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3 years ago

Mrs. Nez owns a small business. When her customers pay with

Mathematics

1 answer:

Amanda [17]3 years ago

3 0

Answer:

$19.16

Step-by-step explanation:

First turn 95.8% into a decimal. Move the decimal two places to the left

.958

Then multiply this number by the 20$

$20*.958$

This equals the amount of money Mrs. Nez will receive from the credit card company.

=$ $19.16$

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Circle the equations that represent quadratic functions a. y=3x+1 b. y=x^2+3 c. y=x^3-3 d. x^2+3y=8

Elena L [17]

Answer:

$B. y=x^2+3 \\\\D.$ $x^2+3y=8$

Step-by-step explanation:

A quadratic function is a function in which the highest power of the unknown variable is 2.

Formally, a quadratic function is defined as a function of the form:

$f(x)=ax^2+bx+c, a\neq 0$

From the given options, only B and D has the highest power as 2. Therefore, the equations that represent quadratic functions are:

$B. y=x^2+3 \\\\D.$ $x^2+3y=8$

4 0

3 years ago

Darnell went to the movies with his freinds.the movie started at 2:35 p.m and lasted 1 hour 45 minutes.what time did the movie e

mixas84 [53]

The movie ended at 4:20 p.m

7 0

4 years ago

The liquid base of an ice cream has an initial temperature of 86°C before it is placed in a freezer with a constant temperature

Karolina [17]

The temperature of the ice cream 2 hours after it was placed in the freezer is 37.40 °C

From Newton's law of cooling, we have that

$T_{(t)}= T_{s}+(T_{0} - T_{s})e^{kt}$

Where

$(t) = \ time$

$T_{(t)} = \ the \ temperature \ of \ the \ body \ at \ time \ (t)$

$T_{s} = Surrounding \ temperature$

$T_{0} = Initial \ temperature \ of \ the \ body$

$k = constant$

From the question,

$T_{0} = 86 ^{o}C$

$T_{s} = -20 ^{o}C$

∴ $T_{0} - T_{s} = 86^{o}C - -20^{o}C = 86^{o}C +20^{o}C$

$T_{0} - T_{s} = 106^{o} C$

Therefore, the equation $T_{(t)}= T_{s}+(T_{0} - T_{s})e^{kt}$ becomes

$T_{(t)}=-20+106 e^{kt}$

Also, from the question

After 1 hour, the temperature of the ice-cream base has decreased to 58°C.

That is,

At time $t = 1 \ hour$ , $T_{(t)} = 58^{o}C$

Then, we can write that

$T_{(1)}=58 = -20+106 e^{k(1)}$

Then, we get

$58 = -20+106 e^{k(1)}$

Now, solve for $k$

First collect like terms

$58 +20 = 106 e^{k}$

$78 =106 e^{k}$

Then,

$e^{k} = \frac{78}{106}$

$e^{k} = 0.735849$

Now, take the natural log of both sides

$ln(e^{k}) =ln( 0.735849)$

$k = -0.30673$

This is the value of the constant $k$

Now, for the temperature of the ice cream 2 hours after it was placed in the freezer, that is, at $t = 2 \ hours$

From

$T_{(t)}=-20+106 e^{kt}$

Then

$T_{(2)}=-20+106 e^{(-0.30673 \times 2)}$

$T_{(2)}=-20+106 e^{-0.61346}$

$T_{(2)}=-20+106\times 0.5414741237$

$T_{(2)}=-20+57.396257$

$T_{(2)}=37.396257 \ ^{o}C$

$T_{(2)} \approxeq 37.40 \ ^{o}C$

Hence, the temperature of the ice cream 2 hours after it was placed in the freezer is 37.40 °C

Learn more here: brainly.com/question/11689670

6 0

2 years ago

Read 2 more answers

the sum of the digits 2014 is 7. How many whole numbers between 100 and 999 have 9 as the sum of their digits?

s344n2d4d5 [400]

Answer:

Step-by-step explanation:

this should be correct :)

There are 9 in the 100's

108

117

126

135

144

153

162

171

180

There are 8 in the 200's (starting to see a pattern?)

207

216

225

234

243

252

261

270

There are 7 in the 300's

306

315

324

333

342

351

360

9+8+7+6+5+4+3+2+1 = 45

3 0

3 years ago

A local club is arranging a charter flight to Hawaii. The cost of the trip is $586 each for 80 passengers, with a refund of $

professor190 [17]

Answer:

a) The number of passengers that will maximize the revenue received from the flight is 99.

b) The maximum revenue is $48,609.

Step-by-step explanation:

We have to analyse two cases to build a piecewise function.

If there are 80 or less passengers, we have that:

The cost of the trip is $586 for each passenger. So

$R(n) = 586n$

If there are more than 80 passengers.

There is a refund of $5 per passenger for each passenger in excess of 80. So the cost for each passenger is

$R(n) = (586 - 5(n-80))n = -5n^{2} +400n + 586n = -5n^{2} + 986n$ .

So we have the following piecewise function:

$R(n) = \left \{ {{586n}, n\leq 80 \atop {-5n^{2} + 986n}, n > 80} \right$

The maxium value of a quadratic function in the format of $y(n) = an^{2} + bn + c$ happens at:

$n_{v} = -\frac{b}{2a}$

The maximum value is:

$y(n_{v})$

So:

(a) Find the number of passengers that will maximize the revenue received from the flight.

We have to see if $n_{v}$ is higher than 80.

We have that, for $n > 80$ , $R(n) = -5n^{2} + 986n$ , so $a = -5, b = 986$

The number of passengers that will maximize the revenue received from the flight is:

$n_{v} = -\frac{b}{2a} = -\frac{986}{2(-5)} = 98.6$

Rounding up, the number of passengers that will maximize the revenue received from the flight is 99.

(b) Find the maximum revenue.

This is $R(99)$ .

$R(n) = -5n^{2} + 986n$

$R(99) = -5*(99)^{2} + 986*(99) = 48609$

The maximum revenue is $48,609.

8 0

3 years ago