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2 years ago

The distance to the nearest exit doir is no more than 150 feet. Use d to represent the distance in feet to the nearest exit door

Mathematics

1 answer:

il63 [147K]2 years ago

5 0

Answer: $d\leq150$

Step-by-step explanation:

1. You have the following information given in the problem:

- The distance to the nearest exit door is no more than 150 feet.

- $d$ represents the distance to the nearest exit door, in feet.

2. Therefore, keeping the information above on mind, you know that the distance to the nearest exit door ( $d$ ) must be less than or equal to 150 feet, then, you can express this as following:

$d\leq150$

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Surveys indicate that 5% of the students who took the SATs had enrolled in an SAT prep course. 30% of the SAT prep students were

Nesterboy [21]

Answer: The probability he didn't take an SAT prep course = 0.985

Step-by-step explanation:

Let us first assume that he took SAT prep.

Surveys indicate that 5% of the students who took the SATs had enrolled in an SAT prep course. 30% of the SAT prep students were admitted to their first choice college. That is,

30/ 100 of 5 = 0.3 × 5 = 1.5

The probability he did take an SAT prep course and got admission into the college of first choice will be

P(prep) = 1.5 / 100 = 0.015

The probability he didn't take an SAT prep course will be:

P(not prep) = 1 - P(prep)

P(not prep) = 1 - 0.015

P(not prep) = 0.985

4 0

2 years ago

You are a first year police officer in Swanton, Ohio. You are earning a monthly salary of $2,200. Next year you will be given a

Step2247 [10]

About $290.83.

Hope this helps!

3 0

2 years ago

Line segments XY and ZY are tangent to circle O. Circle O is shown. Triangle X Y Z has points X and Z on the circle. Lines X Y a

pickupchik [31]

Answer:

The correct option is;

An isosceles triangle

Step-by-step explanation:

The parameters given are;

Line segments XY and ZY are tangents to circle O.

ΔXYZ has points X and Z on the circle.

XY and ZY are tangents that intersect at point Y outside the circle'

Therefore, given the circle has center O, then;

OY ≅ OZ = Radius of circle with center O

∠OXY ≅ ∠OZY = 90° (The radius line from the circle center to the tangent point is perpendicular)

OY ≅ OY (Reflexive property)

ΔOYX and ΔOYZ are right triangles (Triangle with one angle = 90°

ΔOYX ≅ ΔOYZ (Hypotenuse Leg, HL, rule of congruency)

Therefore;

XY = ZY (Corresponding Parts of Congruent Triangles are Congruent CPCTC)

Triangle XYZ is an isosceles triangle (Triangle with two equal sides).

4 0

2 years ago

The general form of the equation of a circle is x2 + y2 + 42x + 38y − 47 = 0. The equation of this circle in standard form is (x

DaniilM [7]

We have the following equation:
x2 + y2 + 42x + 38y - 47 = 0
We rewrite the equation:
x2 + 42x + y2 + 38y - 47 = 0
x2 + 42x + y2 + 38y = 47
Rewriting we have:
x2 + 42x + (42/2) ^ 2 + y2 + 38y + (38/2) ^ 2 = 47 + (42/2) ^ 2 + (38/2) ^ 2
x2 + 42x + 441 + y2 + 38y + 361 = 47 + 441 + 361
Rewriting we have:
(x + 21) ^ 2 + (y + 19) ^ 2 = 849
The center of the circle is:
(x, y) = (-21, -19)
The radio is:
r = root (849)
r = (849) ^ 2

A circle of the same radius is given by:
x ^ 2 + y ^ 2 - 50x - 30y + 1 = 0
Let's check:
x ^ 2 - 50x + y ^ 2 - 30y + 1 = 0
x ^ 2 - 50x + y ^ 2 - 30y = - 1
x ^ 2 - 50x + (-50/2) ^ 2 + y ^ 2 - 30y + (-30/2) ^ 2 = - 1 + (-30/2) ^ 2 + (-50/2) ^ 2
x ^ 2 - 50x + (-50/2) ^ 2 + y ^ 2 - 30y + (-30/2) ^ 2 = - 1 + 225 + 625
(x-25) ^ 2 + (y-15) ^ 2 = 849
Answer:
(x + 21) ^ 2 + (y + 19) ^ 2 = 849
(x, y) = (-21, -19)
r = (849) ^ 2
x ^ 2 + y ^ 2 - 50x - 30y + 1 = 0

5 0

2 years ago

Ribbon is only sold by the spool. A spool contains 25 yards of ribbon. Shannon needs 58 yards of ribbon to wrap all the presents

ella [17]

Answer:

$\boxed{\text{3 spools}}$

Step-by-step explanation:

$\text{1 spool =25 yd}\\\text{Spools needed } = \text{58 yd} \times \dfrac{\text{1 spool}}{\text{25 yd}} = \text{2.32 spools}\\\\\text{However, Shannon can't buy part of a spool. She must $\textbf{round up}$ to the next integer.}\\\text{Shannon must buy $\boxed{\textbf{3 spools}}$ of ribbon}$

6 0

2 years ago

Read 2 more answers