The parameter to be tested is z.
We would set up the hypothesis test.
For the null hypothesis,
µ ≥ 4.2
For the alternative hypothesis,
µ < 4.2
It is a left tailed test.
Since the population standard deviation is given, z score would be determined from the normal distribution table. The formula is
z = (x - µ)/(σ/√n)
where
x = sample mean
µ = population mean
σ = population standard deviation
n = number of samples
From the information given,
µ = 4.2
x = 4.3
σ = 0.4
n = 37
z = (4.3 - 4.2)/(0.4/√37) = 1.53
Looking at the normal distribution table, the probability corresponding to the z score is 0.933
The p value gotten is to the right of the normal curve. Since it is a left tailed test, we need the p value to the left of the curve. Therefore,
p = 1 - 0.933 = 0.067
Since alpha, 0.05 < than the p value, 0.067, then we would fail to reject the null hypothesis. Therefore, At a 5% level of significance, there is no significant evidence that mean GPA of these graduates does not exceed 4.30
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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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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
find intervals when the graph is growing or increasing or constant
The function shown in the graph is increasing over the interval (-1, 0) and (1, ∞). It is decreasing over the interval (-∞, -1) and (0, 1). The function does not remain constant.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
The function shown in the graph is increasing over the interval (-1, 0) and (1, ∞). It is decreasing over the interval (-∞, -1) and (0, 1). The function does not remain constant.
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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 xWhich 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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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
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]
Given the function defined in the table below, find the average rate of change, in
simplest form, of the function over the interval 3 ≤ x ≤ 6.
Answer:
OC
1
2
ين
3
4
5
6
f(x)
69
64
59
54
49
44
Need Help
Answer:
this question is not clear i have read it twice an still dont understand it. Sorry
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
21. For the following exercises, use the descriptions of each pair of lines given below to find the slopes of Line 1 and Line 2. Is each pair of lines parallel, perpendicular, or neither?
21. Line 1: Passes through (1, 7) and (5, 5)
Line 2: Passes through (−1, −3) and (1, 1)
Answer:
The given lines are perpendicular.
Step-by-step explanation:
In the question, two lines are given as line 1 passes through (1,7) and (5,5). Whereas, line 2 passes through (-1,-3) and (1,1).
It is required to find the slope of given lines and figure out whether they are perpendicular, parallel or neither.
To solve this question, first find the slope of both lines. Check if their product is equal to -1, then they are perpendicular. If the slopes are equal the lines are parallel.
Step 1 of 2
Find the slope of first line.
[tex]$$\begin{aligned}m_{1} &=\frac{5-7}{5-1} \\m_{1} &=\frac{-2}{4} \\m_{1} &=-\frac{1}{2}\end{aligned}$$[/tex]
Step 2 of 2
Find the slope of first line.
[tex]$$\begin{aligned}&m_{2}=\frac{1-(-3)}{1-(-1)} \\&m_{2}=\frac{4}{2} \\&m_{2}=2\end{aligned}$$[/tex]
And
[tex]$$\begin{aligned}&m_{1} m_{2}=-\frac{1}{2}(2) \\&m_{1} m_{2}=-1\end{aligned}$$[/tex]
Since, both slopes are reciprocal of each other.
Therefore, the lines are perpendicular.
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 $17.
Hence we can say that the game is profitable since the payout is always less than what you earn.
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I need the answer for number 8
Answer:
Step-by-step explanation:
I'm going to assume you want it to be a perfect triangle, so then we would have the equation 4x=24. So we can divide each side by 4 to get rid of the 4 and get x by itself. So 24/4= 5. So x=5
Geometry question confused
Answer:
my ans will be wrong also and right also 50%5$chances it is an opposite angle so it is in out manner so iys sum is 180 so we have to subbtract
Step-by-step explanation:
65०to 180०(180०-65०=115०) i think ans is 115०the missing angle measurement is 115०in my opinion
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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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
Question 1 of 15
Solve 18x+62 12x+18.
A. x ≥ 4
B. x≤ 4
C. x≤2
D. x ≥ 2
Answer:
18+62=80x
12+18=30x
x=80÷30=2
x>2
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:
CAN ANYONE HELP ME WITH THIS QUESTION?
Answer:
try 4
Step-by-step explanation:
8x4= 32
32-7=25
30. 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.
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
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
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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A trader sold a tv for sh .18000 making a 20percent loss.For how much was he supposed to sell it in order to make 20percent profit.
Answer:
The trader was supposed to cell the TV for sh. 27000 in order to make 20% profit
==============
Let the cost price is x.
We have:
x - 20% = 18000Solve it for x:
x - 0.2x = 180000.8x = 18000x = 18000/0.8x = 22500The cost is 22500, find selling price with 20% profit:
22500 + 20% = 22500 + 0.2*22500 = 22500*1.2 = 27000United 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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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]
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
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.
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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SOMEONE PLS HELP MEEEE
The solutions to the quadratic equations are:
a) [tex]x = \frac{3 \pm \sqrt{19}}{5}[/tex]
b) x = -8, x = 5.
A quadratic function is given according to the following rule:
[tex]y = ax^2 + bx + c[/tex]
The solutions are:
[tex]x_1 = \frac{-b + \sqrt{\Delta}}{2a}[/tex]
[tex]x_2 = \frac{-b - \sqrt{\Delta}}{2a}[/tex]
In which:
[tex]\Delta = b^2 - 4ac[/tex]
Item a:
The coefficients are a = 5, b = -6, c = -2, hence:
[tex]\Delta = (-6)^2 - 4(5)(-2) = 76[/tex][tex]x_1 = \frac{6 + \sqrt{76}}{10} = \frac{6 + 2\sqrt{19}}{10} = \frac{3 + \sqrt{19}}{5}[/tex][tex]x_2 = \frac{6 - \sqrt{76}}{10} = \frac{6 - 2\sqrt{19}}{10} = \frac{3 - \sqrt{19}}{5}[/tex]Item b:
The equation is:
x² + 3x = 40
x² + 3x - 40 = 0.
It can be simplified as follows:
(x - 5)(x + 8) = 0.
Hence the solutions are:
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