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Arada [10]
2 years ago
9

A rock climber is planning to climb a mountain cliff over two days. The climb begins at an altitude of 6,400 feet above sea leve

l. The rock climber figures
he can climb at an average pace of 360 feet per hour. He wants to climb to an altitude higher than 8,020 feet above sea level by the end of the first day of
climbing.
Which inequality and solution describe how many hours the climber must climb on the first day to reach his goal?
A
360h + 6,400 < 8,020, with a solution of h < 4
2
B
360h + 6,400 < 8,020, with a solution of h < 7
71
C
360h + 6,400 > 8,020, with a solution of h > 75
18
D
360h + 6,400 > 8,020, with a solution of h > 4.
2

Mathematics
1 answer:
Furkat [3]2 years ago
3 0

Answer:

D

Step-by-step explanation:

360h+6,400 >8,020, with a solution is h> 4.

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A cake shop bakes a variety of brownies. The top-selling brownies are ones with toppings of chocolate chip, walnuts, or both. A
umka2103 [35]

Answer:

0.3

Step-by-step explanation:

the total of all probabilities is 1.00, or 100%.

In the Venn diagram, we have the probabilities 0.2, 0.4 and 0.1; these sum to

0.2+0.4+0.1 = 0.6+0.1 = 0.7.

This leaves us 1.00-0.7 = 0.3 for the remaining probability of no toppings.

7 0
2 years ago
Read 2 more answers
A house painter charges $14 per hour for the first 45 hours he works, time and a half for the 10 hours after that, and double ti
Digiron [165]

Answer: $1,540

Step-by-step explanation:

Given the following amount charged by a worker :

First 45 hours = $14 per hour

time and half for the next 10 hours

Double time for all hours after that:

If he worked for 80 hours :

First 45 hours = (45 × $14) = $630

Next 10 hours:

Time and half for 10 hours is equivalent to (10 × 1.5) = 15 hours

(15 × $14) = $210

Double time for all subsequent hours :

80 - (45 + 10) = 80 - 55 = 25

Double time : (2 × 25) = 50 hours

(50 × 14) = $700

Hence, total amount earned :

($630 + $210 + $700)

= $1,540

4 0
2 years ago
A room with a length of 270 cm and width 150 cm is to be covered with square tiles .What is the largest size of tiles to be used
Damm [24]

Find the greatest common factor of both numbers:

Factors for 150:

150: 1, 2, 5 , 6, 10, 15, 25, 30, 50, 75, 150

Factors for 270:

1, 2, 3, 5, 6 , 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, 270

The largest number they both have in common is 30, so the largest tile could be 30 cm^2.

5 0
2 years ago
For the binomial expansion of (x + y)^10, the value of k in the term 210x 6y k is a) 6 b) 4 c) 5 d) 7
Sloan [31]

Answer:

a) 6

Step-by-step explanation:

Expanding the polynomial using the formula:

$(x+y)^n=\sum_{k=0}^n \binom{n}{k} x^{n-k} y^k $

Also

$\binom{n}{k}=\frac{n!}{(n-k)!k!}$

I think you mean 210x^6y^4

We can deduce that this term will be located somewhere in the middle. So I will calculate k= 5; k=6 \text{ and } k =7.

For k=5

$\binom{10}{5} (y)^{10-5} (x)^{5}=\frac{10!}{(10-5)! 5!}(y)^{5} (x)^{5}= \frac{10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5! }{5! \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1 } \\ =\frac{30240}{120} =252 x^{5} y^{5}$

Note that we actually don't need to do all this process. There's no necessity to calculate the binomial, just x^{n-k} y^k

For k=6

$\binom{10}{6} \left(y\right)^{10-6} \left(x\right)^{6}=\frac{10!}{(10-6)! 6!}\left(y\right)^{4} \left(x\right)^{6}=210 x^{6} y^{4}$

5 0
2 years ago
Given: PRST square
Zigmanuir [339]

Answer:

7a²/16

Step-by-step explanation:

Area of the triangle PTS

½ × a × a

a²/2

Length of PS:

sqrt(a² + a²)

asqrt(2)

Length of MS:

¼asqrt(2)

Triangles MCS and TPS are similar

With sides in the ratio:

¼asqrt(2) : a

sqrt(2)/4 : 1

Area of triangle SMC:

A/(a²/2) = [(sqrt(2)/4)]²

2A/a² = 1/8

A = a²/16

Area of PTMC

= a²/2 - a²/16

= 7a²/16

Step-by-step explanation:

4 0
2 years ago
Read 2 more answers
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