The possible length of the third side of a triangle with sides of 9 units and 6 units must be more than 3 units and less than 15 units, according to the triangle inequality theorem.
To determine the possible length of the third side of a triangle when two sides are known, we can use the triangle inequality theorem. The theorem states that the length of any side of a triangle must be less than the sum of the other two sides and greater than their difference. In this case, Millie's triangle has sides of 9 units and 6 units.
The sum of these two sides is 9 units + 6 units = 15 units, and their difference is 9 units - 6 units = 3 units. Therefore, the third side of the triangle must be greater than 3 units but less than 15 units.
The third side must be greater than 3 units.
The third side must be less than 15 units.
To summarize, the third side could have any length that is more than 3 units but less than 15 units.
A geologist has collected 10 specimens of basaltic rock and 10 specimens of granite. The geologist instructs a laboratory assistant to randomly select 15 of the speci- mens for analysis. a. What is the pmf of the number of granite specimens selected for analysis
Answer:
Thus, the pmf of the number of granite specimens selected for analysis is [tex]P(X=x)={20\choose x}0.50^{x}(1-0.50)^{20-x}[/tex].
Step-by-step explanation:
The experiment consists of collecting rocks.
The sample consisted of, 10 specimens of basaltic rock and 10 specimens of granite.
The total sample is of size, n = 20.
Let the random variable X be defined as the number of granite specimen selected.
The probability of selecting a granite specimen is:
[tex]P(Granite)=p=\frac{10}{20}=0.50[/tex]
A randomly selected rock can either be basaltic or granite, independently.
The success is defined as the selection of granite rock.
The random variable X follows a Binomial distribution with parameter n = 20 and p = 0.50.
The probability mass function of X is:
[tex]P(X=x)={20\choose x}0.50^{x}(1-0.50)^{20-x}[/tex]
What is the measure of angle a1?
--> This was difficult for me. Is there anybody can help?
Answer:
40°
Step-by-step explanation:
Alternate angles
Angles BAC and ACD are equal
Please help me!!!!!!!!!!!!
Answer:
1215
Step-by-step explanation:
Using the Binomial theorem
With coefficients obtained from Pascal's triangle for n = 6, that is
1 6 15 20 15 6 1
and the term 3x decreasing from [tex](3x)^{6}[/tex] to [tex](3x)^{0}[/tex]
and the term - y increasing from ([tex](-y)^{0}[/tex] to [tex](- y)^{6}[/tex]
Thus
[tex](3x-y)^{6}[/tex]
= 1 × [tex](3x)^{6}[/tex] [tex](-y)^{0}[/tex] + 6 × [tex](3x)^{5}[/tex] [tex](-y)^{1}[/tex] + 15 × [tex](3x)^{4}[/tex] [tex](-y)^{2}[/tex] + .........
The term required is
15 × [tex](3x)^{4}[/tex] [tex](-y)^{2}[/tex]
= 15 × 81[tex]x^{4}[/tex] y²
with coefficient 15 × 81 = 1215
that is 1215[tex]x^{4}[/tex]y²
If a baseball is projected upward from ground level with an initial velocity of 64 feet per second, then it’s height is a function of time, given by s= -16t^2+64t. What is the maximum height reached by the ball?
Answer:
64 ft
Step-by-step explanation:
The equation can be factored as ...
s = -16t(t -4)
This is the equation of a downward-opening parabola with t-intercepts of 0 and 4. The maximum height is at the vertex, halfway between those values, at t=2. At that time, the height is ...
s = -16(2)(2-4) = 64 . . . . feet
The maximum height is 64 feet and it occurs at 2 seconds.
A polynomial is an expression consisting of the operations of addition, subtraction, multiplication of variables. There are different types of polynomials such as linear, quadratic, cubic, etc.
A quadratic equation is of degree two and it has only two solution.
Given that s= -16t²+64t
The maximum height is at ds/dt = 0
Hence:
ds/dt = -32t + 64
-32t + 64 = 0
32t = 64
t = 2 seconds
The maximum height is at 2 seconds, hence:
Maximum height = -16(2)² + 64(2) = 64 feet
The maximum height is 64 feet and it occurs at 2 seconds.
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A chef planning for a large banquet thinks that 2 out of every 5 dinner guests will order his soup appetizer he excepts 800 guests at the banquet use equivalent ratios to estimate how many cups of soup he should prepare
Answer:
The Chef planner should prepare 320 cups of soups
Step-by-step explanation:
Number of guests expected to come = 800
2 out of every 5 guest will order for soup appetizer
Hence using equivalent ratios
2:5 = X :800
X = (800 × 2) ÷ 5 = 320
Hence the Chef planner should prepare 320 cups of soups
I woke up at 6:47 a.M. I spent 25 minutes showering and getting dressed then I walked down stairs. I got down stairs at blank I then ate breakfast and read a book for blank minutes before leaving the house at 7:42 a.M.
Answer:
a. Blank time = 7:12 am
b. Blank Minutes = 30 minutes
Step-by-step explanation:
The individual got downstairs 25 minutes after 6:47am
Hence Blank time = 6:47am + 25 minutes = 7:12 am
To calculate amount of blank minutes he spent reading books
7:42am - 7:12am = 30 minutes
The equation of the piecewise function f(x) is below. What is the value of f(3)?
Option B: 5 is the value of f(3)
Explanation:
The equation of the piecewise function is given by
[tex]f(x)=\left\{\begin{aligned}-x^{2}, & x<-2 \\3, &-2 \leq x<0 \\x+2, & x \geq 0\end{aligned}\right.[/tex]
We need to find the value of [tex]f(3)[/tex]
The value of the function f can be determined when [tex]x=3[/tex] by identifying in which interval does the value of [tex]x=3[/tex] lie in the piecewise function.
Thus, [tex]x=3[/tex] lies in the interval [tex]x\geq 0[/tex] , the function f is given by
[tex]f(x)=x+2[/tex]
Substituting [tex]x=3[/tex] in the function [tex]f(x)=x+2[/tex], we get,
[tex]f(3)=3+2[/tex]
[tex]f(3)=5[/tex]
Thus, the value of [tex]f(3)[/tex] is 5.
Therefore, Option B is the correct answer.
Nathaniel and Grant go to the movie theater and purchase refreshments for their friends . Nathaniel bought 4 candies and 10 bags of popcorn for a total of 99.50 dollars. Grant bought 3 candies and 5 bags of popcorn for a total of 56.50 dollars. You may use decimals for this problem.
Answer:
A candy costs $6.75 and a bag of popcorn costs $7.25
Step-by-step explanation:
Let the cost of one 1 candy=$x
Let the cost of one bag of popcorn=$y
Now, Total Cost Per Item=Number of Item Bought X Price Per Unit Item.
If Nathaniel bought 4 candies and 10 bags of popcorn for a total of 99.50 dollars.
4x+10y=99.50
Grant bought 3 candies and 5 bags of popcorn for a total of 56.50 dollars.
3x+5y=56.50
Solving the two equations simultaneously
4x+10y=99.50 (I)
3x+5y=56.50 (II)
Multiply Equation (I) by 3 and Equation (II) by 4 to eliminate x
12x+30y=298.5
12x+20y=226
Subtracting
10y=72.5
y=$7.25
Now, from (II)
3x+5y=56.50
3x+5(7.25)=56.50
3x+36.25=56.50
3x=20.25
x=20.25/3=$6.75
Therefore a candy costs $6.75 and a bag of popcorn costs $7.25
Answer:
candy costs - $6.75
a bag of popcorn costs - $7.25
Step-by-step explanation:
Math triangle fun please help!
Answer:
Step-by-step explanation:
You can use the cosine rule to solve this problem:
cos(∠KLJ) = (KL² + JL² - KJ²)/(2*JL*KL) = 21463/21960 = 0.97737
∠KLJ = cos⁻¹(0.97737) = 12.2°
Answer:
Step-by-step explanation:
We would apply the law of Cosines which is expressed as
a² = b² + c² - 2abCosA
Where a,b and c are the length of each side of the triangle and A is the angle corresponding to a. Likening the expression to the given triangle, it becomes
JL² = JK² + KL² - 2(JK × KL)CosK
122² = 39² + 90² - 2(39 × 90)CosK
14884 = 1521 + 8100 - 2(3510)CosK
14884 = 9621 - 7020CosK
7020CosK = 9621 - 14884
7020CosK = - 5263
CosK = - 5263/7020
CosK = - 0.7497
K = Cos^- 1(- 0.7497)
K = 138.6° to the nearest tenth
Determine which rectangle was transformed to result in rectangle E. A) rectangle A B) rectangle B C) rectangle C D) rectangle D
Asuming the added image is part of the complete question...
Answer:
C) rectangle C
Step-by-step explanation:
Observing the image we can see that when the rectangle C is reflected across the x-axis and then moved up 2 units, it will land exactly where the rectangle E is.
I hope you find this information useful and interesting! Good luck!
Answer:
C) Triangle C.
Step-by-step explanation:
The triangle C satisfies all the conditions described in the statement.
Computer towers purchased for $30900 depreciates at a constant rate of 12.6% per year. Write the function that models the value of the computer towers after (t)years from now. What will the computer towers be worth after 8 years
Answer: the computer towers will be worth $10521 after 8 years
Step-by-step explanation:
We would apply the formula for exponential decay which is expressed as
A = P(1 - r)^t
Where
A represents the value of the computer towers after t years.
t represents the number of years.
P represents the initial value of the computer towers.
r represents rate of decay.
From the information given,
P = $30900
r = 12.6% = 12.6/100 = 0.126
Therefore, the function that models the value of the computer towers after (t)years from now is
A = 30900(1 - 0.126)^t
A = 30900(0.874)^t
Therefore, when t = 8 years, then
A = 30900(0.874)^8
A = $10521
is 2 a prime number?
Answer:
Yes.
Step-by-step explanation:
A prime number is a number that is ony divisible by itself and 1.
2 is only divisible by 2(=1) and 1 (=2)
Answer:
YES
Step-by-step explanation:
PRIME NUMBERS A prime number is a whole number greater than 1 whose only factors are 1 and itself. A factor is a whole number that can be divided evenly into another number. The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29. ... The number 1 is neither prime nor composite.
An earthquake measuring 6.4 on the Richter scale struck Japan in July 2007, causing extensive damage. Earlier that year, a minor earthquake measuring 3.1 on the Richter scale was felt in parts of Pennsylvania. How many times more intense was the Japanese earthquake than the Pennsylvania earthquake
Japanese earthquake is 1996 times intense than the Pennsylvania earthquake.
What is ratio?A ratio is a comparison between two amounts that is calculated by dividing one amount by the other. The quotient a/b is referred to as the ratio between a and b if a and b are two quantities of the same kind and with the same units, such that b is not equal to 0. Ratios are represented by the colon symbol. As a result, the ratio a/b has no units and is represented by the notation a: b.
Given:
An earthquake measuring 6.4 on the Richter scale struck Japan in July 2007.
and, a minor earthquake measuring 3.1 on the Richter scale was felt in parts of Pennsylvania.
Mow, Mj= log Ij/S and Mp = log Ip/ S
Where S is the standard earthquake intensity.
Then,
6.4 = log Ij/S and 3.1 = log Ip/ S
S x [tex]10^{6.4[/tex] = Ij and S x [tex]10^{3.1[/tex] = Ip
So, ratio of the intensities
Ij : Ip= [tex]10^{6.4[/tex] / [tex]10^{3.1[/tex]
= [tex]10^{3.3[/tex]
= 1996
Hence, Japanese earthquake is 1996 times intense than the Pennsylvania earthquake.
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if a triangle has lengths of 27 m and 11 m, check all the possible lengths for the third side
The possible length of the third side of a triangle with sides of 27 m and 11 m, as per the Triangle Inequality Theorem, ranges between 16 m and 38 m.
Explanation:In mathematics, the possible length of the third side of a triangle, given the other two sides, is determined using the Triangle Inequality Theorem. This theorem states that the length of any side of a triangle is less than the sum of the lengths of the other two sides and more than the absolute value of the difference between those two sides.
Given side lengths of 27 m and 11 m, the possible length of the third side (let's call it 's') is between 27 m - 11 m and 27 m + 11 m.
Therefore, s > 16 m and s < 38 m. So, any value between 16 m and 38 m could be the length of the third side of the triangle.
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Decide whether the table represents a linear or exponential function circle with a linear exponential then write the function formula.
The table represents an exponential function, and the function formula is: [tex]\[ y = 3 \cdot 2^x \][/tex]
To determine whether the table represents a linear or an exponential function, we need to examine the rate of change in the `y` values as `x` increases.
For a linear function, the rate of change (the difference between one `y` value and the next) is constant.
For an exponential function, the rate of change is multiplicative – the `y` value is multiplied by a constant factor as `x` increases by a regular increment.
Looking at the provided table:
- When `x` increases by 1 (from 0 to 1, from 1 to 2, etc.), the `y` values are:
- At `x=0`, `y=3`
- At `x=1`, `y=6`
- At `x=2`, `y=12`
- At `x=3`, `y=24`
- At `x=4`, `y=48`
- At `x=5`, `y=96`
- At `x=6`, `y=192`
- At `x=7`, `y=384`
Each time `x` increases by 1, `y` is doubled. This is a characteristic of an exponential function.
The pattern suggests that `y` is being multiplied by 2 as `x` increases by 1. Therefore, we can express the function as:
[tex]\[ y = ab^x \][/tex]
where `a` is the initial value of `y` when `x` is 0 (which is 3 in this case), and `b` is the factor by which `y` is multiplied each time `x` increases by 1 (which is 2 in this case).
So the exponential function that fits the table is:
[tex]\[ y = 3 \cdot 2^x \][/tex]
Thus the table represents an exponential function, and the function formula is:
[tex]\[ y = 3 \cdot 2^x \][/tex]
PLS HELP
What is (f−g)(x)?
f(x)=x3−2x2+12x−6
g(x)=4x2−6x+4
Answer:
x^3-6x^2+18x-10
Step-by-step explanation:
(f-g) (x) =f(x) - g(x) =
x^3-2x^2+12x-6-(4x^2 - 6x+4)=
x^3-2x^2+12x-6-4x^2+6x-4=
x^3-6x^2+18x-10
Answer:
Solution given:
f(x)=x3−2x2+12x−6
g(x)=4x2−6x+4
now
(f-g)(x)=f(x)-f(g)=x3−2x2+12x−6-4x²+6x-4
=x³-6x²+18x-10
Question 10. A tree 38 feet high casts a shadow 75 feet long. Find the measure of the angle of elevation of the sun. *
Answer:
26.9 degrees to the nearest tenth.
Step-by-step explanation:
The height = opposite side and length of the shadow = the adjacent side, so we use the tangent function.
If the angle of elevation is x degrees, then
tan x = 38/75
x = 26.9 degrees.
In her backyard jess is planting rows of squash. To plant a row of squash jess needs 6/7 square feet. There are 12 square feet in jess's backyard, so how many rows of squash can jess plant?
Answer:
14 rows.
Step-by-step explanation:
We have been given that Jess is planting rows of squash. To plant a row of squash Jess needs 6/7 square feet. There are 12 square feet in Jess's backyard.
To find number of rows that Jess can plant, we will divide total area of backyard by area needed to plant each row as:
[tex]\text{Number of rows that Jess can plant}=12\div\frac{6}{7}[/tex]
[tex]\text{Number of rows that Jess can plant}=\frac{12}{1}\div\frac{6}{7}[/tex]
Convert into multiplication problem by flipping the 2nd fraction:
[tex]\text{Number of rows that Jess can plant}=\frac{12}{1}\times \frac{7}{6}[/tex]
[tex]\text{Number of rows that Jess can plant}=\frac{2}{1}\times \frac{7}{1}[/tex]
[tex]\text{Number of rows that Jess can plant}=14[/tex]
Therefore, Jess can plant 14 rows of squash in her backyard.
During the mayoral election,two debates were held between the canidates. The first debate lasted 1 4/5 hours. The second one lasted 1 4/5 times as long as the first one. How long was the second debate? Estimate the product. Then find the actual product.
Answer:
[tex]3\frac {6}{25} hrs \ or \ 3 hrs\ 14 mins \ 24 sec[/tex]
Step-by-step explanation:
The question calls requires one to get the product of the given time. Since first debate lasted for :
[tex]1\frac {4}{5} \ hrs[/tex]
-and the second lasted
[tex]1\frac {4}{5} hrs[/tex] times more than the first then the second took then the first step will involve converting the mixed fractions into improper fraction which will be:
[tex]\frac {9}{5}[/tex]
-Now multiplying
[tex]\frac {9}{5}\times\frac{9}{5}\\\\=\frac{81}{25}=3\frac{6}{25}[/tex]hrs
The measure of angle W is 19 degrees more than three times the measure of angle V if the sum of the measures of the two angles is 199 degree find the measure of each angle
Answer: angle w = 154 degrees
v = 45 degrees
Step-by-step explanation:
Let w represent the measure of angle W.
Let v represent the measure of angle V.
The measure of angle W is 19 degrees more than three times the measure of angle V. This is expressed as
w = 3v + 19
if the sum of the measures of the two angles is 199 degree, it means that v + 3v + 19 = 199
4v = 199 - 19
4v = 80
v = 180/4 = 45
w = 3v + 19 = (3 × 45) + 19
w = 154
Which of the following segments is a proper way to call the method readData four times? Group of answer choices int i = 0; while (i < 4) { readData(); i = i + 1; } double k = 0.0; while (k != 4) { readData(); k = k + 1; } int i = 0; while (i <= 4) { readData(); i = i + 1; } int i = 0; while (i < 4) { readData(); }
Answer:
int i = 0; while (i < 4) { readData(); i = i + 1; }
Step-by-step explanation:
the above method is proper way to call the method readData four times because it will start from zero and will call readData until i=3, if i=4 it will stop calling readData.
double k = 0.0; while (k != 4) { readData(); k = k + 1; }
This is not the proper way to call readData four times because it will call readData only if k!=4 otherwise condition k!=4 will not be true and readData will not be called.
int i = 0; while (i <= 4) { readData(); i = i + 1; }
This is not the proper way to call readData four times because condition i<=4 will call readData five times starting from zero to 4.
int i = 0; while (i < 4) { readData(); }
This is not the proper way to call readData four times because it will call readData only one time i.e. value of is not incremented.
The proper way to call the 'readData()' method four times is by using a 'while' loop with a counter that starts at 0 and continues until it is less than 4, incrementing by 1 in each iteration.
The correct way to call the method readData() four times using a while loop is:
int i = 0;This loop initializes a counter variable i to 0, then enters a while loop that continues to iterate as long as i is less than 4. Inside the loop, the method readData() is called, and after each call, the counter i is incremented by 1. The loop will execute a total of four times before the condition i < 4 becomes false, thereby stopping the loop.
Suppose that two teams play a series of games that end when one of them has won i games. Suppose that each game played is, independently, won by team A with probability p. A) Find the expected number of games that are played when (a) i= 2 and (b) i= 3. B) Find P(X = 4).
Answer:
Step-by-step explanation:
Please look at the 2 photos below, they may be your correct answers.
Which of the following is the cheapest route to visit each city using the "Brute Force Method" starting from A and ending at A.
Group of answer choices
ABCDA, $960
ACDBA, $900
ACBDA, $960
None of the Above
Answer:
ACDBA, $900
Step-by-step explanation:
The cheapest route will be the one with the lowest cost. Of the routes listed, the cost $900 is the lowest, so route ACDBA is the cheapest.
_____
The "Brute Force Method" requires you compute the costs of the possible routes and pick the lowest. The answer choices have done that for you.
The cost of ACDBA is AC +CD +DB +BA = 240 +230 +210 +220 = 900, as shown in the answer selections.
The three routes listed, and their reverses (which are the same cost), are the only possible routes starting and ending at A.
On a quiz, Kieran is asked to write an expression that contains at least two factors, a product, a quotient, and an odd coefficient. He writes the expression . Does his expression meet all the requirements? If not, explain why not.
Answer:
No
Step-by-step explanation:
I think your full question is attached in this photo
My answer:
No, because the expression does not involve a quotient
When one number dividend is divided by another number divisor, the result obtained is known as Quotient. I dont see the result in his expression
The voltage across the capacitor increases as a function of time when an uncharged capacitor is placed in a single loop with a resistor and a battery.
What mathematical function describes this behavior?
1. Exponential2. Linear 3. Quadratic 4. Power
Answer:
1. Exponential
Step-by-step explanation:
The simplest RC-Circuit, that is, a capacitor and a resistor in a series configuration can be modeled by using Ohm's Law and Kirchhoff's Circuit Laws:
[tex]C \cdot \frac{dV}{dt} + \frac{V}{R} = 0[/tex]
By rearranging the formula, an homogeneous linear first-order differential equation is found:
[tex]\frac{dV}{dt} + \frac{1}{R \cdot C} \cdot V = 0[/tex]
Whose solution has the form of a exponential model:
[tex]V(t) = V_{o} \cdot e^{-\frac{t}{R \cdot C} }[/tex]
Which of the following is the point and slope of the equation y + 9 = -2/3(x - 3)?
(3, -9), 2/3
(3, -9), -2/3
(-3, 9), -2/3
(-3, -9), -2/3
Answer:
the answer is going to be B
Step-by-step explanation:
if you you plug in the number witch is 3 for your x and -9 for y and solve it you notice that the statement is true for instance
-9+ 9 = -2/3(3 - 3)
0=-6/3+6/3
0=-2+2
0=0
if you subtract a negative with a positive its zero.
in the multiplication negative times negative turn positive
The point and slope of the equation y + 9 = -2/3(x - 3) are (3, -9), -2/3 respectively.
The equation y + 9 =-2/3(x - 3) is given in point-slope form. The point-slope form of a line's equation is y - y1 = m(x - x1), where (x1, y1) is a point on the line, and m is the slope of the line. To find the point and the slope from the given equation, consider that x1 and y1 will have opposite signs to those in the equation because they get subtracted in the formula. Therefore, the point on the line is (3, -9), and the slope, m, which is the coefficient of x in the equation, is -2/3.
Two welders worked a total of 46 h on a project. One welder made $34/h, while the other made $39/h. If the gross earnings of the two welders was $1,669 for the job, how many hours did each welder work?
Answer:
25 and 21 hours respectively
Step-by-step explanation:
Let the number of hours worked by each welder be x and y respectively.
They worked a total of 46 hours. This means :
x + y = 46 hours.......(I)
Now, given their hourly charges, since we have the total amount of money realized, we can make an equation out of it. This means:
34x + 39y = 1669........(ii)
We then solve both simultaneously. From I, x = 46 -y
We can substitute this into ii
34(46 -y) + 39y = 1669
1564 -34y + 39y = 1669
5y = 1669 - 1564
5y = 105
y = 105/5 = 21
x = 46 - y
x = 46 - 21 = 25 hours
The numbers of hours worked by the welders are 25 and 21 respectively
Final answer:
To determine the hours worked by each welder, we set up two equations based on their hourly rates and solve them. A system of equations is used to find that each welder worked 23 hours, each earning $782, summing to the total earnings of $1669.
Explanation:
To solve the problem of how many hours each welder worked, we need to set up two equations based on the given information. Let's designate x as the number of hours the first welder worked, and y as the number of hours the second welder worked. The first welder's rate is $34 per hour, and the second welder's rate is $39 per hour. We know that x + y = 46 because together they worked a total of 46 hours. We also have the total earnings equation, which is 34x + 39y = $1669.
We can now solve these equations using substitution or elimination. For instance, if we solve the first equation for x, we get x = 46 - y. Substituting this into the second equation gives us 34(46 - y) + 39y = $1669. After distributing and combining like terms, we can find the value for y, and then substitute back to find x.
After solving, we would find that the first welder worked 23 hours and the second welder worked 23 hours as well. Each welder earned $782, which adds up to the total earnings of $1669.
In 2/3 Of a minute aaron 5 Liter mountain bike tire loss 8/9 of a liter of air is the tie continues to lose air at this rate how long will it take for the tire to be completely flat
Answer:
3.75 minutes
Step-by-step explanation:
For every 2/3 minutes, Aaron's Tire loses 8/9 of a liter of air
Total Volume of Air in the Tyre = 5 liters
Now, we divide the total volume by volume of air lost every stated interval to know how many air loss it will take the Tyre to be empty
[tex]\dfrac{5}{8/9} =\dfrac{5X9}{8} =\dfrac{45}{8}[/tex]
Then, to get when the tire will be completely flat in:
[tex](\frac{2}{3}X\frac{45}{8}) minutes[/tex]=3.75 minutes=3 minutes 45 seconds
The tyre will be empty in 3 minutes 45 seconds
Montarello and Martins (2005) found that fifth grade students completed more mathematics problems correctly when simple problems were mixed in with their regular math assignments. To further explore this phenomenon, suppose that a researcher selects a standardized mathematics achievement test that produces a normal distribution of scores with a mean of µ= 100 and a standard deviation of σ = 18. The researcher modifies the test by inserting a set of very easy problems among the standardized questions and gives the modified test to a sample of n = 36 students. If the average test score for the sample is M = 104, is this result sufficient to conclude that inserting the easy questions improves student performance? Use a one-tailed test with α = .01.
Answer:
There is no significant improvement in the scores because of inserting easy questions at 1% significance level
Step-by-step explanation:
given that Montarello and Martins (2005) found that fifth grade students completed more mathematics problems correctly when simple problems were mixed in with their regular math assignments. To further explore this phenomenon, suppose that a researcher selects a standardized mathematics achievement test that produces a normal distribution of scores with a mean of µ= 100 and a standard deviation of σ = 18. The researcher modifies the test by inserting a set of very easy problems among the standardized questions and gives the modified test to a sample of n = 36 students.
Set up hypotheses as
[tex]H_0: \bar x= 100\\H_a: \bar x >100[/tex]
(right tailed test at 1% level)
Mean difference = 104-100 =4
Std error of mean = [tex]\frac{\sigma}{\sqrt{n} } \\=3[/tex]
Since population std deviation is known and also sample size >30 we can use z statistic
Z statistic= mean diff/std error = 1.333
p value = 0.091266
since p >0.01, we accept null hypothesis.
There is no significant improvement in the scores because of inserting easy questions at 1% significance level
Final answer:
Using a one-tailed test with α = .01 and the provided test scores' information, the calculated z-value was 1.33, which did not surpass the critical value of 2.33. Therefore, it was concluded that there is insufficient evidence to support that inserting easy questions improves performance on the mathematics achievement test.
Explanation:
To determine if inserting easy questions into a standardized mathematics achievement test improves student performance, we conduct a hypothesis test using the given information: the test has a normal distribution of scores with mean µ = 100 and standard deviation σ = 18. A sample of n = 36 students took the modified test, scoring an average of M = 104. We use a one-tailed test with α = .01.
Step 1: Formulate the Hypotheses
Null Hypothesis (H0): µ = 100; the modifications do not affect test scores.
Alternative Hypothesis (H1): µ > 100; the modifications improve test scores.
Step 2: Calculate the Test Statistic
Use the formula for the z-score: z = (M - µ) / (σ/√n)
Substituting values: z = (104 - 100) / (18/√36) = 4 / 3 = 1.33
Step 3: Determine the Critical Value
For α = .01 in a one-tailed test, the critical z-value is approximately 2.33.
Step 4: Make a Decision
Since the calculated z-value of 1.33 is less than the critical value of 2.33, we do not reject the null hypothesis. Therefore, there is not sufficient evidence at the .01 level of significance to conclude that inserting easy questions improves student performance on the math achievement test.
Rewrite 2 ^ x = 128as a logarithmic equation !???
Answer:
log 2 ( 128 ) = x So C.
Step-by-step explanation: