a. The hypotheses are:
Null hypothesis: the average test scores are the same for the different teaching methods.
Alternative hypothesis: the average test scores are different for the different teaching methods.
b. To determine the degree of freedom for the F test: we must find two sources of variation such that we have two variances. The two sources of variation are: Factor (between groups) and the error (within groups) and add this up. Or use (N - 1). N is number in sample
c. With a p value of of 0.0168 and using a standard significance level of 0.05, we will reject the null hypothesis as 0.0168 is less than 0.05 and conclude that the average test scores are different for the different teaching methods.
Hence we get the required answer.
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A bank pays 3% per annum compound interest, calculate how much interest would you get if you invested £45 for 3 years
Answer:
405
Step-by-step explanation:
don't forget to follow rate like
Two angles are complementary to each other. One angle measures 32°, and the other angle measures (12x − 20)°. Determine the value of x. 64 6.5 32.5 6
Answer:
B) 6.5
Step-by-step explanation:
Complementary angles are angles that are put together to equal 90 degrees.
Angle one is 32 degrees.
90-32= 58
So we need to get the number 58 for it to be complementary. The reason for this is because 32+58=90. Which would make it complementary.
When we plug in 6.5 we get 58, which is what we want.
12(6.5)- 20= 90
78-20=58
Hope this helps!!!
The value of x is 6.5.
Complimentary angles are known as angles which makes the sum of 90°.
The angles sum up to form a right angle. When two angles complement each other they sum up to be 90°.
According to question one angle - 32° and other angle [12x - 20].
⇒ 32 + [12x - 20] = 90
⇒ 12x - 20 = 58
⇒ 12x = 78
⇒ x = 6.5
Hence, the value of x is 6.5.
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Determine the concavity of the graph of f(x) = 4 - x^2 between x= -1 and x = 5 by calculating average rates of change over intervals of length 2. 1. The average rate of change over the interval 3 ≤ 2 < 5 =
Given the function:
[tex]f(x)=4-x^2[/tex]For the given function, we will determine the concavity between x = -1 and x = 5
By the average rate of change over the interval 3 ≤ x < 5
We will use the following formula:
[tex]\frac{f(5)-f(3)}{(5)-(3)}[/tex]First, we will find the value of f(5) and f(3)
[tex]\begin{gathered} x=5\rightarrow f(5)=4-5^2=-21 \\ x=3\rightarrow f(3)=4-3^2=-5 \end{gathered}[/tex]Substitute into the formula:
So, the average rate of change will be as follows:
[tex]\frac{f(5)-f(3)}{(5)-(3)}=\frac{(-21)-(-5)}{5-3}=\frac{-16}{2}=-8[/tex]As the average rate of change is negative, the concavity of the graph will be concave down
let f(x)=3x+5 and g(x) =3x^2 -x-10. find (f/g)(x) and state it’s domain
(f/g)(x) = f(x)/f(g)
[tex]\begin{gathered} =\text{ }\frac{3x+5}{3x^2-x-10} \\ =\text{ }\frac{3x+5}{(3x+5)(x-2)} \\ =\frac{1}{(X-2)} \end{gathered}[/tex]Domain: x cannot equal 2
Can some one help me with 7 , 8 and 9 please?
7) The angle asked is ajacent to the leg given and we also have the hypotenuse. So we can use cossine:
[tex]\begin{gathered} \cos x=\frac{8}{18}=\frac{4}{9} \\ x=\arccos (\frac{4}{9})=64\degree \end{gathered}[/tex]8) Here we want the hypotenus given an angle an its opposite leg. So we can use sine:
[tex]\begin{gathered} \sin (65\degree)=\frac{10}{x} \\ x=\frac{10}{\sin (65\degree)}=11.0 \end{gathered}[/tex]9) We want the leg which is opposite of a given angle and we have the hypotenuse. So we can use sine again:
[tex]\begin{gathered} \sin (28\degree)=\frac{x}{15} \\ x=15\cdot\sin (28\degree)=7.0 \end{gathered}[/tex]A school band performed a concert on four different days. The band soldtickets and snacks each day of the concert for a fundraiser. The first tableshows the numbers of tickets sold and the amounts of money collected fromticket sales. The second table shows the numbers of snacks sold and theamounts of money collected from snack sales.
Part A:
To determine the price per snack, just multiply any value of the column Amount collected, by its corresponding value in the column of Number of snakcs sold:
53.75/43 = 1.25
Hence, the price per snack is 1.25 dollars
Part B:
The equation is a linear equation. The general formula for a linear equation is:
y - yo = m(x - xo)
where m is the slope and (xo,yo) is a pair of values of the table.
m is calculate as follow:
m = (y2 - y1)/(x2 - x1)
m =
using this input output machine,f(x)=?input. 2,3,5,7output. 9,15,33,59x^2+x+3x^2-x+3x^2+x-3x*2-5
We have values of x and f(x) and choices for the expression of f(x).
We can easily found the correct option just evaluating the expressions in the x values and see which have the correct value of f(x):
For x=2 the outpur=f(x)=9:
[tex]\begin{gathered} x^2+x+3\Rightarrow2^2+2+3=4+5=9,\text{ Correct!!!} \\ x^2-x+3\Rightarrow2^2-2+3=4+1=5 \\ x^2+x-3\Rightarrow2^2+2-3=4-1=3 \\ x\cdot2-5\Rightarrow2\cdot2-5=4-5=-1 \end{gathered}[/tex]You can evaluate in the other values of x and proof that the corretc option is the first.
Use Composition of FunctionsBOX OFFICE A movle theater charges $8.50 for each of the xtickets sold. The manager wants to determine how much the movietheater gets to keep of the ticket sales If they have to glve thestudlos 75% of the money earned on ticket sales t(x). If the amountthey keep of each ticket sale is k(x), which composition representsthe total amount of money the theater gets to keep?
Given: The amout charged per ticket is $8.50
If x tickets are sold
Then the total revenue (amount made) will be =>
[tex]8.5\text{ x }x\text{ = \$8.50x}[/tex]If t(x) represents how much the studio collects
and k(x) represents how much is kept
Given: t(x) = 75% then
k(x)= (100 -75)%= 25 %
So that
The total amount that will be kept will be
25% of $8.50x
=>
[tex]\frac{25}{100}\text{ x (\$8.50x) }[/tex][tex]\frac{25\text{ x \$8.50x}}{100}\text{ = }\frac{212.5x}{100}=\text{ \$2.125x}[/tex]The amount that will be kept will be
= > $2.125x
Where x is the number of tickets
Name the relationship between the pair of angles and find the value of x.
Consecutive interior angles (Same side)
x = -8
Explanations:The two angles are 136 + x and x + 56
The two angles are consecutive-interior angles because they are on the same side of the transversal.
Note that consecutive -interior angles are supplementary and they add up to 180 degrees.
Applying this rule to the diagram shown:
(136 + x) + (x + 56) = 180
136 + 56 + x + x = 180
192 + 2x = 180
2x = 180 - 196
2x = -16
x = -16 / 2
x = -8
How can i calculate the number of students that graduated from the university faculty of natural sciences in 2002? how can i determine the sector angle that will represent the number of graduates in each subject? how can i hence construct a pie chart of radius 4cm to represent the information given in the table?
A table showing the number of graduates by subject from a university's faculty of natural science in 2002.
1) To calculate the number of students that graduated, find the sum of the number of graduates from each subject.
[tex]9+15+19+12+5=60[/tex]The number of students that graduated is 60.
2) To determine the sector angle that will represent the number of graduates in each subject, divide the number of graduates in each subject by the total number of students and then multiply by 360º.
3) To construct a pie chart with radius, 4cm to represent the information, draw a circle of radius 4cm and partition it into sectors with central angles as calculated in (2) above.
8. Determine the most precise name for quadrilateral PQRS.-8 -6P(-1, 1)-4 -28642-2-4-6-8Q(0, 2)R(1, 1)2S(0, -2)468
Answer:
[tex]Kite[/tex]Explanation:
Here, we want to determine the most precise name for the quadrilateral
At first sight, the image plot looks like a kite. We will have to confirm this using the properties of a kite
One of the important properties is to check that the diagonals intersect at right angles
Looking at the plot, QS and PR must be perpendicular
This is correct as they meet at right angles at the line through the origin
Also, for us to have a kite, PQ and QR must be equal
This is also correct as PQ and QR are equal in length
Furthermore, PS and RS must be equal in length
This is alo correct as the two are equal in length
We thus conclude that the quadrilateral is a kitecohis is als
plot looks like a kite. We will have to confirm this using the properties of a kite
plot looks like a kite. We will have to confirm this using the properties of a kite
Which number line represents the solution set for the inequality 3(8 - 4x) < 6(x - 5)?-5-4-3-2 -1 01+4123on++at-5-2+ o+1-1234501-5-4-3+o-2-1+1N+W+A+5++-5-4-3-2+o-1NT1345
To find the solution, lets first simplify the inequality:
[tex]undefined[/tex]The line with a slope of -1 and that contains the point (1, 3).Find the equation of the line in standard form.
ANSWER
x + y = 4
EXPLANATION
The standard form of a linear equation is given as:
ax + by = c
To do this, we have to find the equation of the line using point-slope method:
y - y1 = m(x - x1)
where (x1, y1) is the point the line passes through
m = slope
The given slope is -1 ad the point the line passes through is (1, 3).
Therefore, we have:
y - 3 = -1(x - 1)
y - 3 = -x + 1
=> x + y = 1 + 3
x + y = 4
That is the equation of the line in standard form.
4)Erica and Megan each improved theiryards by planting daylilies and shrubs.They bought their supplies from thesame store. Erica spent $200 on 9daylilies and 10 shrubs. Megan spent$185 on 13 daylilies and 5 shrubs. Whatis the cost of one daylily and the cost ofone shrub?Type text here
One daylily $10 and 1 shrub $11
1) Gathering the data from the question
Erica spent $200 on 9 daylillies and 10 shrubs
Megan spent $185 on 13 daylilies and 5 shrubs
9d+10s=200
13d+5s=185
2) Let's solve this system of linear equations now
9d+10s=200
13d+5s=185 Multiply by (-2)
9d +10s=200
-26d-10=-370
----------------------
-17d =-170
17d=170
d=10
9(10) +10s=200
90+10s-90=200-90
10s=200-90
10s=110
s=11
So the cost of one daylily is$10 and 1 shrub is $11
6. Solve by any method:3x - 2y = 6x + y = 2
we can take any equation and solve for any variable, for example y will solve x from the second equation
[tex]\begin{gathered} x+y=2 \\ x=2-y \end{gathered}[/tex]now replace the value of x on the first equation
[tex]\begin{gathered} 3x-2y=6 \\ 3(2-y)-2y=6 \\ \end{gathered}[/tex]simplify
[tex]\begin{gathered} 6-3y-2y=6 \\ 6-5y=6 \end{gathered}[/tex]and solve for y
[tex]\begin{gathered} -5y=6-6 \\ -5y=0 \\ y=\frac{0}{-5} \\ \\ y=0 \end{gathered}[/tex]Value of y is 0 now we can replace y=0 on any equation and solve for x
for example I will replace y=0 on the second equation to find x
[tex]\begin{gathered} x+y=2 \\ x+(0)=2 \\ x=2 \end{gathered}[/tex]Value of x is 2
If we want to represent the solution as a point, the solution is
[tex](2,0)[/tex]Please help me with this problem I am not able to help my son to understand we keep getting it wrong please help.The function y=−16x^2+v0x models Lindy's height in feet above a trampoline x seconds after she jumps straight up. In the equation of the function, v0 is her initial velocity in feet per second. Lindy lands back on the trampoline 1 second after she jumps. What is the value of v0?Enter your answer in the box.v0= ft/s
EXPLANATION:
We are given the function which models Lindy's height x seconds after she jumps straight up a trampoline. The function is expressed as;
[tex]y=-16x^2+v_0[/tex]Where x is the time in seconds after she jumps, and v_0 is the initial velocity. The result of the function is her height after jumping with the given time x.
If she lands back on the trampoline one second after she jumps, then she is at a height of zero.
The function can now be re-written as follows;
[tex]\begin{gathered} \text{With;} \\ x=1\text{ (time)} \\ y=0\text{ (height)} \end{gathered}[/tex][tex]0=-16(1)^2+v_0[/tex]We can now simplify;
[tex]-16(1)^2+v_0=0[/tex]Add
[tex]-16(1)^2[/tex]to both sides;
[tex]\begin{gathered} v_0=16(1)^2 \\ v_0=16 \end{gathered}[/tex]Therefore;
ANSWER:
The value of v_0( her initial velocity) is;
[tex]v_0=16[/tex]if 5 guys are putting yogurt in a girl's mouth and each liter is 5 liters how much is the girl carrying in her mouth ️️
5 guys are putting yogurt in a girl's mouth
Each of the yogurt is 5 liters
The total yogurt the girl is carrying = 5 x 5
= 25
The answer is 25 liters of yogurt
The vertices of a figure are A(1, -1), B(5.-6), and C(1, - 6). Rotate the figure 90 counterclockwise about the origin. Find the coordinates of the image. Polygon Undo Redo x Reset 7A 6. 5 4 3 2. 1 --7-6-5--4 -3 -2 -1 1 1 2 a 4 - 2 -3 -5 -6 -7 The coordinates of the image are:
The vertices of the given figure are
A(1, -1), B(5.-6), and C(1, - 6).
For a 90 counterclockwise about the origin, a coordinate, (x, y) would be (- y, x)
This means that after the 90 degrees rotation,
coordinate A would be (- - 1, 1) = (1, 1)
Coordinate B would be (- - 6, 5) = (6, 5)
Coordinate C would be (- - 6, 1) = (6, 1)
By which Theorem or postulate is Change ABC congruent Change BAD?
Solution
we are given that
[tex]\begin{gathered} |AB|=|BC| \\ We draw the diagram as followsNotice the lettering on each triangle, they both represent the triangle we are given in the question
The postulate here is Sides, Angle, Sides (SAS)
Option C
use the display of data to find the mean, median, mode, and midrange 10,3, 11,3, 12,4, 13,5, 14,2, 15,3
The mean, median, mode and midrange of the given data is 7.92, 7.5, 3 and 8.2 respectively.
What is median and midrange?The mid-way between the least value and the greatest value of the data set is called the midrange, and the median is the middle number in a sorted list of numbers.
Given a data 10,3, 11,3, 12,4, 13,5, 14,2, 15,3
Mean = (2+3+3+3+4+5+10+11+12+13+14+15)/12 = 7.92
Median = 15/2 = 7.5
Mode = 3
Midrange = (2+15)/2 = 8.2
Hence, The mean, median, mode and midrange of the given data is 7.92, 7.5, 3 and 8.2 respectively.
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What would be the correct way to solve this?[tex] {x}^{2} - 5x - 84[/tex]
Answer:
(x + 7 ) ( x - 12 )
Explanation:
We know that if we multiply any two expressions x + a and x + b then we have
[tex](x+a)(x+b)=x^2+(a+b)x+ab[/tex]Now similarly,
[tex]x^2+(a+b)x+ab=x^2-5x-84[/tex]meaning
[tex]\begin{gathered} a+b=-5 \\ ab=-84 \end{gathered}[/tex]In other words, what are the two numbers that if I add them together I get -5 and If I multiply them I get -84. The answer comes from educated guesses. We guess that if we add 7 and -12 we get 5 and if we multiply then we get -84; therefore,
[tex]\begin{gathered} a=7 \\ b=-12 \end{gathered}[/tex]Hence, the expression can be factored as
[tex]=x^2-5x-84=(x-12)(x+7)[/tex]which is our answer!
solve 10 + 15x - 30 = 40
We have the next equation
[tex]10+15x-30=40[/tex]We sum similar terms
[tex]15x-20=40[/tex]then we clear x
[tex]\begin{gathered} 15x=40+20 \\ 15x=60 \\ x=\frac{60}{15} \\ x=4 \end{gathered}[/tex]the value of x=4
in the figure above
Since AB is tangent to the circle, the angle BAO equals π/2.
The same happens to BC, so the angle BCO also equals π/2.
Now, for any quadrilateral, the sum of the internal angles is 2π. Therefore:
ABC + AOC + BAO + BCO = 2π
ABC + 3π/7 + π/2 + π/2 = 2π
ABC = 2π - 3π/7 - π/2 - π/2 = π - 3π/7 = (7π - 3π)/7
ABC = 4π/7
A batter averaged 11 hits in 30 times at bat during the first half of the baseball season. He averaged 5 hits in 7 times at bat for the second half of the season. What was his average batting rate for the season?
*Find the answer to the nearest thousandth.
*(Compare total hits to total times at bat; the average of the two halves gives a wrong answer.)
Average batting rate for the season is 0.432.
Given,
Number of hits in first half of the season =11
Number of hits in second half of the season = 5
Number of times at bat during first half of the season = 30
Number of times at bat during second half of the season = 7
then,
Total number of hits in the season = 11+5 = 16
Total number of times at bat during the season = 30+7 =37
To find average batting rate use formula,
[tex]Average batting rate of season =\frac{Total number of hits in season}{Total number of at bat during season} \\\\=\frac{16}{37}\\\\ =0.432[/tex]
Hence, the batter's average batting rate for the season is 0.432.
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Ari took their partner out for dinner and got a check for $60.67. Ari wants to leave a 20% tip. How much is the tip? How much is the total cost for the meal? SHOW ALL OF YOUR WORK.
Given the following question:
Check = $60.67
Ari wants to leave a 20% tip
To find the answer we have to find 20% of $60.67
[tex]\frac{20\times60.67}{100}=20\times60.67=1213.4\div100=12.134[/tex][tex]\begin{gathered} 12.134 \\ 4\text{ < 5} \\ 12.13 \end{gathered}[/tex]The tip is $12.13
The total cost = tip + check
[tex]12.13\text{ + 60.67=}72.8[/tex]The total costs = $72.8
What is the approximate probability thata point chosen inside the rectangle is inthe shaded region?
In order to determine the required probability, calculate the total area of the shaded regions frist:
Consider that there is a rectangle and a triangle with shaded area, then, you have:
A1 = (1 ft)(2 ft) = 2 ft² rectangle area
A2 = (2 ft)(2 ft)/2 = 2ft² triangle area
Then, the total shaded area is:
A = A1 + A2
A = 2 ft² + 2 ft²
A = 4 ft²
Next, calculate the total area of the given figure:
A' = (3 ft + 1 ft)(2 ft) = 8 ft²
Next, the probability is the quotient in between the area of th shaded regions over the area of the total figure:
p = A/A'
p = (2 ft²)/(4 ft²)
p = 0.50
Hence, the probability that a point chosen is inside a shaded region is 0.50
the table shows the scores of 20 people who took the paramedics licensing test. Find the mean and the standard deviation of the data. the deviation answer needs to be rounded to three decimal places as needed.
a) Mean = 76
b) Standard deviation = 6.728
Explanation:The data set has frequency. So we will apply the formula:
[tex]\text{Mean = }\frac{\sum ^{}_{}fx}{\sum ^{}_{}f}[/tex][tex]\begin{gathered} \text{Mean = }\frac{(69\times7)\text{ + (70}\times1)+(75\times3)\text{ + (81}\times6)\text{ + (82}\times2)+\text{ (92}\times1)}{7\text{ + 1 + 3+6+2+1}} \\ \text{Mean = }\frac{483\text{ + 70}+225\text{ + 486 + 164}+\text{ 9}2}{7\text{ + 1 + 3+6+2+1}} \\ \text{Mean = }\frac{1520}{20} \\ \text{Mean = 76} \end{gathered}[/tex]To get the standard deviation, we will apply the formula:
[tex]\begin{gathered} \sigma\text{ = }\sqrt[]{\frac{\sum^{}_{}f(x_i-\mu)^2}{n\text{ - 1}}} \\ \text{where }\sigma\text{ = standard deviation} \\ \mu\text{ = mean, }x_i\text{ = values of x} \\ n\text{ = }\sum ^{}_{}f=20 \end{gathered}[/tex][tex]\begin{gathered} \sigma\text{ = }\sqrt[]{\frac{860}{20-1}} \\ \sigma\text{ = }\sqrt[]{\frac{860}{19}} \\ \sigma\text{ = }\sqrt[]{45.2632} \\ \sigma\text{ = 6.7}28 \\ \\ \text{Standard deviation = 6.7}28 \end{gathered}[/tex]Can you pls help me with number 6 my treacher said that it was d but I got b is me correct or my treacher
Given the algebraic expression below
[tex]6a+4y+a+2a[/tex]Collect like terms
[tex]6a+2a+a+4y[/tex]Add possible like terms using the distributive property of algebra
[tex]\begin{gathered} (6+2+1)a+4y \\ 9a+4y \end{gathered}[/tex]Hence, the final answer is 9a + 4y
Option D is correct
10. Quadrilateral PQRS with P(-5,1). Q(-2,6), R(3,7), and S(6,4); dilate by a factor of 1/2 12 a. Is this an enlargement or reduction? How do you know? 14 b. What are the vertices of the image after the transformation?
a.
The dilation is a reduction, this comes from the fact that the dilation factor is less than 1.
b.
A point after a dilation is given as:
[tex](x,y)\rightarrow(kx,ky)[/tex]where k is the dilation factor.
In this case we need to divide all the coordinates by two, then we have that:
[tex]\begin{gathered} P^{\prime}(-\frac{5}{2},\frac{1}{2}) \\ Q^{\prime}(-1,3) \\ R^{\prime}(\frac{3}{2},\frac{7}{2}) \\ S^{\prime}(3,2) \end{gathered}[/tex]Describe in words where cube root of 30 would be plotted on a number line.
Between 3 and 4, but closer to 3
Between 3 and 4, but closer to 4
Between 2 and 3, but closer to 2
Between 2 and 3, but closer to 3
Cube root of 30 is 3.107.
How to find cube root of a number?
Cube root is the number that needs to be multiplied three times to get the original number.
The cube root of a number can be determined by using the prime factorization method. In order to find the cube root of a number:
Step 1: Start with the prime factorization of the given number.
Step 2: Then, divide the factors obtained into groups containing three same factors.
Step 3: After that, remove the cube root symbol and multiply the factors to get the answer. If there is any factor left that cannot be divided equally into groups of three, that means the given number is not a perfect cube and we cannot find the cube root of that number.
We have to find the cube root of 30.
Prime factorization of 30 = 2*3*5.
Therefore the cube root of 30 = ∛(2*3*5)= ∛30 .
As ∛30 cannot be reduced further, then the result for the cube root of 30 is an irrational number as well.
So here we will use approximation method to find the cube root of 30 using Halley's approach:
Halley’s Cube Root Formula: ∛a = x[(x³ + 2a)/(2x³ + a)]
The letter “a” stands in for the required cube root computation.
Take the cube root of the nearest perfect cube, “x” to obtain the estimated value.
Here we have a = 30
and we will substitute x = 3 because 3³ = 27< 30 is the nearest perfect cube.
Substituting a and x in Halley's formula,
∛30 = 3[(3³ + 2*30)/(2*3³ + 30)]
= 3[(27+60)/(54+30)]
= 3(87/84)
= 3*1.0357
∛30 = 3.107.
Therefore the cube root of 30 is 3.107.
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