Two towers are constructed, each by stacking 30 segments of concrete vertically. The height (in inches) of a randomly selected segment is uniformly distributed in the interval (35.5, 36.5). A roadway can be laid across the 2 towers provided the heights of the 2 towers are within 4 inches of each other. Find the probability that the roadway can be laid. Be careful to justify the steps in your argument, and state whether the probability is exact or approximate.

Answer:

There is 30 2 pt questions and 10 4 pt questions

Step-by-step explanation:

x  is number of two-point questions

y is number of four-point questions

There is a total of 100 points.

There is a total of 40 questions.

Now, we solve by substitution

Plug 30 back in to solve for y

The graph that shows a proportional relationship that passes through the point (2, 1) is Graph A.

A line is defined as a shortest distance between two points. In order to determine the graph that shows a proportional relationship that passes through the point (2, 1), we will need to multiply the coordinate by a scale factor and determine whether the point is on the line.

Using a factor of 2;

New coordinate = 2(2, 1)

New coordinate = (4, 2)

From the given graph, you can see that the only graph that has the coordinate point (4, 2) is the Graph A.

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Answer:

3² = 9

Step-by-step explanation:

45 =  3² × 5

81  = 3⁴

================

HCF = 3²

Answer:

Step-by-step explanation:

the student buys a total of 8 magazines for $14.00

x+y = 8

x = 8-y

2x+1.6y = 14

2(8-y)+1.6y = 14

16-2y+1.6y = 14

16-0.4y = 14

0.4y =16-14 = 2

y = 2/0.4 = 5

x = 8-y = 3

The correct equation best represents the situation is,

⇒ x + y = 8

And, 2x + 1.60y = 14.00

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

A student buys (x) fashion magazines and (y) sports magazines.

And, Each fashion magazine costs $2.00 and each sports magazine costs $1.60.

Here, The student buys a total of 8 magazines for $14.00.

Hence, We can formulate;

⇒ x + y = 8

And, 2x + 1.60y = 14.00

Thus, The correct equation best represents the situation is,

⇒ x + y = 8

And, 2x + 1.60y = 14.00

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To factor the polynomial x^2-4x-12 using the method of factoring by grouping, we can first find two numbers whose product is -12 and whose sum is -4. These numbers are -6 and 2, because (-6) * (2) = -12 and (-6) + (2) = -4.

Using this information, we can rewrite the polynomial as:

x^2 - 6x + 2x - 12

Next, we can group the first two terms and the last two terms and factor out the common factors:

x(x - 6) + 2(x - 6)

Notice that both terms have a common factor of (x - 6), so we can factor it out:

(x - 6)(x + 2)

Therefore, the factored form of the polynomial x^2-4x-12 is (x-6)(x+2).

So, Simon should write the value -2 on the line.

Answer:

9y - 45

Step-by-step explanation:

9(−5+y)

=(9)(−5+y)

=(9)(−5)+(9)(y)

=−45+9y

=9y−45

Answer: =9y−45

Step-by-step explanation:

=(9)(−5+y)

=(9)(−5)+(9)(y)

=−45+9y

Answer:

C!

Step-by-step explanation:

The equation of the plane through the points (6,3,1),(4,0,2) and is perpendicular to the plane 2z=5x+4y is given by -2(x - 6) + 9(y - 3) + 22(z - 1) = 0.

Given that the two points are A(6, 3, 1) and B(4, 0, 2). First, we find the vector AB = B - A = (-2, -3, 1). We have a plane perpendicular to the plane 2z = 5x + 4y, which means that the normal vector to the plane is <5, 4, -2>.

Now let us find the equation of the plane containing A and is perpendicular to the given plane. We know that the normal vector to this plane is perpendicular to both the plane and AB.

Vector n × AB = <5, 4, -2> × <-2, -3, 1>

= <-2, 9, 22>.

The normal vector to the plane through A is given by <-2, 9, 22>.

The equation of the plane is -2(x - 6) + 9(y - 3) + 22(z - 1) = 0.

The equation of the plane through the points (6,3,1),(4,0,2) and is perpendicular to the plane 2z=5x+4y is given by -2(x - 6) + 9(y - 3) + 22(z - 1) = 0.

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Answer:

-23m-18m^4

Step-by-step explanation:

-10m+2m^4-13m-20m^4

(-10m+-13m)+(2m^4-20m^4)

-23m+-18m^4

-23m-18m^4

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The probability that the committee will consist of all faculty members is 1/5.

To find the probability that the committee will consist of all faculty members,

we need to calculate the total number of possible committees and the number of committees that consist of all faculty members.
The total number of possible committees can be calculated using combinations.

We have 5 faculty volunteers, and we need to choose 4 members from this group.

This can be written as C(5,4), which is equal to 5.
The number of committees that consist of all faculty members is simply 1, as there is only one way to select all 4 members from the faculty volunteers.
The probability that the committee will consist of all faculty members is the number of committees that consist of all faculty members divided by the total number of possible committees.

In this case, it is 1/5.
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A system of equations that could be used to  determine the number of cans of soup purchased and the number of frozen dinners  purchased is:

350x + 500y = 4800

y = 2x

x = number of cans of soup purchased

y = number of frozen dinners purchased.

The system of equations are known as simultaneous equations. Simultaneous equations are group of equations that have to be solved together in order to determine the required values.

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Answer:

between 10 and 12

Step-by-step explanation:

Given the measure of angles:

m∠B = 70°

m∠C = 60°

m∠A = 50°

Following this information, since the side lengths are directly proportional to the angle measure they see:

Angle B is the largest angle. Therefore, side AC is the longest side of the triangle since it is opposite of the largest angle.

Angle C is the smallest angle, so the side AB is the shortest side.

Therefore, side BC must be between 10 and 12 inches.

Answer:

The total length of the string is 7.85 feet and  the center should be 2.236 feet far the string be nailed into the base

Step-by-step explanation:

Circumference of ellipse = \(\pi(a+b)\)

Circumference of semi-ellipse = \(\frac{\pi(a+b)}{2}\)

we are given that The opening is to have a height of 2 feet at the center and a width of 6 feet along the base.

So, \(a = \frac{6}{2}=3 , b = 2\)

Circumference of semi-ellipse =\(\frac{3.14(3+2)}{2}=7.85 feet\)

Distance from center =\(\sqrt{a^2-b^2}=\sqrt{3^2-2^2}=2.236 feet\)

Hence the total length of the string is 7.85 feet and  the center should be 2.236 feet far the string be nailed into the base

Answer:

Function A

Step-by-step explanation:

doesn't have vertical points

I agree with the other persons answer.

Answer:

Step-by-step explanation:

9514 1404 393

Answer:

 45.6

Step-by-step explanation:

9514 1404 393

Answer:

 45.6

Step-by-step explanation:

There is a geometric mean rule that is derived from the fact that all of these right triangles are similar. It tells you the side (27) is the geometric mean of the hypotenuse (z) and the segment of it adjacent to that side (16).

 27 = √(16z)

 z = 27²/16 = 45.5625

 z ≈ 45.6

!

Answer:

y = x - 12

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = 1 , then

y = x + c ← is the partial equation

To find c substitute (13, 1) into the partial equation

1 = 13 + c ⇒ c = 1 - 13 = - 12

y = x - 12 ← equation of line

Answer:

D. 29 I just know the awnser sorry

To find the value of f(−2), we substitute −2 for x in the function f(x):

f(−2) = 4(-2)^2 − 3(-2) + 7

= 4(4) − 3(2) + 7

= 16 − 6 + 7

= 11

Therefore, f(−2) = 11.

Answer:

45

Step-by-step explanation:

Answer: 5 players go in two groups

Answer:: the equation is 7m + 19

Step-by-step explanation:

Therefore, the exact values of the six trigonometric functions of the angle are: sin = 5/√29, cos = -2/√29, tan = -5/2, csc = √29/5, sec = -√29/2, cot = -2/5.

To determine the exact values of the six trigonometric functions of the angle, we can use the coordinates of the point (-4, 10) and apply the definitions of the trigonometric functions.

Let's label the given point as P(-4, 10). To find the values of the trigonometric functions, we need to determine the relevant sides of the right triangle formed by the point P and the origin.

First, let's calculate the hypotenuse of the triangle using the Pythagorean theorem:

hypotenuse = √((-4)^2 + 10^2) = √(16 + 100) = √116 = 2√29

Now, let's determine the values of the trigonometric functions:

Sine (sin) = opposite/hypotenuse = 10/(2√29) = 5/√29

Cosine (cos) = adjacent/hypotenuse = -4/(2√29) = -2/√29

Tangent (tan) = sine/cosine = (5/√29)/(-2/√29) = -5/2

Cosecant (csc) = 1/sin = 1/(5/√29) = √29/5

Secant (sec) = 1/cos = 1/(-2/√29) = -√29/2

Cotangent (cot) = 1/tan = 1/(-5/2) = -2/5

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Answer:

a

Step-by-step explanation:

The Fourth coordinate is (4, 3) and 35 unit squared.

A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.

Given:

From the graph the fourth coordinate of rectangle is

At x axis = 4

and, y- axis = 3

So, the Area of rectangle ABCD is

= lw

= 7 x 5

= 35 unit squared.

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The most appropriate units to describe the cost of the sandbox would indeed be dollars.

When describing the cost of an item or service, it is essential to use the unit that represents the currency being used for the transaction. In this case, the total cost of the sand for the school's sandbox is given in dollars. To maintain consistency and clarity, it is best to express the cost in the same unit it was provided.

Using dollars as the unit for the cost allows for clear communication and understanding among individuals involved in the transaction or discussion. Dollars are widely recognized as the standard unit of currency in many countries, including the United States, where the dollar sign ($) is commonly used to denote monetary values.

Using meters, the unit for measuring the dimensions of the sandbox, to describe the cost would be inappropriate and could lead to confusion or misunderstandings. Mixing units can cause ambiguity and hinder effective communication.

Therefore, it is most appropriate to describe the cost of the sand in dollars, aligning with the unit of currency provided and commonly used in financial transactions. This ensures clarity and facilitates accurate comprehension of the cost associated with the sand purchase for the school's sandbox.

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Answer:

y = - 9, y = 3

Step-by-step explanation:

Calculate distance d using the distance formula

d = \(\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }\)

with (x₁, y₁ ) = (2, - 3) and (x₂, y₂ ) = (10, y)

d = \(\sqrt{(10-2)^2+(y+3)^2}\)

   = \(\sqrt{8^2+(y+3)^2}\)

Given distance between points is 10, then

\(\sqrt{64 +(y+3)^2}\) = 10 ( square both sides )

64 + (y + 3)² = 100 ( subtract 64 from both sides )

(y + 3)² = 36 ( take the square root of both sides )

y + 3 = ± \(\sqrt{36}\) = ± 6 ( subtract 3 from both sides )

y = - 3 ± 6 , thus

y = - 3 - 6 = - 9

y = - 3 + 6 = 3

If p > 5 is prime and p is divided by 10, then the remainders are 1, 3, 7, or 9

The given information, we know that p is a prime number greater than 5, and that p is divided by 10. This means that p must end in either 0 or 5. since those are the only digits that allow for a number to be divisible by 10.

However, we also know that p is prime, which means it cannot be divisible by any number other than 1 and itself. This rules out the possibility of p ending in 0. since any number ending in 0 is divisible by 10 (and therefore not prime).

Therefore, p must end in 5. This means that p can be written in the form:

p = 10n + 5

where n is some integer. Now, let's consider what happens when we divide p by 10:

p/10 = (10n + 5)/10 = n + 0.5

Since p/10 is not an integer (it has a decimal component of 0.5), we know that p cannot be evenly divided by 10. Therefore, when p is divided by 10, there must be a remainder.

To determine what possible remainders there could be, we can look at the possible values for the last digit of p. Since p ends in 5, the last digit can only be 1, 3, 7, or 9 (since these are the only digits that, when multiplied by 5 and added to 10n, result in a number ending in 5).

Therefore, if p > 5 is prime and p is divided by 10, the remainder must be either 1, 3, 7, or 9.

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Answer:

The answer is 1

Step-by-step explanation:

28:7=4

√9=3

4-3=1

Answer:

1

Step-by-step explanation:

Square root of 9=3

28/7= 4

So 4-3=1

Answer is 1

Hope it is correct

A correlation coefficient is a statistic that tells us the strength and direction of the linear relationship between two variables.

The correlation coefficient is a measure of the degree of association between two variables. It quantifies how closely the data points align along a straight line. The coefficient can range from -1 to +1, where -1 represents a perfect negative linear relationship, +1 represents a perfect positive linear relationship, and 0 indicates no linear relationship.

The sign of the coefficient indicates the direction of the relationship, while the magnitude indicates the strength. A correlation coefficient of 0 does not necessarily imply the absence of any relationship; it only means that there is no linear association between the variables. It is important to note that correlation does not imply causation, as other factors may be influencing the relationship.

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Answer:

34.3%

Step-by-step explanation: