Bill takes the commuter train to work every day. during the morning commute, a train arrives every 25 min. if bill arrives at the station at a random time for the morning commute, what is the probability that he will have to wait at least 5 min for a train?

To solve for the measure of the central angle (x) in the arc length formula, rearrange the formula such that [tex]x = (L/2\pi r) * 360.[/tex] This method allows you to determine the degree measure of the arc once you know the arc length (L) and the radius (r) of the circle.

Given that the formula for finding the length of an arc in a circle is [tex]L=2\pi r(x/360)[/tex], you can solve for x if L and r are known. In this formula, r stands for the radius of the circle and x represents the measure of the central angle of the arc in degrees. So, to isolate x, you would need to rearrange the formula, giving us: [tex]x = (L/2\pi r) * 360.[/tex]

This effectively means that the degree measure of the arc (x) is equivalent to the ratio of the arc length to the circumference (which is 2πr) times 360 degrees.

For instance, let's consider a circle where r=5 and the arc length L has a value of 10 units. We would substitute these values into our newly rearranged formula thus: [tex]x = (10/2\pi *5) * 360 = 36[/tex] degrees. This tells us that the central angle for this particular arc on a circle with a radius of 5 units is 36 degrees.

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The required months are x = 0.60 months where at the cost become same.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

Here,
Let the total cost be y and the month be x
Apartment A has a $1000 security deposit and costs $1200 each month.
y = 1200x +1000 - - - - - (1)
Apartment B has $1500 and costs $1175 each month.
y = 1175x + 1500
From equation 1
1200x + 1000 = 1175x + 1500

1200x - 1175x = 500
825x = 500
x = 500 / 825
x = 0.60 months,
y = 1200*0.60 + 1000
y = 1,720

Thus, the required months are x = 0.60 months where the cost becomes the same.

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Answer-

[tex]\boxed{\boxed{QR=12}}[/tex]

Solution-

Triangle Midpoint Theorem-

The line segment connecting the midpoints of two sides of a triangle is parallel to the third side and is congruent to one half of the third side.

As given in the question,

QV = SV, so V is the mid point of QS,

SU = RU, so R is the mid point of RS.

Hence, UV is the line joining the midpoints of QS and RS.

Applying Triangle Midpoint Theorem,

[tex]\Rightarrow UV=\dfrac{1}{2}QR[/tex]

[tex]\Rightarrow QR=2UV[/tex]

[tex]\Rightarrow QR=2\times 6[/tex]

[tex]\Rightarrow QR=12[/tex]

Therefore, the side length of QR is 12 units.

From the graph, it is obtained that there is a reflection on the x-axis.

It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.

It is obtained that, the x-coordinate of a point that is reflected across the x-axis stays constant, but the y-coordinate is assumed to be the additive inverse. The x-axis' reflection of point (x, y) is (x, -y).

The new reflected graph's reflection equation will be y=f(x) y = f (x) given an equation of the form y=−f(x) y = − f ( x ). To put it another way, the function may be simply multiplied by 1, which results in a curve that is mirrored across the x-axis.

Thus, from the graph, it is obtained that there is a reflection on the x-axis.

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An open sentence is a mathematical sentence that has an unknown.

The solution set for t is (a) Null set

The equation is given as:

[tex]\mathbf{2t - t = 0}[/tex]

The set is given as:

[tex]\mathbf{\{1,2,3,4\}}[/tex]

First, we solve for t in: [tex]\mathbf{2t - t = 0}[/tex]

[tex]\mathbf{t = 0}[/tex]

The above equation implies that, the value of t is 0

0 is not represented in the given set, [tex]\mathbf{\{1,2,3,4\}}[/tex]

Hence, the solution set for t is (a) Null set

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The measure of angle TSK is 130°, because it is an inscribed angle that intercepts the same arc as angle TRK, and angle TRK is half the measure of the central angle that intercepts the same arc.

The correct answer is option C.

The center of the circle is S, and the measure of angle TRK is 32.5°. We want to find the measure of angle TSK.

We can use the following theorem to solve this problem:

Inscribed Angle Theorem: An inscribed angle is half the measure of the central angle that intercepts the same arc.

In other words, if an angle is inscribed in a circle and intercepts a certain arc, then the measure of that angle is half the measure of the central angle that intercepts the same arc.

In this problem, angle TRK is an inscribed angle that intercepts arc KT. Therefore, the measure of angle TRK is half the measure of the central angle that intercepts arc KT.

Let's call the central angle that intercepts arc KT θ. Since angle TRK measures 32.5°, we know that θ measures 32.5° * 2 = 65°.

Now, we can use the Inscribed Angle Theorem again to find the measure of angle TSK.

Angle TSK is an inscribed angle that intercepts arc KT, and the measure of the central angle that intercepts arc KT is 65°. Therefore, the measure of angle TSK is half the measure of the central angle that intercepts the same arc, which is 65° * 2 = 130°.

The measure of angle TSK is 130° making option C the correct option.

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The question probable may be:

The center of the circle is S. Note: Figure not drawn to scale. If mangle TRK equal 32.5 ° , what is mangle TSK ? A. 32.5 ° B. 65 ° C. 130 ° D. 16.25 °

Answer:

6.5 km

Step-by-step explanation:

1:50,000

13 cm on a map, multiply both sides by 13 which leaves us with:

13:650,000

However, we need to calculate the distance in kilometers, not centimeters. To do that, we have to divide 650,000 by 100,000 which leaves us with 6.5 km

According to the Five-pan strategy ,

For given problem :

Step 1. 48 pounds of sand are used to fill 12 bags.

To find : how many pounds of sand should she find each bag will hold?

Step 2. We need to divide the total amount of sand require to fill 12 bags by 12.

Step 3. Amount of sand require to fill one bag = (amount of sand require to fill 12 bags) ÷ 12

= (48) ÷ 12

= 4 pounds

Step 4. Checking our answer as

Amount of sand require to fill 12 bags = 12 x (Amount of sand require to fill one bag)

= 12 x 4 = 48 pounds which is given, thus our answer is correct.

Step 5. She should fill 4 pounds of sand in each bag.

To find two consecutive integers whose product is 5 less than the square of the smaller number, let the smaller number be x and use algebraic equations to solve for x.

To find two consecutive integers whose product is 5 less than the square of the smaller number, we can let the smaller number be x. The larger number would then be x + 1. The product of the two consecutive integers is x(x + 1) and the square of the smaller number is x^2. According to the problem, x(x + 1) = x^2 - 5. We can solve this equation to find the values of x and x + 1.

Expanding x(x + 1) gives us x^2 + x. So, the equation becomes x^2 + x = x^2 - 5. We can simplify this equation by canceling out x^2 on both sides, which leaves us with x = -5.

So the consecutive integers are -5 and -4.

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Answer:

Option C is the answer.

Step-by-step explanation:

Option A. [tex]y=\sqrt{x-5}+3[/tex]

For domain of this function

(x - 5) ≥ 0

x ≥ 5

For range of the function

for every value of x ≥ 0

y ≥ 3

Opttion B. [tex]y=\sqrt{x+5}-3[/tex]

For Domain

(x + 5) ≥ 0

x ≥ (-5)

and for every value of x ≥ (-5) range of the function will be

y ≥ (-3)

Option C.

y = -√(x -5) + 3

For domain

x - 5 ≥ 0

x ≥ 5

For range

y ≤ 3

Option D. [tex]y=-\sqrt{x+5}-3[/tex]

For domain (x + 5) ≥ 0

x ≥ -5

For range

y ≤ (-3)

Therefore option C will be the answer.