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Setler
23 days ago
10

The outside temperature at midnight today in Polina's hometown was 18 degrees Fahrenheit. The temperature increases by 1.2 degre

es Fahrenheit each hour over the next 15 hours. Polina's school does not send students outside for recess if the outside temperature is 32 degrees Fahrenheit or lower. Recess at her school always starts on the half hour or hour. Which statement is true about recess at Polina's school?
Mathematics
1 answer:
PIT_PIT [12.4K]23 days ago
4 0

Answer:

Students who have recess scheduled at 12 p.m. or later are the only ones who may go outside

Step-by-step explanation:

Let t represent the time elapsed since midnight, and y represent the temperature. Given that the temperature rises at a rate of 1.2 degrees Fahrenheit per hour, the time needed to reach 32 degrees Fahrenheit can be derived as:

y = 1.2t + 18

Setting y = 32

32 = 1.2t + 18

1.2t = 14

t = 14/1.2 = 11.67 hours

Recess starts on the half-hour or hour, hence, it would commence at t = 12 hours, or 12 p.m.

This means only those students with recess at 12 p.m. or later are permitted to go outside

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The bottom part of this block is a rectangular prism. The top part is a square pyramid. You want to cover the block entirely wit
Zina [12379]

Response:

Total paper needed is 57 cm²

Detailed explanation:

Provided information

slant height b = 4 cm

base side h = 3 cm

block height  h1 = 2 cm

Solution

The surface area of a right square pyramid is determined by summing the areas of all four triangular faces expressed as

area = 4 × Area of Triangles

area = 4 × \frac{bh}{2}  

area = 4 × \frac{4\times 3}{2}  

area = 24 cm²

Also,

the surface area of the box includes the area of its four side faces plus the base

area = 4 × ( h × h1 ) + h²  

area = 4 × ( 3 × 2 ) + 3²

area = 24 + 9

area = 33 cm²

Thus, the total paper required is = 24 + 33

therefore, the total paper needed equals 57 cm²

6 0
19 days ago
X=4/5 Y=4/X+SQRT X +0.2 -5X What is the value of Y
Inessa [12570]
It seems you are stating that Y=4/X+SQRT X +0.2 -5X, with x given as 4/5. To compute <span>Y=4/X+SQRT X +0.2 -5X, substitute every instance of x with 4/5:

y = 4 / (4/5) + sqrt(4/5) + 0.2 - 5(4/5)
= 5 + 2 / sqrt(5) + 0.2 - 4.
Can this expression be further simplified?

</span>
5 0
1 month ago
A square rotated about its center by 360º maps onto itself at: a) 1 B) 2 C) 3 D) 4 different angles of rotation. You can reflect
PIT_PIT [12445]

Answer: A square that undergoes rotation around its center by 360º aligns with itself at D) 4 distinct angles during the process. Furthermore, a square can be reflected onto itself over B) 4 various lines.

Explanatory breakdown:

A square is a geometric shape characterized by equal-length sides and right angles ( 90^{\circ} ).

Thus, it is capable of being rotated around its center by 360^{\circ}.

It reverts to its original outline at 4 unique rotation angles ( at every 90^{\circ} angle).

The square can also be reflected onto itself across 4 lines (2 through the non-parallel sides and 2 through the corners).

4 0
1 month ago
Read 2 more answers
Suppose that 70% of the orders on a particular website are shipped to the person who is making the order and the remaining 30% a
tester [12383]

Answer:

a) P=0.24

b) P=0.31

c) Not independent.

Step-by-step explanation:

The question is incomplete.

a) What’s the probability that a randomly chosen order will be wrapped and sent to a different person?

P(W\&SOP)=P(SOP)*P(W|SOP)=0.30*0.60=0.24

W: wrapped

SOP: sent to different individuals

b) What’s the probability that a randomly selected order will be gift wrapped?

P(W)=P(SOP)*P(W|SOP)+P(SR)*P(W|SR)\\\\P(W)=0.3*0.6+0.7*0.1=0.24+0.07=0.31

SR: sent to the correct recipient

c) Is gift wrapping independent of the order’s destination? Please provide a statistical justification.

To establish their independence, both conditions must be satisfied:

  • P(x|y) = P(x), for all values of X and Y.
  • P(x ∩ y) = P(x) * P(y), for all values of X and Y.

Starting with the second condition.

P(W\cap SR)=0.1\\\\P(W)*P(SR)=0.31*0.7=0.217\\\\\\P(W\cap SR)\neq P(W)*P(SR)

This condition is unmet, indicating that these variables are not independent.

4 0
19 days ago
Henry wants to double a cake recipe that uses 2 cups and 10 tbsp of flour. How much flour will he need?
AnnZ [12381]

Answer:

20 tablespoons of flour OR 1.25 or 1 \frac{1}{4}cups of flour

Step-by-step explanation:

To double the amount of flour needed:

10 tablespoons of flour

× 2

____________

20 tablespoons of flour OR 1.25 or 1 \frac{1}{4}cups of flour

5 0
1 month ago
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