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.
what does it mean when someone’s says “ Ion like clowns “
Answer:
Lol it either means that they don't like a clown such as comic performer who employs slapstick or similar types of physical comedy, often in a mime style.
or a person that's been fooled and has been called a clown.
Please help. Trig: Laws of Cosines
If a rhombus whose side measures 6 and the smaller angle is 145*, find the length of the larger diagonal, to the nearest tenth.
Answer:
11.4 units
Step-by-step explanation:
diagonal² = 6² + 6² - 2(6)(6)cos(145)
diagonal² = 130.9789471888
diagonal = 11.444603409
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 problem statement is insufficient to describe the behavior.
_____
The capacitor's voltage is described by a differential equation such that its rate of change is proportional to the difference of the battery voltage and the capacitor voltage. The solution to the differential equation is a function that is exponential with time.
Do bicycle riders start from the same point and ride in opposite directions. Rider x moves twice as fast a rider y and In three hours they are 72 miles apart
Complete question:
Two bicycle riders start from the same point and ride in opposite directions. Rider x moves twice as fast as rider y and in three hours they are 72 miles apart. Find the rate (speed) of each rider.
Answer:
y = 8 miles/hour
x = 16 miles/hour
Step-by-step explanation:
We can solve this question by first setting up the following equations:
Rider x travels twice as fast as rider y:
x = 2*y - Equation 1
In three hours they are 72 miles apart:
3*x + 3*y = 72 -Equation 2
Solving equations 1 and 2 simultaneously we get:
y = 8 miles/hour
x = 16 miles/hour
This question is done simply by writing down the question statements as equations. This can be seen being done in Equation 1 and Equation 2 above.
Prior to ________ many school systems attempted to circumvent the racial desegregation process by using standardized tests and testing procedures to place minority children into segregated programs within public schools
Answer:
Hobson v. Hansen (1967)
Step-by-step explanation:
Hobson v. Hansen (1967) was a federal court case filed by civil rights activist Julius W. Hobson against Superintendent Carl F. Hansen and the District of Columbia's Board of Education on the charge that the current educational system underprivileged blacks and the poor of their right to equal educational opportunities relative to their white and affluent peers, on account of race and socioeconomic status.
Before the landmark 1954 Brown v. Board of Education decision, school systems used standardized tests to maintain segregated programs in public schools. This was in violation of federal laws and highlighted by the Coleman Report, which sparked a debate about desegregation and testing bias.
Explanation:Prior to the Brown v. Board of Education ruling in 1954, many school systems employed a variety of tactics to circumvent the racial desegregation process. Standardized tests and testing procedures were frequently used to place minority children into segregated programs within public schools, reinforcing educational segregation. This practice was a violation of Title VI of the Civil Rights Act of 1964 and other federal legislations aimed at ensuring equal opportunity in education.
After the Coleman Report in 1966, the debate around desegregation, busing, and cultural bias in standardized testing intensified. New policies like mandated busing were implemented to correct the discriminatory practices and to achieve the goals of desegregation. Despite these efforts, many districts faced challenges in successfully integrating schools, resulting in a variety of voluntary and court-ordered methods to promote equal education.
Write an R-program to sample n = 1000 values from the BlackwellMacQueen Pólya urn for µ = αH where H is a non-atomic bivariate distribution of your choice.
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Need help on the last problem please...
Answer:
y = 97°
Step-by-step explanation:
z = 180 - 55 - 42 = 83
Total angle in a triangle is 180°
y = 180 - z = 180 - 83 = 97°
Supplementary angles
(Will give brainliest if correct. Keep it simple)
cylinder and a cone have the same diameter: 8 inches. The height of the cylinder is 9 inches. The height of the cone is 18 inches. Use π = 3.14. What is the relationship between the volume of this cylinder and this cone? Explain your answer by determining the volume of each and comparing them. Show all your work.
Each of the 50 students participating in a workshop is either an undergraduate or a graduate student. If P is the probability that a randomly selected participant will be a female graduate student, is P less than \small \frac{1}{2} ?
Answer:
no
Step-by-step explanation:
no
The middle school camera club sold 242 bulbs and 360 daffodil bulbs. Students to buy the bulbs into 100 bags to sell at the school fair. Write an expression to show how many bulbs went into each of the 100 bags with students put the same number of each kind of bulb in each bag.??? I need the expression not like 600 equals 100 X like 240÷360 equals 100×300 like that I am confused can someone please help me
Answer:
345
Step-by-step explanation:
345
Austin scored 85 on the calculus midterm. If the final exam counts twice as much as the midterm exam, then for what range of scores on the final would Austin get an average between 85 and 96? Both tests have a maximum of 100 points.
Answer:
Austin should score between 85 and 100 in the final exam to have an average between 85 and 95, since reaching 96 is mathematically impossible.
Step-by-step explanation:
The problem has to be solved in two parts, the first to obtain an average of 85 and the second to obtain an average of 96.
In the first part with an average of 85 would be as follows.
Let x be the final exam grade.
Weighted average = (85 + 2 * X) / 3
85 = 85/3 + (2/3) * X
Rearranging
X = (3/2) * (85- (85/3))
Resolving
X = 85, therefore you must take 85 in the final test to get an average of 85.
The second part with an average of 96:
96 = 85/3 + (2/3) * X
Rearranging
X = (3/2) * (96- (85/3))
Resolving
X = 101.5, therefore you must take 101.5 in the final test to get an average of 96, therefore it is impossible to have an average of 96, because the highest score is up to 100.
Taking 100 your average would be:
Weighted average = (85 + 2 * 100) / 3 = 95
Then Austin should score between 85 and 100 in the final exam to have an average between 85 and 95, since reaching 96 is mathematically impossible.
Austin should score between [tex]85[/tex] and [tex]100[/tex] in the final exam to have an average between [tex]85[/tex] and [tex]95[/tex].
Average :Let us consider that [tex]X[/tex] be the final exam grade.
So that, Weighted average [tex]= \frac{85 + 2 * X}{3}[/tex]
[tex]85 =\frac{85}{3} + \frac{2}{3} X\\\\\frac{2}{3} X=85-\frac{85}{3} \\\\X=85[/tex]
Thus, you must take 85 in the final test to get an average of 85.
The second part with an average of 96:
[tex]96 = \frac{85}{3} + \frac{2}{3} X\\\\\frac{2}{3}X=96-\frac{85}{3}\\ \\ X=101.5[/tex]
Thus, it is impossible to have an average of 96, because the highest score is up to 100.
Taking 100 your average would be:
Weighted average [tex]=\frac{85 + 2 * 100}{3} =95[/tex]
Hence, Austin should score between 85 and 100 in the final exam to have an average between 85 and 95.
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Write the polar equation in rectangular form.
r = 6 sin θ
Y=-6x
Y=x-3
X^2+(y-3)^2=9
(X-3)^2+y^2=9
Answer:
Step-by-step explanation:
The identities you need here are:
[tex]r=\sqrt{x^2+y^2}[/tex] and [tex]r^2=x^2+y^2[/tex]
You also need to know that
x = rcosθ and
y = rsinθ
to get this done.
We have
r = 6 sin θ
Let's first multiply both sides by r (you'll always begin these this way; you'll see why in a second):
r² = 6r sin θ
Now let's replace r² with what it's equal to:
x² + y² = 6r sin θ
Now let's replace r sin θ with what it's equal to:
x² + y² = 6y
That looks like the beginnings of a circle. Let's get everything on one side because I have a feeling we will be completing the square on this:
[tex]x^2+y^2-6y=0[/tex]
Complete the square on the y-terms by taking half its linear term, squaring it and adding it to both sides.
The y linear term is 6. Half of 6 is 3, and 3 squared is 9, so we add 9 in on both sides:
[tex]x^2+(y^2-6y+9)=9[/tex]
In the process of completing the square, we created within that set of parenthesis a perfect square binomial:
[tex]x^2+(y-3)^2=9[/tex]
And there's your circle! Third choice down is the one you want.
Fun, huh?
The polar equation r = 6 sinθ is converted to rectangular form using the sine and cosine functions, eventually leading to a quadratic equation in terms of x and y as (x^2 + y^2)y^2 = 36x^2 + 36y^2..
To convert the polar equation r = 6 sinθ into rectangular form, we use the relationships
x = rcosθ and y = r *sinθ.
Substituting for r from the given equation, we have
y = (6sinθ) * sinθ = 6 sin^2θ. Now, since sin^2θ = 1/2 - 1/2cos(2θ), and
cos(2θ) = 1 - 2sin^2θ,
we can express this in terms of x and y as
cos(2θ) = 1 - 2(y/6)^2.
Therefore, y =1/2 - 1/2(1 - 2(y/6)^2) simplifies to y^2 = 36(1 - cos^2 θ).
Since cos^2 θ =x^2/r^2 = x^2/x^2+y^2, we plug this back into the equation to get
y^2 = 36 -36x^2/x^2+y^2.
Multiplying through by (x^2+y^2) we end up with (x^2 + y^2)y^2 = 36x^2 + 36y^2.
A pentagon has all sides equal. A rectangle has width twice as long as the side of the pentagon and length four times as long. The perimeter of the rectangle is 30 inches. What is the perimeter of the pentagon?
Answer: the perimeter of the Pentagon is 12.5 inches
Step-by-step explanation:
Let x represent the length of each side of the Pentagon.
A rectangle has width twice as long as the side of the pentagon. This means that the width of the rectangle, w is 2x
The rectangle has length four times as long as the side of the pentagon. This means that the length of the rectangle, l is 4x
The formula for determining the perimeter of a rectangle is expressed as
Perimeter = 2(l + w)
The perimeter of the rectangle is 30 inches. This means that
2(2x + 4x) = 30
12x = 30
x = 30/12 = 2.5
A Pentagon has 5 sides. This means that the perimeter of the Pentagon is
5 × 2.5 = 12.5 inches
SOMEBODY CAN YOU HELP?
Answer:
A.
Step-by-step explanation:
Since the line goes down 4 and right 5, your slope would be -4/5 and since your y-intercept is at (0,-5) you would plug that in for b.
I hope this helped! Please mark Brainliest if you can :)
The point (4, –3) is on the terminal side of an angle in standard position. Determine the value of r, and the exact value of sin, cos, and tan for this angle.
Answer:
The answer to your question is below
Step-by-step explanation:
Data
A (4 , -3)
r = ?
sin = ?
cos = ?
tan = ?
Process
1.- Plot the point
This point is in the fourth quadrangle
2.- Calculate r
We have the Opposite side and the Adjacent side
tan Ф = -3/4
tan⁻¹ Ф = Ф = 323.1
Ф = 323.1°
3.- sinФ =
Calculate the hypotenuse
c² = 4² + (-3)²
c² = 16 + 9
c² = 25
c = 5
sinФ = -3/5
cos Ф = 4/5
tan Ф = -3/4
The value of r is 5. The exact value of sin is -3/5, cos is 4/5, and tan is -3/4.
Explanation:The value of r can be found using the Pythagorean theorem, which states that for any point (x, y) on the terminal side of an angle in standard position, the value of r can be calculated as √(x^2 + y^2). In this case, we have (x, y) = (4, -3), so r = √(4^2 + (-3)^2) = √(16 + 9) = √25 = 5.
The exact value of sin for this angle can be calculated as y/r, so sin = -3/5.
The exact value of cos for this angle can be calculated as x/r, so cos = 4/5.
The exact value of tan for this angle can be calculated as y/x, so tan = -3/4.
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An album sells for $12.00 through an online music service. If the album is 20% off, and sales tax is 5%, what is the total price of the album including tax?
Answer:
Total price of the album including tax is $10.08
Step-by-step explanation:
Sales price without discount and tax = $12
% discount = 20%
Sales price with discount = 12 - (20/100 × 12) = 12 - 2.4 = $9.6
% sales tax = 5%
Tax = 5/100 × 9.6 = $0.48
Total price of the album including tax = $9.6 + $0.48 = $10.08
Answer:
Final price = 9.6*(105/100) = 9.6*1.05 = 10.08 $
Step-by-step explanation:
The original price of the album is 12 to find out the price after the discount is applied we need to compute 100% - 20% = 80% of the original price. So we can use the following expression:
Price after discount = original price * (80/100)
Price after discount = 12 * (80/100)
Price after discount = 12 * 0.8 = 9.6 $
Now we have to include the sale tax of 5%, since it's a tax we need to add it to the original value so 100% + 5% = 105% of the sale's price:
Final price = Price after discount * (105/100)
Final price = 9.6*(105/100) = 9.6*1.05 = 10.08 $
A coin is flipped 10 times where each flip comes up either heads or tails. How many possible outcomes (a) contain exactly two heads? (b) contain at most three tails? (c) contain the same number of heads and tails?
Answer:
a. 45
b. 176
c. 252
Step-by-step explanation:
First take into account the concept of combination and permutation:
In the permutation the order is important and it is signed as follows:
P (n, r) = n! / (n - r)!
In the combination the order is NOT important and is signed as follows:
C (n, r) = n! / r! (n - r)!
Now, to start with part a, which corresponds to a combination because the order here is not important. Thus
n = 10
r = 2
C (10, 2) = 10! / 2! * (10-2)! = 10! / (2! * 8!) = 45
There are 45 possible scenarios.
Part b, would also be a combination, defined as follows
n = 10
r <= 3
Therefore, several cases must be made:
C (10, 0) = 10! / 0! * (10-0)! = 10! / (0! * 10!) = 1
C (10, 1) = 10! / 1! * (10-1)! = 10! / (1! * 9!) = 10
C (10, 2) = 10! / 2! * (10-2)! = 10! / (2! * 8!) = 45
C (10, 3) = 10! / 3! * (10-3)! = 10! / (2! * 7!) = 120
The sum of all these scenarios would give us the number of possible total scenarios:
1 + 10 + 45 + 120 = 176 possible total scenarios.
part c, also corresponds to a combination, and to be equal it must be divided by two since the coin is thrown 10 times, it would be 10/2 = 5, that is our r = 5
Knowing this, the combination formula is applied:
C (10, 5) = 10! / 5! * (10-5)! = 10! / (2! * 5!) = 252
252 possible scenarios to be the same amount of heads and tails.
A forest ranger is on a 90-foot fire watch tower. He spots a fire at an angle of depression to the fire that is 7 degrees. What is the horizontal distance between the tower and the fire
Answer: the horizontal distance between the tower and the fire is 732.89 feet
Step-by-step explanation:
Considering the situation, a right angle triangle is formed. The height of the fire watch tower represents the opposite side of the right angle triangle.
The horizontal distance, h between the tower and the fire represents the adjacent side of the right angle triangle.
If the angle of depression to the fire that is 7°, the angle of elevation from of the tower watcher from the fire is also 7° because they are alternate angles.
To determine h, we would apply
the tangent trigonometric ratio.
Tan θ, = opposite side/adjacent side. Therefore,
Tan 7 = 90/h
h = 90/tan7 = 90/0.1228
h = 732.89 feet
A school district need 3 teachers for every 70 children . They expect to have 14,700 in the district next year. At this time they have 612 teachers so how many more do they need
Answer: They need 18 teachers more.
Step-by-step explanation:
Hi, to solve this problem, first, we have to divide the expected number of children (14,700) by 70.
14,700 / 70 = 210 groups of 70 childrenWe obtain that they are expecting 210 groups of 70 children each. Since the school district needs 3 teachers for every 70 children, we have to multiply the number of groups (210) by the number of teachers per group (3).
210 x 3 = 630 teachersWe obtained the total number of teachers needed for 14,700 children.
Since at this time the district has 612 teachers, to find the teachers missing we have to subtract the actual number of teachers (612) to the number of teachers needed (630).
630 - 612 = 18They need 18 teachers more.
The perimeter of a square must be greater than 148 inches but less than 196 inches. Find the range of possible side lengths that satisfy these conditions. (Hint: The perimeter of a square is given by P=4s, where s represents the length of a side).
The possible range for the side length of the square is that it is greater than 37 inches, but less than 49 inches.
Explanation:The perimeter of a square is given by the formula P=4s, where s is the length of one side of the square. Since we know the perimeter must be greater than 148 and less than 196 inches, we can create inequality equations to solve for the side lengths, s.
Given the lowest limit, 148 < 4s. Divide both sides by 4, we get 37 < s.
Given the highest limit, 4s < 196. Again, divide both sides by 4, we get s < 49.
So, we conclude that the length of a side, s, must be less than 49 inches but greater than 37 inches to meet the required conditions of the question.
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Suppose the position of an object moving in a straight line is given by s (t )equals 4 t2+ 5 t+ 5. Find the instantaneous velocity when t equals 2. What expression can be used to find the instantaneous velocity at the given time?
Answer:
[tex] v(t) = 8t +5[/tex]
And that represent the instantaneous velocity at a given time t.
And then we just need to replace t =2 in order to find the instantaneous velocity and we got:
[tex] v(t=2) = 8*2 + 5 = 16+5 = 21[/tex]
Step-by-step explanation:
For this case we have the position function s(t) given by:
[tex] s(t) = 4t^2 + 5t+5[/tex]
And we can calculate the instanteneous velocity with the first derivate respect to the time, like this:
[tex] v(t) = s'(t)= \frac{ds}{dt}[/tex]
And if we take the derivate we got:
[tex] v(t) = 8t +5[/tex]
And that represent the instantaneous velocity at a given time t.
And then we just need to replace t =2 in order to find the instantaneous velocity and we got:
[tex] v(t=2) = 8*2 + 5 = 16+5 = 21[/tex]
Write a statement that declares and initializes two integer variables. Call the first one age and initialize it to 15, and call the second one weight and initialize it to 90.
Answer:
First is to define the language in which to make the statement, I chose the language C, because it is the most common. To initialize the variable, the first thing is to define the type, in this case it is an integer type.
In language C, that is determined by int, then the name of the variable, in this case it would be age. We close with; To finish the order. Then we give the courage that asks us to initiate.
In the end, it would look like this:
int age;
age = 15;
int weight;
weight = 90;
Final answer:
To declare and initialize two integer variables called age and weight, one can use the code 'int age = 15, weight = 90;'.
Explanation:
To declare and initialize two integer variables in most programming languages, you can use a single line of code. For the variables age and weight, the statement might look like this:
int age = 15, weight = 90;
This line of code creates two variables of type integer named age and weight. The variable age is initialized with the value 15, and weight is initialized with the value 90.
The use of the comma in the statement allows for both variables to be declared and initialized in one concise statement.
Based on your budget, which transportation option is the best financial decision for you? Explain your answer in at least two sentences.
Answer:
compare your total monthly incoming with your total monthly outgoing. How balanced is your budget at this point? Remember that you estimated some of your expenditures. You can't know for sure until you actually track your expenses for at least a month and have real numbers to work with.
Step-by-step explanation: Basically it helps you decide how you want to manage your budget
Option C is the best choice to make the best financial decision to make.
What is up front cost?An upfront cost is an initial sum of money owed in a purchase or business venture.
What is Monthly payment?The monthly payment is the amount paid per month to pay off the loan in the time period of the loan.
According to me the best choice is Option C buy used.this is because it's upfront front cost is less comparable to other two.
Whereas, Option A is not good choice, because the monthly payments will be too high .and, Option B is not a good choice.This is because it requires high up-front cost as compared to other and there will be problem, mileage restriction.
For third option, the person will get the car outright once the loan is paid and it's cheaper.
option C is the best financial decision to make.
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Bill spent 60 dollars on fertilizer and weed killer for his lawn. Each pound of fertilizer costs 75 cents, and each ounce of weed killer costs $2.50. What equalion can represent the relationship between the number of pounds of fertilizer bill bought, x , and the number of ounces of weed killer he bought, y?
The equation 0.75x + 2.5y = 60 represents the relationship between the number of pounds of fertilizer (x), and the number of ounces of weed killer (y) that Bill bought with his $60.
Explanation:The question is asking for an equation that could describe how the 60 dollars was spent on fertilizer and weed killer. To represent this relationship, we can set up a linear equation, with x representing the pounds of fertilizer and y representing the ounces of weed killer. Given that each pound of fertilizer costs 75 cents and each ounce of weed killer costs $2.50, the total amount spent on these two items can be represented as 0.75x + 2.5y = 60. This equation depicts how Bill's 60 dollars were allocated to the two items.
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You can find a rectangle's perimeter by ________. A multiplying its length by its width B multiplying its length by 2 and multiplying its width by 2 and adding the products C subtracting its length from its width D dividing its length by 2 and dividing its width by 2 and adding the quotients
Answer:
B
Step-by-step explanation:
the reason why b is the answer is because the perimeter is the outside of the rectangle and you are just ummm yea its b. another way is to add all the sides up and you would get your answer.
Four friends went out to lunch. They each started with the same amount of money, and they each spent 6 They ended with a combined total of 12 How much money did each of them have to start?
Answer:
3 pls pass brainlist
Step-by-step explanation:
because 3*4 is 12
Somebody pls help!!! WILL GIVE BRAINLIEST IF CORRECT!!!!
MAKE IT SIMPLE
A cylinder and a cone have the same diameter: 8 inches. The height of the cylinder is 9 inches. The height of the cone is 18 inches.
Use π = 3.14.
What is the relationship between the volume of this cylinder and this cone? Explain your answer by determining the volume of each and comparing them. Show all your work.
The relationship between the volume of the cylinder and cone is the volume of the cone is 1.5 times bigger than the volume of the cylinder.
Explanation:
The radius is given by [tex]r=\frac{d}{2} =\frac{8}{2} =4[/tex]
The volume of the cone can be determined using the formula,
[tex]V=\pi r^{2} \frac{h}{3}[/tex]
where [tex]\pi=3.14, r=4, h=18[/tex]
Volume of the cone [tex]=\pi r^{2} \frac{h}{3}[/tex]
[tex]=3.14(4)^2\frac{(18)}{3}[/tex]
[tex]=301.44 \ cm^3[/tex]
The volume of the cone is [tex]301.44 \ {cm}^{3}[/tex]
The volume of the cylinder can be determined using the formula,
[tex]V=\pi r^{2} h[/tex]
where [tex]\pi=3.14, r=4, h=9[/tex]
Volume of the cylinder [tex]=\pi r^{2} h[/tex]
[tex]=3.14(16)(9)[/tex]
[tex]=452.16 \ cm^3[/tex]
Thus, the volume of the cylinder is [tex]452.16 \ {cm}^{3}[/tex]
Hence, the relationship between the volume of the cylinder and cone is the volume of the cone is 1.5 times bigger than the volume of the cylinder.
how to solve for 8^x=2 (I know the answer is 1/3 but i have to show work and i don't know the process to solve it)
Answer:
x = 1/3 . . . . math facts or logarithms are involved; take your pick
Step-by-step explanation:
When you are solving for a variable that is in an exponent, logarithms are often useful. Taking the log of both sides of this equation, you have ...
log(8^x) = log(2)
Using the rules of logarithms, that is ...
x·log(8) = log(2)
x = log(2)/log(8) . . . . . divide by the coefficient of x
You can find the value of this on your calculator, and it will tell you the value is 0.333333333333 or as many digits as your calculator displays. That is a clue that the exact answer is probably 1/3.
__
You should recognize that 8 = 2·2·2 = 2^3, so log(8) = 3log(2) and the above solution becomes ...
x = log(2)/(3log(2)) = 1/3
__
Recognizing that 8 = 2^3, you can make that substitution into the original equation to get ...
(2^3)^x = 2
2^(3x) = 2^1
3x = 1 . . . . . . . matching exponents; equivalent to taking logs base 2
x = 1/3 . . . . . . divide by 3
__
All of the above using 2 as a base of exponents is just dancing around the fact that you already know the math fact ...
8^x = 2 = 8^(1/3)
x = 1/3 . . . . . equating exponents; equivalent to taking logs base 8
An SRS of size n was taken to estimate mean body mass index (BMI) for girls between 13 and 19 years of age. The 95% confidence interval obtained had lower limit 19.5 and upper limit 26.3. Which of the following is NOT true? 1. A total of 95% of all teenage girls have BMI between 19.5 and 26.3. 2. The margin of error is 34. 3. The value z in the margin of error is 1.96. 4. A total of 95% of all SRS of size n contain the true mean BMI
Answer:
Option 1 is the only untrue statement of the 4 statements.
The only wrong statement about the confidence interval above is the one about the total of 95% of all teenage girls having BMI between 19.5 and 26.3.
Step-by-step explanation:
The question provides that for the BMI of girls with age between 13 and 19, the 95% confidence interval has a lower limit of 19.5 and an upper limit of 26.3.
We will take the statement one after the other.
Statement 1: A total of 95% of all teenage girls have BMI between 19.5 and 26.3.
This is a wrong statement. It doesn't not follow the definition for confidence interval for a set of sample.
Rather confidence interval, expresses that the true value (mean) exists in the (lower limit, upper limit) range with a confidence level of 95%.
Statement 2: The margin of error is 34.
The margin of error is usually used to calculate the lower and upper limit of the confidence interval.
Basically, the interval is usually between
(Sample mean ± margin of error)
If the sample mean = xbar
And the margin of error = α
xbar - α = lower limit of the confidence interval = 19.5
xbar + α = upper limit of the confidence interval = 26.3
xbar - α = 19.5
xbar + α = 26.3
summing these together
xbar = (19.5+26.3)/2 = 22.9
and the margin of error = (22.9 - 19.5) or (26.3 - 22.9) = 3.4.
So, this statement is correct!
Statement 3: The value z in the margin of error is 1.96.
The margin of error is given as the product of the z-multiplier (from the z-tables) and the sample standard deviation.
The z-multiplier for a 95% confidence interval, as obtained from literature and the z-tables is truly 1.96.
This statement is very true.
Statement 4: A total of 95% of all SRS of size n contain the true mean BMI.
Just like I described the meaning of confidence interval in the explanation under the first statement, this is as close to the meaning of confidence interval as can be. This statement is also very true.
Hence, only statement 1 is not correct of the 4 statements.
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A parking space is in the shape of a parallelogram. The figure below is a model of the parking space. The measure of Angle B is 80°. What are the measures of the other 3 angles?
In a parallelogram with one given angle of 80°, the opposite angle equals 80°, and the two adjacent angles are 100° each, resulting from the properties of parallelograms.
Explanation:The subject of this question is Mathematics, specifically geometry involving angles in a parallelogram. Given that one angle (Angle B) is 80° in a parallelogram, we can determine the measures of the remaining angles using the properties of parallelograms. Adjacent angles in a parallelogram are supplementary, meaning they add up to 180°. Therefore, if Angle B is 80°, then Angle C (adjacent to B) is 180° - 80° = 100°. Since a parallelogram has two pairs of parallel sides, opposite angles are equal. Therefore, Angle D equals Angle B (80°), and Angle A equals Angle C (100°).