Thus an approximate 95% confidence interval for the average enrollment of all 60,000 faculty members in the two years prior to the survey. which implies that the given statement is true.
According to the statement
Average sample =3700
SD sample =6500
Sample size =400
EV average =3700
SE average =325
Population size =3000
The boundaries of the 68% confidence interval are then 1 standard error from the estimated average:
EV average+1⋅SE average =3700+1⋅325=3700+325=4025
EV average−1⋅SE average =3700−1⋅325=3700−325=3375
Thus an approximate 95% confidence interval for the average enrollment of all 60,000 faculty members in the two years prior to the survey. which implies that the given statement is true.
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A rectangle is divided into two equal parts and a circle is divided into four parts and a circle is divided into four equal parts. One part of rectangle is shaded.
How many parts of the circle should be shaded so that both the figures have the same fraction shaded?(1 Point)
Answer:
2 parts
Step-by-step explanation:
The rectangle has a 1/2 ratio, because there are 4 parts of the circle, you will shade 2. This is because 2/4 ratio is simplified to 1/2.
Given the circle below, find QR.
Answer:
QR=17
Step-by-step explanation:
[tex](12)(x-2)=(3)(3x-1)\\12x-24=9x-3\\3x-24=-3\\3x=21\\x=7[/tex]
[tex]x=7\\\\QR=12+x-2\\=12+(7)-2\\QR=17[/tex]
A store sells 7 different types of envelopes and 6 different types of postage stamps. How many different combinations are tehre to buy an envelope and stamp?
You can by 42 combinations of items from the store
How to determine the number of combination?The given parameters are:
Envelop = 7
Stamp = 6
The number of combination is:
Combination = Envelop * Stamp
So, we have:
Combination = 7 * 6
Evaluate
Combination = 42
Hence, you can by 42 combinations of items from the store
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12. a) Solve the following|x-1|<2.
Work Shown:
| x-1 | < 2
-2 < x-1 < 2 ... see note1 below
-2+1 < x-1+1 < 2+1 ... see note2
-1 < x < 3
Note1: use the rule that |x| < k turns into -k < x < k for some positive real number k.Note2: Add 1 to all sides to isolate x30. For the following exercises, given each set of information, find a linear equation satisfying the conditions, if possible.
30. f(-5) = -4, and f(5) = 2
Answer:
The required linear equation satisfying the given conditions f(-5)=-4 and f(5)=2 is
[tex]$$y=\frac{3}{5} x-1$$[/tex]
Step-by-step explanation:
It is given that f(-5)=-4 and f(5)=2. It is required to find out a linear equation satisfying the conditions f(-5)=-4 and f(5)=2. To find it out, first, represent the given conditions in the form of points and then find the slope of a line passing through these two given points. Then consider one of the points to give the linear equation of the line in the form [tex]$\left(y-y_{2}\right)=m\left(x-x_{2}\right)$[/tex]
Step 1 of 4
Observe, f(-5)=-4 gives the point (5,-4)
And f(5)=2 gives the point (5,2)
This means that the function f(x) satisfies the points (-5,-4) and (5,2).
Step 2 of 4
Now find out the slope of a line passing through the points (-5,-4) and (5,2).
[tex]$$\begin{aligned}m &=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\m &=\frac{2-(-4)}{5-(-5)} \\m &=\frac{2+4}{5+5} \\m &=\frac{6}{10} \\m &=\frac{3}{5}\end{aligned}$$[/tex]
Step 3 of 4
Now use the slope [tex]$m=\frac{3}{5}$[/tex] and use one of the two given points and write the equation in point-slope form:
[tex]$$\left(y-y_{2}\right)=m\left(x-x_{2}\right)$$\\ $$(y-2)=\frac{3}{5}(x-5)$$[/tex]
Distribute [tex]$\frac{3}{5}$[/tex],
[tex]$$\begin{aligned}&y-2=\frac{3}{5} x-\frac{3}{5} \times 5 \\&y-2=\frac{3}{5} x-3\end{aligned}$$[/tex]
Step 4 of 4
This linear function can be written in the slope-intercept form by adding 2 on both sides, [tex]$y-2+2=\frac{3}{5} x-3+2$[/tex]
[tex]$$y=\frac{3}{5} x-1$$[/tex]
So, this is the required linear equation.
I need the answer for number 8
Answer:
Step-by-step explanation:
I'm going to assume you want it to be a perfect triangle, so then we would have the equation 4x=24. So we can divide each side by 4 to get rid of the 4 and get x by itself. So 24/4= 5. So x=5
Aurora is planning to participate in an event at her school's field day that requires her to complete tasks at various stations in the fastest time possible. To prepare for the event, she is practicing and keeping track of her time to complete each station.
The x-coordinate is the station number, and the y-coordinate is the time in minutes since the start of the race that she completed the task.
(1, 3), (2, 6), (3, 12), (4, 24)
Part A: Is this data modeling an arithmetic sequence or a geometric sequence? Explain your answer. (2 points)
Part B: Use a recursive formula to determine the time she will complete station 5. Show your work. (4 points)
Part C: Use an explicit formula to find the time she will complete the 9th station. Show your work. (4 points)
The data is modeling a geometric sequence because they have a common ratio of 2.
Calculations and ParametersThe recursive formula to determine the time she will complete station 5
f(n)=f(n-1)*rf(n)=f(5-1)*2f(n)=f(4)*2f(n)=(24)2f(n)= 48Part C:
The explicit formula to find the time she will complete the 9th station.
f(n)=f(1)*r^n-1f(n)=3*2^8-1f(n)=3*2^7f(n)=3*128f(n)=384Read more about recursive formula here:
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Which equation represents a line that passes through (2,-) and has a slope of 3?
Oy - 2 = 3(x+2)
Oy - 3 = 2(x+1)
Oy+==3(x-2)
Oy + = = 2(x − 3)
Save and Exit
Answer:
y + 1/2 = 3(x - 2)
Step-by-step explanation:
We have to think about this question in point-slope form, which is a form that explicitly gives us the slope of the line and a single point that it passes through. Point-slope form looks like this: y - y1 = m(x - x1), where m is the slope and (x1,y1) is a point that the line goes through. We are given that the line goes through (2, -1/2) which means x1 = 2 and y1 = (-1/2). We are also given that the slope is 3. We can plug these quantities into the equation to solve:
y - (-1/2) = 3(x - 2) OR y + 1/2 = 3(x - 2)
The equation of the line is y + 1/2 = 3(x - 2).
The correct option is (3).
What is slope?The slope of a line indicates its direction and steepness. Finding the slope of lines in a coordinate plane can help predict whether the lines are parallel, perpendicular, or have no relationship at all without actually using a compass.
As per the given data:
We have to find out the equation of the line that passes through (2, -1/2) and has a slope of 3.
As we know a point at the slope of the line, we can use the point slope form:
[tex]y - y_1 = m(x-x_1)[/tex] , where m is the slope and [tex](x_1, y_1)[/tex] is the point through which the line passes.
y - (-1/2) = 3(x - 2)
y + 1/2 = 3(x - 2)
The equation of the line is y + 1/2 = 3(x - 2).
Hence, The equation of the line is y + 1/2 = 3(x - 2).
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what is y= (x+2) ^2 vertex, axis of symmetry, direction of opening, max or min and y intercept
Answer:
Vertex: (-2, 0)
Axis of symmetry: x = -2
Direction of opening: Upwards
Min: 0
Y-intercept: 4
Step-by-step explanation:
Let us graph this line, and then pull out the details we need. See attached.
What do all of these different things mean?
Vertex: This is where the graph intercepts the axis of symmetry (x = -2, see below) and is at point (-2, 0) for this graph.
Axis of Symmetry: This is the line that the graph is symmetrical across. The "center" of the graph. Here, it is x = -2.
Direction of Opening: The direction that the graph is going/opening towards. In this case, it is upwards.
Min: The minimum (in this case) value, the lowest y-coordinate. This is 0 here.
Y-intercept: The point at which the line intercepts the y-axis. This is 4 here.
HELP ASAP
Given: ABCD is a parallelogram.
Prove: A is congruent to FCE.
Answer:
Step-by-step explanation:
Hi!
A is congruent to angle C. Because angle FCE is on the other side of the angle C which is equal to A, angle FCE has to equal A
Create your own games fair game with 4 or more outcomes using a binomial situation presented in this lesson (simulated with a spinner or random number) and adjust the point values so that a cost of 10 points would make the game profitable. be sure to justify why it is profitable and explain the process it took to find profitable outcomes.
The game is profitable since the payout is always less than what you earn.
Given that a fair game with 4 or more outcomes using a binomial situation presented in this lesson (simulated with a spinner or random number) and adjust the point values the so cost of the 10 points will make the game profitable.
Let's discuss the Lucky 7 game
The game is played with the two fair dice rolls.
You put your money on either of 3 things: Above 7, Lucky 7 or below 7
The game below is designed in Excel:
Each cell formula to generate the game:
They are 36 possible outcomes.
7 is the most likely number coming up
6/36=1/6
of the time.
Thus the expected value of the bet is:
(5/12)x₂+(5/12)x₂+(1/6)x₃=26/12
Which, of course, can not make any sense. so, the good idea from the standpoint of the bank is to pay two times on only one of the two possibilities, not a seven, and to give the bet back on the 7. This then gives:
(5/12)x₂+(5/12)x₀+(1/6)x₁=12/12=1
Which is a perfectly fair game.
Of course, the bank wouldn't approve either, so we probably need more restrictions. The way 7 comes out is: 2 ways for each case, (1,5), (2,5), (3,4), then a constraint like not to pay on (5,1) would be added.
Then the 7 returns the money
4/36 = 1/9.
The new case then yields:
(5/12)x₂+(5/12)x₀+(1/9)x₁=34/36=17/18
This says that for every $18 handled in bets the bank expects to pay out $17.
Hence we can say that the game is profitable since the payout is always less than what you earn.
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A rotation is a transformation where an object . A translation is a transformation where an object
A translation is a transformation in which an object at every point according to a given vector and a rotation is a transformation in which an object is moved angularly with respect to a point.
What is the nature of two rigid transformations?
In this question we have two rigid transformations to be defined: (i) Rotation, (ii) Translation. Rigid transformations are transformations applied on geometric loci such that Euclidean distance is conserved. Herein we must describe the characteristic of a rotation and a translation.
A translation is a transformation in which an object at every point according to a given vector and a rotation is a transformation in which an object is moved angularly with respect to a point.
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Answer:
A rotation is a transformation where an object-
moves in a circular arc around a point
A translation is a transformation where an object-
moves a specified distance along a line parallel to a specified line
Step-by-step explanation:
Plato answer
Stan walked a distance of 15km in 3 hours. At what average speed did stan walk?
Hello,
[tex]Speed = \frac{Distance}{Time} = \frac{15 km}{3 h} = \boxed{5 km/h}[/tex]
Stan walked at 5 km/h
On a coordinate plane, 2 quadrilaterals are shown. Quadrilateral Q R S T has points (negative 1, 0), (5, 0), (3.5, negative 6) and (negative 2.5, negative 6). Quadrilateral Q prime R prime S prime T prime has points (negative 1, 2), (1, 2), (0.5, 0), and (negative 1.5, 0).
Quadrilateral QRST is dilated and translated to form similar figure Q'R'S'T'. What is the scale factor for the dilation?
Based on the calculations, the scale factor for this dilation is equal to 1/3.
How to determine the scale factor for this dilation?First of all, we would use the distance formula to find the length of side QR and Q'R' as follows:
Distance = √[(x₂ - x₁)² - (y₂ - y₁)²]
Substituting the given points into the formula, we have;
Distance QR = √[(5 - (-1))² + (0 - 0)²]
Distance QR = √[(5 + 1)² + (0)²]
Distance QR = √[6² + 0]
Distance QR = √36
Distance QR = 6 units.
For side Q'R', we have:
Distance Q'R' = √[(1 - (-1))² + (2 - 2)²]
Distance Q'R' = √[(1 + 1)² + (0)²]
Distance Q'R' = √[2² + 0]
Distance Q'R' = √4
Distance Q'R' = 2 units.
Now, the scale factor for this dilation is given by:
Scale factor = Q'R'/QR
Scale factor = 2/6
Scale factor = 1/3.
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Answer:
Step-by-step explanation:
its 1/3
PLEASE HELP ASAP
Find the equation of the line.
y =
1
1×-8
Enter
Answer:
the Slope: 11
the y-intercept: (0, - 8) x y
0 -8
1 3
Step-by-step explanation:
Answer:
[tex]y=\frac{11}{8}x+\frac{1}{2}[/tex]
United and city are playing each other in the final. it has been calculated that the probability of united winning is three fifths. what is the probability of united not winning?
The probability of not winning of united is [tex]\frac{2}{5}[/tex] .
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Given that the probability of winning of united is [tex]P(A)=\frac{3}{5}[/tex] .
Usually, we take the total probability is 1
So, the probability of not winning of united is [tex]1-\frac{3}{5}[/tex]
[tex]=\frac{5-3}{5}\\=\frac{2}{5}[/tex]
Therefore, the probability of not winning of united is [tex]\frac{2}{5}[/tex] .
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12. Which one is not a polynomial? a) 4x² + 2x - 1 b) y - 3/y b) y² + √5y + 1
pls help ASAP
Answer:
b is not a polynomial
Step-by-step explanation:
b is not a polynomial because in y-3/y the y in denomination means y to the power -1 when it is taken to numerator and if power is negative then it is not a polynomial
jackie has been averaging 3 hits for every 10 times at bat. What is the probability that she will get eactly 2 hits in her net 5 times at bat?
Answer:
the chance is 1.5 out of 5
5
Select the correct answer.
Which expression is equivalent to the given expression? Assume the denominator does not equal zero.
4m5n2
m²n
OA 64m9n3
OB. 64m135
OC. 12m6n4
OD. 12m21n9
Answer:
OC
Step-by-step explanation:
4×3=12m
5+1=6n
4÷1=4
Which of the following rational functions is graphed below?
During a local high school football game, the height h feet of a football after t seconds can be represented by the function h(t) = −16t2+ 58t + 2. Find h(2.5) and explain its meaning.
h(2.5) = 47, and this mean that the height of the football after 2.5 seconds is 47 feet, using the quadratic function h(t) = -16t² + 58t + 2.
In the question, we are given that during a local high school football game, the height of h feet of a football after t seconds can be represented by the quadratic function h(t) = -16t² + 58t + 2.
We are asked to find h(2.5) and explain its meaning.
To find h(2.5), we substitute t = 2.5, in the quadratic function h(t) = -16t² + 58t + 2.
Thus,
h(2.5) = - 16(2.5)² + 58(2.5) + 2,
or, h(2.5) = - 16(6.25) + 145 + 2,
or, h(2.5) = -100 + 147,
or, h(2.5) = 47.
Hence, h(2.5) = 47, and this mean that the height of the football after 2.5 seconds is 47 feet, using the quadratic function h(t) = -16t² + 58t + 2.
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Thaddeus models the number of hours of daylight in his town as
d(t) = 2sin(xt) + 12, where dis the number of daylight hours and tis the
time in months since january 1.
what are the least and greatest numbers of daylight hours over the course of
a year?
a. least: 10 hours; greatest: 14 hours
b. least: 6 hours; greatest: 12 hours
c. least: 2 hours; greatest: 12 hours
o d. least: 7 hours; greatest: 14 hours
submit
Option (A) : least: 10 hours; greatest: 14 hours
The function f(x) = sin x has all real numbers in its domain, but its range is
−1 ≤ sin x ≤ 1.
How to solve such range questions?
Such questions in which every term is in addition and its range is asked is simplest ones to solve if we know the range of each of term. This can be seen from this question
Given: d(t) = 2sin(xt) + 12
= −1 ≤ sin (xt) ≤ 1.
= −2≤ 2 sin (xt) ≤ 2.
= 10 ≤ 2sin (xt) + 12 ≤ 14
= 10 ≤d(t) ≤ 14
Thus least: 10 hours; greatest: 14 hours
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Which of the following expressions are equivalent to -0.5(1.7+1.7)−0.5(1.7+1.7)minus, 0, point, 5, left parenthesis, 1, point, 7, plus, 1, point, 7, right parenthesis? Choose all answers that apply: Choose all answers that apply: (Choice A) A -0.5\cdot1.7-0.5\cdot 1.7−0.5⋅1.7−0.5⋅1.7minus, 0, point, 5, dot, 1, point, 7, minus, 0, point, 5, dot, 1, point, 7 (Choice B) B 2(-0.5)(1.7)2(−0.5)(1.7)2, left parenthesis, minus, 0, point, 5, right parenthesis, left parenthesis, 1, point, 7, right parenthesis (Choice C) C None of the above
The expressions equivalent to -0.5(1.7+1.7) are -0.5(1.7) - 0.5(1.7)
and 2(-0.5(1.7))
Distributive law of expansionGiven the expression below;
-0.5 (1.7 + 1.7)
According to the distributive law;
A(B+C) = AB + AC
Expand
-0.5(1.7) + (-0.5)(1.7)
-0.5(1.7) - 0.5(1.7)
2(-0.5(1.7))
Hence the expressions equivalent to -0.5(1.7+1.7) are -0.5(1.7) - 0.5(1.7)
and 2(-0.5(1.7))
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Which of the following are geometric sequences? This homework assignment is confusing.
Julissa is printing out copies for a work training. it takes 4 minutes to print a color copy, and it takes 2 minutes to print a grayscale copy. she needs to print no fewer than 8 copies within 25 minutes. which system of inequalities represents the number of color copies, x, and grayscale copies, y, that julissa can print to meet her goal? a. 2x 4y ≤ 25 x y ≥ 8 b. 4x 2y ≥ 25 x y ≥ 8 c. 4x 2y ≤ 25 x y ≤ 8 d. 4x 2y ≤ 25 x y ≥ 8
The system of inequalities represents the number of color copies, x, and grayscale copies, y, that julissa can print to meet her goal is;
x + y ≥ 8
x + y ≥ 84x + 2y ≤ 25
Inequalitylet
Number of color copies = xNumber of grayscale copies = yTime to print color copies = 4 minutesTime to print grayscale copies = 2 minutesTotal copies = 8Total time = 25 minutesx + y ≥ 8
4x + 2y ≤ 25
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Use synthetic division to find the expression for the area of the base of a rectangular prism with height x 4 and volume x3 2x2 – 17x – 36.
Hence, the area of base is [tex]x^2 - 2x - 9[/tex]
What is division?Division in maths is breaking a number into equal parts and finding out how many equal parts can be made.
How to solve?The volume of a rectangular prism is,
Volume = Area x Height
Substituting the given expressions,
[tex]x^3 + 2x^2 - 17x - 36 = Area x (x + 4)[/tex]
Area = [tex](x^3 + 2x^2 - 17x - 36) / (x + 4)[/tex]
Now, let's use synthetic division,
-4 | 1 2 -17 -36
---- __-4___8___36
1 -2 -9 0
The expression for the area is [tex]x^2 - 2x - 9[/tex]
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How may sides would a regular polygon have if each exterior angle measures 6 degrees
Answer:
60 sidesStep-by-step explanation:
Since the sum of all exterior angles in a polygon is 360°, we have to divide 360 by 6 to find the number of sides.
360/6 = 60.
So, the polygon has 60 sides.
Hope this helps! (:
Answer:
14
Step-by-step explanation:
because it is a small angle that will indooor more sides
Multiply Conjugates Using the Product of Conjugates Pattern
In the following exercises, multiply each pair of conjugates using the Product of Conjugates Pattern
323. (c − 5)(c + 5)
Answer:
The product is the difference of squares is [tex]$$\left(c-5\right)\left(c+5\right)={{c}^2}-25$$[/tex]
Step-by-step explanation:
Explanation
The given expression is (c-5)(c+5).We have to multiply the given expression.Square the first term c. Square the last term 5 .[tex]$$\begin{aligned}&(c-5)(c+5)=(c)^{2}-(5)^{2} \\&(c-5)(c+5)=c^{2}-25\end{aligned}$$[/tex]
Find the unknown angle x in each of the following figures.
a. x = 120°
b. x = 88°
c. x = 146°
Determining the value of x
A. We have that x and angle 80° as shown in the diagram is on a straight
Angles on a straight line = 180°
Then,
x + 80° = 180°
Make 'x' subject
x = 180° - 80°
x = 100°
B. From the diagram, we can see that 'x' at ∠BCD is alternate to ∠EDC which is 88°
It is important to note that alternate angles are equal
Then,
x = 88°
C. From the diagram, we can see that 'x' at CDE is on a straight line with ABC
Angles on a straight line are equal
Then,
x + 34° = 180°
Make 'x' subject of formula
x = 180° - 34°
x = 146°
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What is the solution to the equation 3√x+4+3/2x+8 = 0?
Ox=-12
Ox= -4
x = 4
O x = 12
Answer:
-4
Step-by-step explanation: