
Part F
What is the value of p for your parabola?
Part G
Based on your responses to parts C and E above, write the equation of the parabola in vertex form. Show your work.
Part H
Construct the parabola using the parabola tool in GeoGebra. Take a screenshot of your work, save it, and insert the image below.
Part I
Once you have constructed the parabola, use GeoGebra to display its equation. In the space below, rearrange the equation of the parabola shown in GeoGebra, and check whether it matches the equation in the vertex form that you wrote in part G. Show your work.
Part J
To practice writing the equations of vertical parabolas, write the equations of these parabolas in vertex form:
focus at (-5, -3), and directrix y = -6
focus at (10, -4), and directrix y = 6.
Answer:
Step-by-step explanation:
A. Directrix: y = 4-6 = -2
:::::
B. Axis of symmetry: x = 6
Axis of symmetry intersects directrix at (6,-2)
:::::
C . Vertex is halfway between focus and directrix, at (6,1)
:::::
D. The focus lies above the directrix, so the parabola opens upwards.
:::::
E. Focal length p = 1/(4×0.5)
:::::
F. p = 0.5
::::
G. y = 0.5(x-6)² + 1
Answer:
the one above is correct
Step-by-step explanation:
h.We start with a circle and a line that goes through the center of the circle (C) and one vertex of the triangle (E).
Using the point on the line opposite the vertex as a center (D), we draw an arc with the same radius the circle has.
The two points of intersection with the circle are the other two vertices of the inscribed triangle (F, G).
d = 3.2(t+1)(2t - 3)
An air pump increases the oxygen levels in
an aquarium and reduces the build-up of
waste materials. The equation shown above
gives the depth, d, in inches of an air
bubble beneath the surface of the water t
seconds after it emerges from the air pump.
After how many seconds does the air
bubble reach the surface?
Answer:
3/2=1.5 sec
Step-by-step explanation:
Equate d=0 and solve the expression, t=-1 and 3/2 but t can't be negative.
The air bubble will reach the surface in 1.5 seconds.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.
The given expression is d = 3.2(t+1)(2t - 3) where d is the height of the aquarium and t is the time taken by the bubbles to come to the surface.
When the bubble will come to the surface height D becomes zero.
d = 3.2(t+1)(2t - 3)
3.2(t+1)(2t - 3) = 0
t + 1 = 0 and 2t - 3 = 0
t = -1 and t = 3 / 2 = 1.5
Therefore, the air bubble will reach the surface in 1.5 seconds.
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The height (in meters) of a shot cannonball follows a trajectory given by h(t) = -4.9t^2 + 14t - 0.4 at time t (in seconds). As an improper fraction, for how long is the cannonball above a height of 6 meters? Please show steps. Thank you!
Find the volume of this object.
Use 3 for a
Volume of a Cylinder
V=77r2h
Volume of a Cone
V= r2h
3
8 in
4 in-
13 in
V~ [?]in3
Help
Answer:
[tex]532 cm^{2}[/tex]
Step-by-step explanation:
line I is parallel to line m. if the measure of line 6 is 75 what is the measure of line <4
Answer:
75
Step-by-step explanation:
If the two angles are complementary, find the measure of each of angle.
Answer:
D 40 and 50
Step-by-step explanation:
Complimentary angles are equal to 90
Answer: D, 40 and 50
Steps:
1. Since complementary angles equal 90 degrees, 4r + 5r = 90
2. 4r + 5r is 9r
3. This makes the equation, 9r=90
4. Divide both sides by 9, and then you get r=10
5. Substitute r=10 into 4r and 5r
6. This should make 4(10) and 5(10)
7. Multiply and then get 40 and 50
Aliza is drawing a model of the community swimming pool on grid paper. Each square on the grid is 20 feet by 20
feet.
Answer:
640 feet
Step-by-step explanation:
Count the length of each side. Add the lengths. Multiply by 20.
Start at the top left corner.
6 across
2 down
3 across
3 down
3 across
2 down
6 across
7 up
total = 32
32 X 20 = 640
(2 + i)-(4 - 6/)(-3 +3/)
Answer:
C
Step-by-step explanation:
(2+i)-(4-6i)(-3+3i)
=(2+i)-(-12+12i+18i-18i^2)
=(2+i)-[-12+30i-18(-1)]
=(2+i)-(-12+30i+18)
=(2+i)-(30i+6)
=2+i-30i-6
=-4-29i
Find the tangent line equations for the given functions at the given point(s): f(x) = tan x + 9 sin x at (π, 0)
Answer:
[tex]{ \bf{f(x) = \tan x + 9 \sin x }}[/tex]
For gradient, differentiate f(x):
[tex]{ \tt{ \frac{dy}{dx} = { \sec }^{2}x + 9 \cos x }}[/tex]
Substitute for x as π:
[tex]{ \tt{gradient = { \sec }^{2} \pi + 9 \cos(\pi ) }} \\ { \tt{gradient = - 8 }}[/tex]
Gradient of tangent = -8
[tex]{ \bf{y =mx + b }} \\ { \tt{0 = ( - 8\pi) + b}} \\ { \tt{b = 8\pi}} \\ y - intercept = 8\pi[/tex]
Equation of tangent:
[tex]{ \boxed{ \bf{y = - 8x + 8\pi}}}[/tex]
Which set of statements explains how to plot a point at the location (Negative 3 and one-half, negative 2)?
A: Start at the origin. Move 3 and one-half units right because the x-coordinate is Negative 3 and one-half. Negative 3 and one-half is between 3 and 4. Move 2 units down because the y-coordinate is -2.
B: Start at the origin. Move 3 and one-half units down because the x-coordinate is Negative 3 and one-half. Negative 3 and one-half is between -3 and -4. Move 2 units left because the y-coordinate is -2.
C: Start at the origin. Move 3 and one-half units down because the x-coordinate is Negative 3 and one-half. Negative 3 and one-half is between -3 and -4. Move 2 units right because the y-coordinate is -2.
D: Start at the origin. Move 3 and one-half units left because the x-coordinate is Negative 3 and one-half. Negative 3 and one-half is between -3 and -4. Move 2 units down because the y-coordinate is -2.
Answer:
D: Start at the origin. Move 3 and one-half units left because the x-coordinate is Negative 3 and one-half. Negative 3 and one-half is between -3 and -4. Move 2 units down because the y-coordinate is -2.
surface areas of two similar figures are given. the volume of the larger figure is given. find the volume of the smaller figure
9514 1404 393
Answer:
216 in³
Step-by-step explanation:
The ratio of volumes is the 3/2 power of the ratio of areas.
small volume = ((small area)/(large area))^(3/2) × (large volume)
= (212/1325)^(3/2) × 3375 in³ = (4/25)^(3/2) × 3375 in³ = (8/125)×3375 in³
small volume = 216 in³
Suppose you know the population average wage in the manufacturing industry in California is $24.66 per hour. You take a survey 30 people that work in manufacturing in Utah to answer the following research question. Is the population average manufacturing wage in Utah less than $24.66 per hour, the population average manufacturing wage in the California?
Answer:
Yes
Step-by-step explanation:
Given:
Number of people (n) = 30
Mean wage in california = 24.66
Incomplete information;
Sample mean =23.41
Standard deviation = 2.35
Yes, the population average manufacturing wage in Utah less than $24.66 per hour, the population average manufacturing wage in the California
I need help pls help me in geometry homework
Find the missing length Indicated
Answer:
60
Step-by-step explanation:
x² = 144×25
= 3600
x =√3600 =60
Talerie has a bathtub that she needs to fill with wa-
ter to fill the tub, she first needs to fill a bucket
with water and then dump this into the bathtub. If
the bucket is a cylinder with a radius of 6 in, and a
height of 12 in, how many buckets will it take to
fill the 5 ft. x3 ft. x3 ft. tub?
a 50 buckets
B. 48 buckets
C. 57 buckets
D. 62 buckets
Answer:
áedw
Step-by-step explanation:
đá
Solve - 2x - 7 > X+ 8.
O A. x<-3
O B. x<-5
O C. x>-5
O D. x>-3
Answer:
x < -5
Step-by-step explanation:
- 2x - 7 > x+ 8
Add 2x to each side
- 2x+2x - 7 > x+2x+ 8
-7 > 3x+8
Subtract 8 from each side
-7-8 > 3x+8-8
-15 > 3x
Divide by 3
-15/3 > 3x/3
-5 >x
x < -5
Simplify: 4- (3 1)2 - 6 2 4 2. Combine like terms: 7x3 2x - 5x2 6 x 9 3x3 12x2 3. Simplify: (2x5- ... Multiply: 3x2(4x3 - 2x2 7x - 4) 5. Evaluate: 6x2 ...
Answer:
The complete question is defined in the attached file please find it.
Step-by-step explanation:
For question 1:
[tex]\to 4-(3+1)^2 - 6\div 2 +4 \\\\\to 4-(4)^2 - 6\div 2 +4\\\\\to 4-16 - 3 +4\\\\\to 4-19 +4\\\\\to 4-15\\\\\to -11[/tex]
For question 2:
[tex]\to 7x^3 +2x -5x^2+6+ x+ 9+ 3x^3 +12x^2 \\\\\to 7x^3 +3x^3+12x^2 -5x^2+2x+x+9+6 \\\\\to 10x^3 +7x^2+3x+15 \\\\[/tex]
For question 3:
[tex]\to (2x^5- 3x^2+4)-(x^5+2x^2+7)\\\\\to 2x^5- 3x^2+4-x^5-2x^2-7\\\\\to x^5- 5x^2-3\\\\[/tex]
For question 4:
[tex]\to 3x^2(4x^3- 2x^2+7x -4) \\\\\to 12x^5- 6x^4+21x^3 -12x^2 \\\\[/tex]
For question 5:
[tex]\to 6x^2+9x-7 \ \ \text{when} \ \ x=2\\\\\to 6(2)^2+9(2)-7 \\\\\to 6(4)+9(2)-7 \\\\\to 24+18-7 \\\\\to 24+11 \\\\\to 35[/tex]
Does the point (9, 0) satisfy the equation y = 9x2 + x + 9?
many ® Black pencils cost N75 each and coloured pencils cost N105 each. If 24 mixed pencils cost #2010, how of them were black? (Hint: Let there be x black pencils. Thus there are 24 - x) coloured pencils.)
Answer:
85
Step-by-step explanation:
I hope my answer help you
Find the area of the shaded regions: the green is the shaded area
PLS HELP ME!!!! I NEED THE ANSWER BY THIS EVENING CUZ I HAVE RSM TOMORROW. PLS HELP!!!!!
Answer:
the green area stands for the safe operation space
Step-by-step explanation:
u say b×h meaning say 80degrees ×9cm which is 720..
Find the area of the trapezoid below in square centimeters (cm). The area of the trapezoid is
square centimeters. Enter the answer as decimal number
14 cm
8 cm
7 cm
8 cm
21 cm
The solution is
Answer:
122.5
Step-by-step explanation:
Use the area formula for a trapezoid (attached below as an image):
A = area in sq cm
a = top base
b = bottom base
h = height
Correspond the correct values with the variables:
a = 14
b = 21
h = 7
A = 1/2 * (14 + 21) * 7
A = 1/2*(35)*7
A = 17.5 * 7
A = 122.5 sq cm
Hope this helps (●'◡'●)
help: Write as a polynomial: 7b(4c - b) + 4c(c - 7b)
Answer:
i think its 7b^2+4c^2 ?
Step-by-step explana
The radius of a sphere is 6 units.
Which expression represents the volume of the sphere,
in cubic units?
이 (6)
○ (6)
이 (12)
ㅇ (12)
Answer:
B. ⁴/3π(6)³
Step-by-step explanation:
Formula for volume of a sphere = ⁴/3πr³
Where,
radius (r) = 6 units
Plug in the given value into the volume formula
Volume of the sphere = ⁴/3 × π × (6)³
Volume of the sphere = ⁴/3π(6)³
The expression that represents the volume of the given sphere is therefore ⁴/3π(6)³ cubic units.
The expression for the volume of the sphere is:
V = (4/3)*3.14*(6)^3
Which expression represents the volume?
For a sphere of radius R. the volume is given by:
V = (4/3)*pi*R^3
Where pi = 3.14
Here we know that the radius is 6 units, so we can write the volume as:
V = (4/3)*3.14*(6)^3
As you can see, the second option (counting from the top) is the correct one.
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[tex]\lim_{x \to \4} x^{2} -3x[/tex]
(4)^2-3(4)=4Answer:
Step-by-step explanation:
1 + 1 = 3 is this right
Answer:
1 + 1 = 3 - 1 = 2
Step-by-step explanation:
Im Smart
Jarvis invested some money at 6% interest. Jarvis also invested $58 more than 3 times that amount at 9%. How much is invested at each rate if Jarvis receives $1097.19 in interest after one year? (Round to two decimal places if necessary.)
Use the variables x and y to set up a system of equations to solve the given problem.
9514 1404 393
Answer:
$3309 at 6%$9985 at 9%Step-by-step explanation:
Let x and y represent amounts invested at 6% and 9%, respectively.
y = 3x +58 . . . . . . . the amount invested at 9%
0.06x +0.09y = 1097.19 . . . . . . total interest earned
__
Substituting for y, we have ...
0.06x +0.09(3x +58) = 1097.19
0.33x + 5.22 = 1097.19 . . . . . . . . . simplify
0.33x = 1091.97 . . . . . . . . . . . . subtract 5.22
x = 3309 . . . . . . . . . . . . . . . . divide by 0.33
y = 3(3309) +58 = 9985
$3309 is invested at 6%; $9985 is invested at 9%.
Type your answer into the box. X 30° Calculate the size of angle x. angle x =
Answer:
x = 60°Step-by-step explanation:
We know:
All triangles have internal angles that add up to 180°.
And
All right triangles have acute angles that up to 90°.
Therefore
x + 30° + 90° = 180°
x + 120° = 180° |subtract 120° from both sides
x + 120° - 120° = 180° - 120°
x = 60°orx + 30° = 90° |subtract 30° from both sides
x + 30° - 30° = 90° - 30°
x = 60°The size of angle x will be 60°
TriangleIt is a plane figure with three straight sides and three angles.
What are steps to solve this problem?The steps are as follow:
As per rule of triangle, the sum of all three internal angle must be equal to 180°The given triangle is right angle triangle having one angle 30° and other we have to findGiven:z = 90°
y = 30°
x = ?
∴ x + y + z = 180°
∴ x + 30 + 90 = 180
∴ x + 120 = 180
∴ x = 60°
So the size of angle x will be 60°
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