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Leno4ka [110]
3 years ago
12

The table below shows the fifth powers of different numbers:

Mathematics
1 answer:
leonid [27]3 years ago
3 0
1. The answer would be true
<span>Part A: Does the table represent y as a function of x? Justify your answer.

The function of x is "</span><span>fifth powers of x" which can be write as 
</span>f(x)= x^5
To determine whether the y represent f(x), you can try to put a value of x into the function, then compare the value of f(x) with y.
For x=1 and y=1
f(x)= x^5
f(1)= 1^5
f(1)= 1 = y

For x=2 and y=32
f(x)= x^5
f(2)= 2^5
f(2)= 32 = y

2. 
<span>What is the value of f(4) and what does f(4) represent?
The f(4) means putting 4 as the x value. In the function, the f(x) represent price </span>for renting a bowling lane and the variable x represent the number of hours. Then f(4) represent the price for renting a bowling lane for 4 hours.
The value would be:
<span>f(x) = 2x + 12
</span><span>f(4) = 2(4) + 12
f(4)= 8+12= $20</span>
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Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the temperature varies between 73 and 9
Naddika [18.5K]

Answer: After about 9.03 hours the temperature first reach 82 degrees.

Step-by-step explanation:

The sinusoidal function is given by :

y=A\sin[\omega(x-\alpha)]+C

where, A =  amplitude; \omega=\dfrac{2\pi}{period} ,  α= phase shift on the Y-axis and C = midline.

As per given,

Average daily temperature= C=\dfrac{73+97}{2}=85   [midline is average of upper and lower limit.]

A=  97-85 = 12

Phase shift: \alpha=10

Period = 24 hours;

\omega=\dfrac{2\pi}{24}=\dfrac{\pi}{12}

Substitute all values in sinusoidal function, we get

y=12\sin[\dfrac{\pi}{12}(x-10)]+85

Put y= 82, we get

82=12\sin[\dfrac{\pi}{12}(x-10)]+85\\\\\Rightarrow\ -3= 12\sin[\dfrac{\pi}{12}(x-10)]\\\\=\dfrac{-1}{4}= \sin[\dfrac{\pi}{12}(x-10)]\\\\\Rightarrow\ \dfrac{\pi}{12}(x-10)=\sin^{-1}(\dfrac{-1}{4})\\\\\Rightarrow\ x-10=\dfrac{12}{\pi}(\sin^{-1}(\dfrac{-1}{4}))\\\\\Rightarrow\ x=\dfrac{12}{\pi}(\sin^{-1}(\dfrac{-1}{4}))+10\\\Rightarrow\ x\approx9.03

Hence, After about 9.03 hours the temperature first reach 82 degrees.

3 0
3 years ago
Harvard University accepts 6 students for every 100 applicants. How many students will be accepted in 850 applicants apply for a
LenKa [72]

Answer:

51 students.

Step-by-step explanation:

First you need to establish a rate 6/100+3/50

8*100=800   6*8=48

3/50

850-800=50   3/50

48+3=51



5 0
3 years ago
Read 2 more answers
Sadie has mangos and watermelons in a ratio of 91:11. How many mangos does she have if she has 66 watermelons?
snow_lady [41]

Answer:

546 manogoes

Step-by-step explanation:

Sadie has mangos and watermelons in a ratio of 91:11.

We need to find the number of mangoes if she has 66 watermelons.

It means that,

11x = 66

x = 6

So,

Mangoes = 91x

= 91(6)

= 546

Hence, there are 546 mangoes.

3 0
3 years ago
Suppose that scores on an aptitude test are normally distributed with a mean of 100 and a standard deviation of 4.6. Scores on a
DerKrebs [107]

Answer:

<u>The correct answer is C. Felix's z-score on the aptitude test was 1.30. His z-score on the knowledge test was 2.08. Felix performed better on the knowledge test, comparatively.</u>

Step-by-step explanation:

1. Let's check all the information given to us to answer the question correctly:

Mean of the scores on the aptitude test = 100

Standard deviation of the aptitude test = 4.6

Felix's score on the aptitude test = 106

Mean of the scores on the knowledge test = 70

Standard deviation of the knowledge test = 2.4

Felix's score on the knowledge test = 75

2. Which statement best describes Felix's scores on the two tests comparatively?

Let's recall that z-score in a normal distribution, positive or negative, is the number of times of the standard deviation a certain element is from the mean. If the element is below the mean, then the z-score is negative and if it's above the mean, then the z-score is positive.

Therefore, a score of 106 on the aptitude test, will have the following z-score:

106 - 100 = 6 and it's above the mean.

Now, we calculate the z-score, using the value of the standard deviation this way:

6/4.6 = 1.30

A score of 75 on the knowledge test, will have the following z-score:

75 - 70 = 5 and it's above the mean.

Now, we calculate the z-score, using the value of the standard deviation this way:

5/2.4 = 2.08

The z-scores of Felix were 1.30 on the aptitude test and 2.08 on the knowledge test. He performed better on the aptitude test because 2.08 > 1.30, so the correct statement that best describes Felix's scores on the two tests comparatively is<u> C. Felix's z-score on the aptitude test was 1.30. His z-score on the knowledge test was 2.08. Felix performed better on the knowledge test, comparatively.</u>

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3 years ago
2,10,50 geometric sequence
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