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Murrr4er [49]
3 years ago
15

Natalie practices the piano 588 minutes in 2 weeks. If t represents the total time she

Mathematics
1 answer:
Ostrovityanka [42]3 years ago
4 0

Answer:

T=14D

Step-by-step explanation:

I think? sorry if wrong

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Fit a quadratic function to these three points:<br> (-2,8), (0, -4), and (4, 68)<br> Respuesta
zloy xaker [14]

Answer:

f(x) = 4x^2 + 2x - 4.

Step-by-step explanation:

Let the quadratic function be y = f(x) = ax^2 + bx + c.

For the point (-2, 8)  ( x = -2 when y = 8) we have:

a(-2)^2 + (-2)b + c = 8

4a - 2b + c = 8      For (0, -4) we have:

0 + 0 + c = -4   so c = -4.    For (4, 68) we have:

16a + 4b + c = 68  

So we have 2 systems of equations in a and b ( plugging in c = -4):

4a - 2b - 4 = 8

16a + 4b - 4 = 68

4a - 2b = 12

16a + 4b = 72    Multiplying 4a - 2b = 12 by 2 we get:

8a - 4b = 24  

Adding the last 2 equations:

24a = 96

a = 4

Now plugging a = 4 and c = -4 in the first equation:

4(4) - 2b - 4 = 8

-2b = 8 - 16 + 4 = -4

b = 2.

3 0
3 years ago
Danielle earns an 8.25% commission on everything she sells at the electronics store where she works. She also earns a base salar
Sauron [17]
Lets begin with our y=mx+b, our constant(b) is 800 that she earns as a salary, our x represents the amount she sells, m then represents the commission which is 8.25% so converting that to a decimal and replacing it as m gets us y = 0.0825x+800. Replace $4500 for x and we have y=0.0825(4500)+800 solve and we get $1171.25
7 0
2 years ago
Researchers recorded the speed of ants on trails in their natural environments. The ants studied, Leptogenys processionalis, all
posledela

This question is Incomplete

Complete Question

Researchers recorded the speed of ants on trails in their natural environments. The ants studied, Leptogenys processionalis, all have the same body size in their adult phase, which made it easy to measure speeds in units of body lengths per second (bl/s). The researchers found that, when traffic is light and not congested, ant speeds vary roughly Normally, with mean 6.20 bl/s and standard deviation 1.58 bl/s. (a) What is the probability that an ant's speed in light traffic is faster than 5 bl/s? You may find Table B useful. (Enter your answer rounded to four decimal places.)

Answer:

0.7762

Step-by-step explanation:

We solve using z score formula

z = (x-μ)/σ, where

x is the raw score

μ is the population mean

σ is the population standard deviation.

Population mean = 6.20 bl/s

Standard deviation = 1.58 bl/s.

x = 5 bl/s

z = 5 - 6.20/1.58

z = -0.75949

The probability that an ant's speed in light traffic is faster than 5 bl/s is P( x > 5)

Probability value from Z-Table:

P(x<5) = 0.22378

P(x>5) = 1 - P(x<5)

= 1 - 22378

= 0.77622

Approximately to 4 decimal places = 0.7762

The probability that an ant's speed in light traffic is faster than 5 bl/s is 0.7762

5 0
3 years ago
Melissa wants to check the accuracy the accuracy of the finance charge on her promissory note. She has a $6000, four-year loan a
ValentinkaMS [17]

Answer:

1. Melissa wants to check the accuracy of the finance charge on her promissory note. She has a $6,000, 4-year loan at an APR of 3.11%.

What is her monthly payment?

$133.10

5 0
2 years ago
The Colonel spots a campfire at a bearing N 59∘59∘ E from his current position. Sarge, who is positioned 242 feet due east of th
Rashid [163]

Answer:

i. Colonel is about 201 feet away from the fire.

ii. Sarge is about 125 feet away from the fire.

Step-by-step explanation:

Let the Colonel's location be represented by A, the Sarge's by B and that of campfire by C.

The total angle at the campfire from both the Colonel and Sarge = 59^{0} + 34^{0}

                                           = 93^{0}

Thus,

<CAB = 90^{0} - 59^{0} = 31^{0}

<CBA = 90^{0} - 34^{0} = 56^{0}

Sine rule states;

\frac{a}{Sin A} = \frac{b}{Sin B} = \frac{c}{Sin C}

i. Colonel's distance from the campfire (b), can be determined by applying the sine rule;

\frac{b}{Sin B} = \frac{c}{Sin C}

\frac{b}{Sin 56^{0} } = \frac{242}{Sin 93^{0} }

\frac{b}{0.8290} = \frac{242}{0.9986}

cross multiply,

b = \frac{0.8290*242}{0.9986}

  = 200.8993

Colonel is about 201 feet away from the fire.

ii. Sarge's distance from the campfire (a), can be determined by applying the sine rule;

\frac{a}{Sin A} = \frac{c}{Sin C}

\frac{a}{Sin 31^{0} } = \frac{242}{Sin 93^{0} }

\frac{a}{0.5150} = \frac{242}{0.9986}

cross multiply,

a = \frac{0.5150*242}{0.9986}

  = 124.8073

Sarge is about 125 feet away from the fire.

8 0
3 years ago
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