The reading speed of second grade students is approximately normal, with a mean of 88 words per minute (wpm) and a standard deviation of 12 wpm. a) What is the probability a randomly selected student will read more than 95 words per minute? b) What is the probability that a random sample of 12 second grade students results in a mean reading rate of more than 95 words per minute? c) What is the probability that a random sample of 24 second grade students results in a mean reading rate of more than 95 words per minute? d) What effect does increasing the sample size have on the probability? Provide an explanation for this result.

slopes of two parallel lines are equal

from the equation y=3x-1, slope =3

using slope m=3 and point (-1,3) , we find the y intercept

y=mx+b

3=3(-1) +b

b=6

plugging m=3 and b=6 in slope intercept form to get the equation

y=3x+6

Answer:

Yes, there is a proportional relation.

Step-by-step explanation:

Given,

Ounces of flour for 8 ounces of milk = 15,

So, the ounces for 1 ounces of milk = [tex]\frac{15}{8}[/tex]

Let y be the ounces of flour for x ounces of milk,

∵ The ounces for x ounces of milk = [tex]\frac{15}{8}x[/tex]

[tex]\implies y = \frac{15}{8}x-----(1)[/tex]

Which is the required relation,

Since,

[tex]0=\frac{15}{8}(0)[/tex] ( True )

I.e. line [tex]y=\frac{15}{8}x[/tex] passes through the origin,

Hence, the relationship (1) is proportional.

The number of pencils  she can  buy while staying in her price range is from 12 to 18 pencils

let x represent  the number of pencils she can buy .

First step is to calculate the Total cost

Total cost=2($3.25) + x($0.75)

Total cost=$6.50 + $0.75x

Second step is to write the inequality

Inequality=15 ≤ 6.50 + 0.75p ≤ 20

Third step is to substract $6.50

8.50 ≤ 0.75p ≤ 13.50

Fourth step is to divide each  by 0.75

8.50/0.75=11.33

13.50/0.75=18

11.33 ≤ x ≤ 18

Therefore   The number of pencils  she can  buy while staying in her price range is  from  12 to 18 pencils

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https://brainly.com/question/2189473

Final answer:

The radius of the world's largest pizza with a circumference of 215 feet, using an approximation for pi of 3.14, is approximately 34.2 feet when rounded to the nearest tenth.

Explanation:

To find the radius of the world's largest pizza given its circumference of 215 feet, we use the formula for the circumference of a circle: C = 2πr, where C is the circumference, π (pi) is approximately 3.14, and r is the radius. We rearrange this formula to solve for the radius: r = C / (2π).

Substituting the given values into this equation, we get:

r = 215 feet / (2 × 3.14)

r = 215 / 6.28

r = 34.2356688 feet

Rounding to the nearest tenth gives us:

r ≈ 34.2 feet

The Triangle Inequality Theorem dictates that the impossible distance from town A to town C, given the distances from A to B (5 miles) and B to C (4 miles), is (E) 10 miles because it exceeds the sum of the other two sides.

The question pertains to the Triangle Inequality Theorem, which in the context given, states that the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side. Here we have two sides measured as 5 miles (from town A to town B) and 4 miles (from town B to town C).

To identify which distance could not be from town A to town C, we recognize that the third side must be less than the sum of the other two sides (5 miles + 4 miles = 9 miles), but also greater than the absolute difference between those two sides (5 miles - 4 miles = 1 mile). Therefore, the only impossible distance for the third side, based on the options provided, is 10 miles, as it exceeds the sum of the other two sides.

Options A (1 mile), B (4 miles), C (8 miles), and D (9 miles) all satisfy the Triangle Inequality Theorem and could represent the distance from town A to town C. Hence, the answer is E (10 miles).

Answer:

its 2/5 i took the test

Step-by-step explanation:

Mrs. Winkle downloaded 93 songs and Mr. Winkle downloaded 127 songs, which equals the total of 220 songs they downloaded together.

The total number of songs downloaded by Mr. and Mrs. Winkle is 220. If Mr. Winkle downloaded 34 more songs than Mrs. Winkle, we can set up a system of equations to solve for the number of songs each downloaded. Let x represent the number of songs Mrs. Winkle downloaded, so Mr. Winkle downloaded x + 34 songs.

The equation representing the total number of songs downloaded by both is:

x + (x + 34) = 220

Combining like terms gives us:

2x + 34 = 220

Subtracting 34 from both sides, we get:

2x = 186

Dividing both sides by 2, we find:

x = 93

So, Mrs. Winkle downloaded 93 songs and Mr. Winkle downloaded 93 + 34, which is:

Mr. Winkle downloaded 127 songs.

Answer: Tom

Step-by-step explanation:

time = distance / speed

Samma : 200/25.98 = 7.70 meters per second

Tom : 100 / 12.54 = 7.97 meters per second

so the faster runner is Tom

Final answer:

The difference between a linear equation in one variable and in two variables lies in the number of variables and their graphical representation: a linear equation in one variable like 'x + 5 = 0' represents a point on the x-axis, while a linear equation in two variables like 'y = 2x + 3' represents a straight line on a plane.

Explanation:

Difference between a Linear Equation in One Variable and Two Variables

The main difference between a linear equation in one variable and a linear equation in two variables is the number of variables involved and how they can be graphically represented. A linear equation with one variable can be written in the form ax + b = 0, where a and b are constants, and x is the variable. This equation represents a single straight line in a two-dimensional space, where all points on the line have the same x-coordinate. For example, x + 5 = 0 is the equation of a vertical line represented by the point where x is -5.

On the other hand, a linear equation in two variables typically has the form y = mx + b, which represents a line in two-dimensional space where m is the slope of the line and b is the y-intercept. Here, x is the independent variable and y is the dependent variable. As x changes, y changes in a way that the relationship between them remains constant, making the graph a straight line. For example, y = 2x + 3 is an equation of a line with a slope of 2 and a y-intercept of 3.

When comparing the two types of equations, it's clear that linear equations in two variables can represent a broader range of relationships between two quantities, allowing for a visual representation of the relationship as a slope on a graph.

Rebecca will travel another 610 miles on her way back from Omaha to Indianapolis, not -610 miles, as distance is a scalar quantity and does not adopt a negative sign. The total round trip distance is therefore 1220 miles.

When Rebecca returns home from her trip to Omaha, Nebraska, she will indeed travel another 610 miles. However, the use of -610 miles might be misleading in this context. In mathematics, especially when discussing distance, the concept of negative numbers often represents direction rather than decrement. Therefore, saying Rebecca will travel -610 miles could imply direction, but since she is returning to her starting point, the actual distance traveled is 610 miles, the same as her outbound trip.

Distance, as a quantity, is scalar and therefore always non-negative. When keeping track of total distance travelled, irrespective of direction, the concept of positive and negative doesn’t apply—the distance simply adds up. So, the total distance Rebecca travels (going to Omaha and then back to Indianapolis) would be 1220 miles. This demonstrates the concept of absolute value in mathematics, where the focus is on the magnitude of a number without regard to its sign.