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3 years ago

After 3 hours, Ernie had travelled 195 miles. If he travels at a constant speed, how far will he have

Mathematics

1 answer:

Umnica [9.8K]3 years ago

7 0

Answer:

x = 325 miles

Step-by-step explanation:

$\frac{195}{3} = \frac{x}{5} \\ 3.x = 5.195 \\ 3x = 975 \\ x = \frac{975}{3} \\ x = 325 \: miles$

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Find A-B. Help me please

Softa [21]

I’m not sure but since no one else commented I would think it’s D, I think you take the first number like 6 for a and subtract the first number for b like 3

8 0

2 years ago

To begin a bacteria study, a petri dish had 2800 bacteria cells. Each hour since, the number of cells has increased by 7.2%. Let

Rudiy27

The function that models exponential growth is:

P(t) = P0*(1 + r)^t, where

P0 = P(0) is the initial value of P

r is the growth rate as a decimal

In our case we have:

P(0) = 2800

r = 0.035 or 3.5%

P(t) = 2800*(1 + 0.035)^t

P(t) = 2800*(1.035)^t

The same exponential function written using y and t is:

y = 2800*1.035^t.

Explanation: https://softmath.com/algebra-word-problems/to-begin-a-bacteria-study-a-petri-dish-had-2800-bacteria

7 0

3 years ago

Determine if the two triangles are congruent.

stiks02 [169]

Answer:

SAS

Step-by-step explanation:

The two triangles share a side, so that would be reflexive to show that side is congruent. Also, keep in mind that all right angles are congruent! The picture already tells us that the two outer side are congruent. So in conclusion, the two angles are congruent by SAS.

Hope this helps! :)

3 0

3 years ago

Read 2 more answers

QRINC offered new employees a starting salary of $34,862 in 2013. What would a comparable starting salary have been in 2003?

Vlad1618 [11]

Complete Question

Table of Annual CPI values

2003-184.00

2004-188.90

2005-195.3

2006-201.6

2007-207.342

2008-215.303

2009-214.537

2010-218.056

2011-224.939

2012-229.594

2013-232.957

2014-236.736

QRINC offered new employees a starting salary of $34,862 in 2013. What would a comparable starting salary have been in 2003?

Answer:

$C=27535.5881128$

Step-by-step explanation:

From the question we are told that

CPI for 2003(index)=2003-184.00

CPI for 2013(index)=2013-232.957

Starting salary in 2013 at $34,862

Generally comparable starting salary C is given as

$C=\frac{starting salary}{CPI for 2013(index} *CPI for 2003(index)$

$C=\frac{34,862}{232.957} *184$

Therefore C the comparable starting salary is givrn to be

$C=27535.5881128$

$C=27536 appro$

8 0

3 years ago

Hello people ~

Luden [163]

Cone details:

height: h cm

radius: r cm

Sphere details:

radius: 10 cm

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

From the endpoints (EO, UO) of the circle to the center of the circle (O), the radius is will be always the same.

Using Pythagoras Theorem

(a)

TO² + TU² = OU²

(h-10)² + r² = 10² [insert values]

r² = 10² - (h-10)² [change sides]

r² = 100 - (h² -20h + 100) [expand]

r² = 100 - h² + 20h -100 [simplify]

r² = 20h - h² [shown]

r = √20h - h² ["r" in terms of "h"]

(b)

volume of cone = 1/3 * π * r² * h

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

$\longrightarrow \sf V = \dfrac{1}{3} * \pi * (\sqrt{20h - h^2})^2 \ ( h)$

$\longrightarrow \sf V = \dfrac{1}{3} * \pi * (20h - h^2) (h)$

$\longrightarrow \sf V = \dfrac{1}{3} * \pi * (20 - h) (h) ( h)$

$\longrightarrow \sf V = \dfrac{1}{3} \pi h^2(20-h)$

To find maximum/minimum, we have to find first derivative.

(c)

First derivative

$\Longrightarrow \sf V' =\dfrac{d}{dx} ( \dfrac{1}{3} \pi h^2(20-h) )$

apply chain rule

$\sf \Longrightarrow V'=\dfrac{\pi \left(40h-3h^2\right)}{3}$

Equate the first derivative to zero, that is V'(x) = 0

$\Longrightarrow \sf \dfrac{\pi \left(40h-3h^2\right)}{3}=0$

$\Longrightarrow \sf 40h-3h^2=0$

$\Longrightarrow \sf h(40-3h)=0$

$\Longrightarrow \sf h=0, \ 40-3h=0$

$\Longrightarrow \sf h=0,\:h=\dfrac{40}{3}$

maximum volume: when h = 40/3

$\sf \Longrightarrow max= \dfrac{1}{3} \pi (\dfrac{40}{3} )^2(20-\dfrac{40}{3} )$

$\sf \Longrightarrow maximum= 1241.123 \ cm^3$

minimum volume: when h = 0

$\sf \Longrightarrow min= \dfrac{1}{3} \pi (0)^2(20-0)$

$\sf \Longrightarrow minimum=0 \ cm^3$

6 0

2 years ago

Read 2 more answers