In a poll of students at the baseball championship, 78% of the students say that baseball is better than soccer.

(A) Explain why it is not valid conclusion to say that baseball is more popular than soccer at the school.

(B) Suggest a better method of determining which sport is more popular.

a = 85°

Step-by-step explanation:

Method 1

5x = 2x + 57° (An exterior angle of a triangle is equal to the sum of its two interior opposite angles)

3x = 57°

x = 57/3 = 19°

a = 180 - 57 - 2x

a = 180 - 57 -2(19)

a = 85°

Method 2

2x + a + 57° = 180°

2x + a = 123° ==> 1

5x + a = 180°

x = (180° - a)/5 ==> 2

By substitution

2((180° - a)/5) + a = 123°

(360° - 2a)/5 + a = 123°

(360° - 2a)/5 = 123° - a

360° - 2a = 5(123° - a)

360° - 2a = 615° - 5a

-2a + 5a = 615° - 360°

3a = 255°

a = 85°

the equation for the level surface passing through the point (3, 0, 1) is x + 2y - 3z = 0. The given function is f(x, y, z) = (x - y + 2z) / (2x + y - z). We are asked to find an equation for the level surface passing through the point (3, 0, 1).

To find the equation for the level surface, we need to set the function equal to a constant value and solve for z.

Let's start by substituting the coordinates of the given point into the function:

f(3, 0, 1) = (3 - 0 + 2(1)) / (2(3) + 0 - 1)
           = 5 / 5
           = 1

So, the constant value for the level surface passing through (3, 0, 1) is 1.

Now, let's set the function equal to 1 and solve for z:

1 = (x - y + 2z) / (2x + y - z)

Cross-multiplying, we get:

2x + y - z = x - y + 2z

Rearranging the terms, we have:

x + 2y - 3z = 0

Therefore, the equation for the level surface passing through the point (3, 0, 1) is x + 2y - 3z = 0.

In summary, the equation for the level surface passing through the point (3, 0, 1) is x + 2y - 3z = 0.

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Answer:

I hope this helps!

Step-by-step explanation:

1. M is .25

b is 20

so

y= .25x+20

2. y= 3x+2

Answer:

y = 1x + 3

Step-by-step explanation:

Slope (m) =

\( \frac{y_{2} - y_{1}}{x_{2} - x_{1}} \)

Points: (0,3) & (-3,0)

\( \frac{3 - 0}{0 - ( - 3)} \)

\(m = \frac{3}{3} \)

m = 1

y = 1x + b

To find b:

3 = 1(0) + b

3 = b or b = 3

Final Answer: y = 1x + 3

Double Check:

3 = 1(0) + 3

3 = 3

0 = 1(-3) + 3

0 = - 3 + 3

0 = 0

Answer:

y = x + 3

Hope you could get an idea from here.

Doubt clarification - use comment section.

Answer:

D

Sides: a = 7.841   b = 4.369   c = 8

Step-by-step explanation:

Symbols definition of ABC triangle

You have entered side c, angle α, and angle β.

Acute scalene triangle.

Sides: a = 7.841   b = 4.369   c = 8

Area: T = 16.621

Perimeter: p = 20.211

Semiperimeter: s = 10.105

Angle ∠ A = α = 72° = 1.257 rad

Angle ∠ B = β = 32° = 0.559 rad

Angle ∠ C = γ = 76° = 1.326 rad

Height: ha = 4.239

Height: hb = 7.608

Height: hc = 4.155

Median: ma = 5.116

Median: mb = 7.614

Median: mc = 4.928

Inradius: r = 1.645

Circumradius: R = 4.122

Vertex coordinates: A[8; 0] B[0; 0] C[6.65; 4.155]

Centroid: CG[4.883; 1.385]

Coordinates of the circumscribed circle: U[4; 0.997]

Coordinates of the inscribed circle: I[5.736; 1.645]

Exterior (or external, outer) angles of the triangle:

∠ A' = α' = 108° = 1.257 rad

∠ B' = β' = 148° = 0.559 rad

∠ C' = γ' = 104° = 1.326 rad

Starting from the given system of equations:

Since the variable y is already isolated in the second equation, we can use the substitution method to solve the system.

Replace y by 7x on the first equation:

Then. substitute the value x=1 back into the second equation to find the value of y:

Therefore, the solution for this system of equations is:

True: When a form is created based on two or more tables, a relationship must be defined between queries.

True. When a form is created based on two or more tables, a relationship must be defined between queries in order to ensure that the form displays accurate data. Queries are used to pull data from multiple tables and present it in a single view, so it is important to define the relationships between these tables to avoid inconsistencies or errors in the displayed data. This ensures that the data from the related tables can be properly displayed and managed within the form.

When you drag and search a field from an "other" (unrelated) table, a new one-to-many relationship is created from the table in the list and the table from which you dragged the field. This relationship is established by Access, which does not enforce integrity by default.

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Answer:

6 x (n + 1)

Step-by-step explanation:

Answer:

32

Step-by-step explanation:

2*2=4

9*4=36

36-4=32

The first five terms of the sequence are: 1, 5/8, 25/64, 125/512, 625/4096.

The sequence converges and the limit is 8/3.

To find the first five terms of the sequence with [(1−3/8)][∞]=1, we can start by simplifying the expression in the brackets:

(1−3/8) = 5/8

So, the sequence becomes:

(5/8)ⁿ, where n starts at 0 and goes to infinity.

The first five terms of the sequence are:

(5/8)⁰ = 1
(5/8)¹ = 5/8
(5/8)² = 25/64
(5/8)³ = 125/512
(5/8)⁴ = 625/4096

To determine whether the sequence converges, we need to check if it approaches a finite value or not. In this case, we can see that the terms of the sequence are getting smaller and smaller as n increases, so the sequence does converge.

To find its limit, we can use the formula for the limit of a geometric sequence:

limit = a/(1-r)

where a is the first term of the sequence and r is the common ratio.

In this case, a = 1 and r = 5/8, so:

limit = 1/(1-5/8) = 8/3

Therefore, the limit of the sequence is 8/3.

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99% confidence interval for the number of chocolate chips per cookie is

15.4 ± 1.1115

The mean of sample plus and minus the range of that sample constitutes a confidence interval.

Within a specific level of confidence, this is the range of values anticipated to fall within, if the test is repeated.

Number of cookies in the sample n = 55

Mean μ = 15.4

Standard deviation s = 3.2

Confidence = 99%

For 99% confidence interval Z-value = 2.576

Confidence interval

= μ ± Zs/√n

= 15.4 ± 2.576×3.2/√55

= 15.4 ± (8.2432/7.4162)

= 15.4 ± 1.1115

Hence, 15.4 ± 1.1115 is the 99% confidence interval for the number of chocolate chips per cookie.

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The domain for the function in this problem is given as follows:

0 ≤ x ≤ 5.

The domain of the function in this problem is the number of hours, which is represented by numbers between 0 and 5, as the hours cannot be negative and they played for 5 hours, hence the interval is given as follows:

0 ≤ x ≤ 5.

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Answer:

7/8

Step-by-step explanation:

Use this format for the problem:

Total pounds of candy you received = Pounds of candy received from Grandmother + Pounds of candy received from Sister + Pounds of Candy received from Best Friend

1. Simplify the expression

\(\frac{1}{4}+ \frac{1}{2}+ \frac{1}{8}\)

Find the lowest common denominator:

\(\frac{\left(1\cdot 2\right)}{\left(4\cdot 2\right)}+\frac{\left(1\cdot 4\right)}{\left(2\cdot 4\right)}+\frac{1}{8}\)

Multiply the denominators:

\(\frac{\left(1\cdot 2\right)}{8}+\frac{\left(1\cdot 4\right)}{8}+\frac{1}{8}\)

Multiply the numerators:

\(\frac{2}{8}+\frac{4}{8}+\frac{1}{8}\)

Combine the fractions:

\(\frac{\left(2+4+1\right)}{8}\)

Combine the numerators:

\(\frac{7}{8}\)

Hence, the answer is 7/8.

___________

Why learn this

- Let's say you invite ten friends over for movie night and order four pizzas to split. How do you divide the pizza evenly so everyone gets the same amount of pizza? If each section of the couch can fit 1+1/5 people, how many sections would there need to be to accommodate all of your friends? The whole world is made up of little bits and pieces that are part of something larger, and the key to understanding them is fractions.

Fractions are the mathematical representation of any whole thing that is made up of multiple parts. Knowing how to manipulate them using operations like addition, subtraction, multiplication, and division is one of the most widely applicable math skills in everyday situations and provides an important foundation for other math concepts you will encounter.

Terms and topics

__________________

Level:  5th grade

Unit: Operations with fractions

The formula to determine the total cost of the monthly rental is R300 + (Number of minutes beyond 500 * R0.50)

The formula to calculate the total cost (in rands) for CALL PACKAGE 2 can be expressed as:

Total cost (in rands) = Monthly rental + (Number of minutes beyond the free minutes * Cost per minute)

In this case, the monthly rental for PACKAGE 2 is R300, and the first 500 minutes are free. Calls beyond the free minutes cost R0.50 per minute.

Therefore, the formula becomes:

Total cost (in rands) = R300 + (Number of minutes beyond 500 * R0.50)

This formula calculates the total cost by adding the monthly rental fee to the cost of the minutes used beyond the free minutes, which is calculated by multiplying the number of minutes beyond 500 by the cost per minute, R0.50.

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We can express an inequality that describes this situation like this:

From the statement of the question, we are told that Mr. Hall has $216, then he can spend no more than this amount, then we can express:

spent money ≤ available money

spent money ≤ 216

Now, from the given information, we know that the money is spent buying a bookshelf and some books, then the spent money would be the cost of the bookshelf plus the total cost of all the books.

spent money ≤ 216

Bookshelf cost + books cost ≤ 216

From the statement of the question, we know that the bookshelf cost equals $81 and that each book costs $3, the total books cost equals the cost per book times the number of books x, then we rewrite the expression like this:

Bookshelf cost + books cost ≤ 216

81 + 3*x ≤ 216

From this inequality, if we solve for x, we get:

81 - 81 +3x ≤ 216 - 81

3x ≤ 135

3x/3 ≤ 135/3

x ≤ 27

Then, the answer is x ≤ 27

The probability of seeing exactly 2 meteors during the observation period is approximately 0.1465.

The probability of seeing at least one meteor during the observation period is 1 - e^(-16).

The expected number of meteors during the observation period is 4.

The standard deviation of the number of meteors during the observation period is 2.

To find the requested information, we need to use the properties of a Poisson process. Let's calculate each value step by step:

a) The probability of seeing exactly 2 meteors during the observation period can be calculated using the Poisson probability formula:

P(X = k) = (e^(-λ) * λ^k) / k!

where λ is the intensity of the Poisson process. In this case, λ = 4 (since the intensity is given as 4 per hour) and k = 2.

P(X = 2) = (e^(-4) * 4^2) / 2!

P(X = 2) ≈ 0.1465

b) The probability of seeing at least one meteor during the observation period can be calculated using the complement rule:

P(at least one meteor) = 1 - P(no meteor)

Since the intensity is 4 meteors per hour, the probability of no meteor in one hour is:

P(no meteor) = e^(-4)

To calculate the probability of no meteor during the entire 4-hour observation period, we raise the probability of no meteor in one hour to the power of 4:

P(no meteor) = (e^(-4))^4 = e^(-16)

P(at least one meteor) = 1 - e^(-16)

c) The expected number of meteors during the observation period can be calculated using the mean of a Poisson distribution. The mean (expected value) of a Poisson distribution is equal to the intensity (λ).

In this case, the expected number of meteors is 4 (since λ = 4).

d) The standard deviation of the number of meteors during the observation period can be calculated using the square root of the variance of a Poisson distribution. The variance of a Poisson distribution is equal to the intensity (λ).

In this case, the standard deviation is the square root of 4, which is 2.

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If there are 6 students and one is selected for best student and another is selected for runner up, then 15 different ways that we can arrange the students

Total number of students in the class = 6 students

Number of students for best student = 1 student

Number of students for runner up = 1 students

Total number of students needed = 2

Here we have to use the combination

6\(C_2\) = 6! / 2!(6 - 2)!

= 6! / 2! × 4!

Split the terms and cancel it

= 6 × 5 / 2 × 1

Multiply the terms

= 30 / 2

Divide the numbers

= 15 combinations

Therefore, there are 15 combinations

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The correct choice for the sentence is option c: "Their, to lose."

In the sentence, referring to multiple museums, the possessive pronoun "their" is used to indicate ownership, and the phrase "to lose" appropriately conveys the risk faced by the museums.

The subject of the sentence is "Museums," which is a plural noun. Since the sentence is discussing multiple museums, the possessive pronoun "their" is the correct choice to show ownership. Using "their" indicates that the museums collectively possess something, in this case, their fickle goodwill.

Additionally, the phrase "to lose" accurately portrays the risk faced by the museums. It implies that the museums are at risk of losing their fickle goodwill due to factors like the fickleness of governments and the public. Therefore, option c, "Their, to lose," provides the appropriate usage of the possessive pronoun and conveys the intended meaning of the sentence.

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Answer:

what is the question?

Step-by-step explanation:

Answer:

f(x)x+2

Step-by-step explanation:

because quadrant 1 which is the y and quadrant 4 which is x are positive, therefore. f(x) x+2.

Answer:

-15.

Step-by-step explanation:

G(-5) = 2(-5) - 1

= -10 - 1

= -11

H(-11) = -11 - 4

= -15

Hope this helps!

Answer:

h(g(-5))= -15

Step-by-step explanation:

We are asked to find h(g(-5)).

First, we must find g(-5).

We know that g(x)=2x-1. Therefore, to find g(-5), we must plug -5 in for x.

g(x)= 2x-1

g(-5)= 2(-5) -1

Multiply 2 and -5.

g(-5)= -10 -1

Subtract 1 from -10.

g(-5)= -11

Now, we can substitute -11 in for g(-5).

h(g(-5)

g(-5)= -11

h(-11)

Now, we must find h(-11).

We know that h(x)= x-4. So, we can plug -11 in for x.

h(x)= x-4

h(-11)= -11-4

Subtract 4 from -11.

h(-11)= -15

h(g(-5)=  -15

The solution of the given system using Gaussian elimination is \($\left(\frac{1085}{1582}, \frac{375}{1582}, -\frac{155}{567}\right).$\)

The given linear equation is:

\(x-1/7+y-2/8+z-3/4= 0x+y+z+z= 6x+2/3+2y+z-3/3 = 5\)

The system of equations can be represented in the matrix form as:

\($$\begin{bmatrix}1 & -\frac{1}{7} & \frac{1}{4} & \\ 1 & 1 & 1 & 1\\ 1 & 2 & 1 & 2\end{bmatrix}\begin{bmatrix}x \\ y\\ z \end{bmatrix} = \begin{bmatrix}0\\6\\5\end{bmatrix}$$\)

Gaussian elimination method:The augmented matrix for the given system is given by,

\($$\left[\begin{array}{ccc|c}1 & -\frac{1}{7} & \frac{1}{4} & 0\\1 & 1 & 1 & 6\\1 & 2 & 1 & 5\\\end{array}\right]$$Subtracting row1 from row2, and row1 from row3,$$\left[\begin{array}{ccc|c}1 & -\frac{1}{7} & \frac{1}{4} & 0\\0 & \frac{8}{7} & \frac{3}{4} & 6\\0 & \frac{15}{7} & \frac{3}{4} & 5\\\end{array}\right]$$\)

Multiplying row2 by 15 and subtracting 8 times row3 from it,

\($$\left[\begin{array}{ccc|c}1 & -\frac{1}{7} & \frac{1}{4} & 0\\0 & 1 & \frac{15}{28} & \frac{45}{28}\\0 & \frac{15}{7} & \frac{3}{4} & 5\\\end{array}\right]$\)

Subtracting row2 from row1 and 15 times row2 from row3,

\($$\left[\begin{array}{ccc|c}1 & 0 & \frac{29}{28} & \frac{45}{49}\\0 & 1 & \frac{15}{28} & \frac{45}{28}\\0 & 0 & \frac{99}{28} & -\frac{465}{98}\\\end{array}\right]$$\)

Multiplying row3 by 28/99,

we get,

\($$\left[\begin{array}{ccc|c}1 & 0 & \frac{29}{28} & \frac{45}{49}\\0 & 1 & \frac{15}{28} & \frac{45}{28}\\0 & 0 & 1 & -\frac{155}{567}\\\end{array}\right]$$\)

Subtracting 29/28 times row3 from row1 and 15/28 times row3 from row2,

\($$\left[\begin{array}{ccc|c}1 & 0 & 0 & \frac{1085}{1582}\\0 & 1 & 0 & \frac{375}{1582}\\0 & 0 & 1 & -\frac{155}{567}\\\end{array}\right]$$\)

The given system is

\($x = \frac{1085}{1582}, y = \frac{375}{1582},$ and $z = -\frac{155}{567}$\)

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Option d is false. The study design already compared students who took three versus four years of math.

The study design compared the acceptance rates of 300 students who were required to take a fourth year of math and 300 students who were not permitted to take a fourth year. The results showed that those who took four years had a higher acceptance rate at NC State. The design could be improved by randomly assigning students to take a third or fourth math class to establish cause and effect. Option b suggests that a better inference could be made by taking an SRS from high schools across the state, which would increase the generalizability of the study. Option c is true, as the design included both random assignment and random selection. Option d is false because it suggests an observational study on students who have already made the decision to take three or four years of math, which would not establish causation.

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Answer:

Step-by-step explanation:

23.5% OF 128= ???

so,

% value is 100 and word "of" means multiplication (x)

now,

23.5% OF 128

=> 23.5 x 1/100 x 128

=> 23.5/100 x 128

=> 3,008/100

=> 30.08

so, the answer is 30.08

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The smallest volume  of ice cream in Brand A.

Given:

Brand A:

height of cone = 15 cm

radius of cone base = 4 cm

Brand B:

height of cone = 12 cm

radius of cone base = 5 cm

Volume of cone = 1/3πr² h

Volume of ice cream A = ( π \(4^2\) (15) ) /3 = 240 π/3 = 80 π

Volume of ice cream B = ( π \(5^2\) (12) ) /3 = 300 π/3 = 100 π

In comparison, you can figure out which one would give her more volume of ice cream in Brand A.

Therefore, the correct answer is option A. Brand A.

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Answer:

29

2

.75

Step-by-step explanation:

PLEASE Give Everything

Answer:

Step-by-step explanation:

Inequality "y is less than or equal to 5 and is greater than or equal to -2":

This is the interval:

The endpoints are:

Product of the endpoints:

Answer choices:

y is less than or equal to 5 and greater than or equal to 2.

The expression is

\(\\ \sf\longmapsto -2\leqslant y\leqslant 5\)

Endpoints=-2 and 5

Product

\(\\ \sf\longmapsto -2(5)=-10\)

Option C is correct

The 97% confidence interval for a sample of 204 soda cans with a mean of 12.05 ounces and a standard deviation of 0.08 ounces is approximately (12.026, 12.074) ounces.

To find the 97% confidence interval, follow these steps:

1. Identify the sample size (n=204), sample mean (X-bar=12.05), and standard deviation (σ=0.08).
2. Determine the appropriate z-score for a 97% confidence interval, which is 2.17 (from a standard normal distribution table).

3. Calculate the standard error (SE) by dividing the standard deviation by the square root of the sample size: SE = σ/√n = 0.08/√204 ≈ 0.0056.

4. Multiply the z-score by the standard error: 2.17 * 0.0056 ≈ 0.0122.

5. Subtract this product from the sample mean for the lower bound: 12.05 - 0.0122 ≈ 12.026.

6. Add this product to the sample mean for the upper bound: 12.05 + 0.0122 ≈ 12.074.

Thus, the 97% confidence interval is approximately (12.026, 12.074) ounces.

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Answer:

\(p=-6.25\) or \(p=\displaystyle-\frac{25}{4}\)

Step-by-step explanation:

\(-160=22+8(3p-4)\)

Our goal here is to isolate p on one side of the equation. We will do this by performing inverse operations on both sides.

Subtract 22 from both sides:

\(-160-22=22+8(3p-4)-22\\-182=8(3p-4)\)

Divide both sides by 8:

\(-22.75=3p-4\)

Add 4 to both sides:

\(-22.75+4=3p-4+4\\-18.75=3p\)

Divide both sides by 3:

\(-6.25=p\)

You can also convert this into a fraction:

\(p=\displaystyle-\frac{25}{4}\)

I hope this helps!