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MaRussiya [10]
3 years ago
13

This equation shows how the cost of renting a ballroom depends on how many hours it is rented for. c = 23.7h The variable h repr

esents the number of hours the ballroom is rented for, and the variable c represents the cost in dollars. For $80.58, what is the maximum amount of time that a ballroom can be rented for?
Mathematics
1 answer:
charle [14.2K]3 years ago
5 0

Answer:

The maximum amount of time that the ballroom can be rented is 3.4 h.

Step-by-step explanation:

In order to find the maximum amount of time the ballroom can be rented we can create an inequality in such a way that the cost must be less or equal to $80.58, which is the amount of money that is available. So we have:

c = 23.7*h

80.58 >= 23.7*h

23.7*h =< 80.58

h =< 80.58 / 23.7

h =< 3.4 h

The maximum amount of time that the ballroom can be rented is 3.4 h.

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the earth rotates about its axis once every 23 hours, 56 minutes and 4 seconds. Approximate the number of radians the earth rota
marishachu [46]

Answer:

\frac{\pi}{43082}\text{ radians per second}

Step-by-step explanation:

Given,

Time taken in one rotation of earth = 23 hours, 56 minutes and 4 seconds.

Since, 1 minute = 60 seconds and 1 hour = 3600 seconds,

⇒ Time taken in one rotation of earth = (23 × 3600 + 56 × 60 + 4) seconds

= 86164  seconds,

Now,  the number of radians in one rotation = 2π,

That is, 86164 seconds = 2π radians

\implies 1\text{ second }=\frac{2\pi}{86164}=\frac{\pi}{43082}\text{ radians}

Hence, the number of radians in one second is \frac{\pi}{43082}

4 0
3 years ago
Express each number in scientific notitatio 43,000= 0.0072= 0.0000901=
Maksim231197 [3]

Answer:

43,000: 4.3×10^4

0.0072: 7.2×10^-3

0.0000901: 9.01×10^-5

Step-by-step explanation:

scientific notation: a×10^b, where should be 0<a<10

Step 1. Count the zeros

Step 2. Look at the number left, and determine whether or not it fits in the range of [a]. If not, we divide or multiply 10 to get it fit

------------------------

43,000: 4.3×10^4 (since 43 does not fit, we divide by 10 to get it fit)

0.0072: 7.2×10^-3 (since 0.72 does not fit, we multiply 10 to get it fit)

0.0000901: 9.01×10^-5 (since 0.901 does not fit, we multiply 10 to get it fit)

Hope this helps!! :)

Please let me know if you have any question

7 0
3 years ago
Determine whether (3,6) is a solution of y= 13x - 4
Nonamiya [84]

Answer:

idk

Step-by-step explanation:

3 0
3 years ago
The strength of a certain type of rubber is tested by subjecting pieces of the rubber to an abrasion test. For the rubber to be
My name is Ann [436]

Answer:

Step-by-step explanation:

Hello!

You have the hypothesis that the average weight loss for rubber after an abrasion test is less than 3.5 mg. To test this a large sample of pieces of rubber were sampled and subjected to the abrasion test.

With the given information you must test whether the researcher's hypothesis is sustained or not.

The study variable is,

X: Weight loss of rubber cured in a certain way after being subjected to the abrasion test. (mg)

There is no information about the variable distribution, but since it is said that the sample is a "large number" I'll take it as if it is bigger than 30 and apply the Central Limit Theorem to use the approximation of the sample mean to normal. This way I can use the Z-statistic for the test.

Symbolically the statistic hypothesis is:

H₀: μ ≥ 3.5

H₁: μ < 3.5

α: 0.05 (since is not listed, I'll choose one of the most common signification levels)

You have a one-tailed critical region, this means the p-value will also be one-tailed to the left of the distribution (i.e. →-∞)

The formula of the statistic is:

Z= <u> X[bar] - μ </u> ≈ N(0;1)

        δ/√n

To calculate the statistic you have to use the information given.

The sample mean X[bar]= 3.4 mg

Upper bond of 95% CI= 3.45 mg

The basic structure of a CI for the mean is

"estimator" ± "margin of error"

Upper bound is "estimator" + "margin of error"

Using the formula:

Ub= X[bar] + d ⇒ 3.45= 3.4 + d

⇒ d= 3.45 - 3.4 = 0.05

Where d is the margin of error

d= Z_{1-\alpha /2} * (δ/√n)

d= Z_{0.975} * (δ/√n)

d/Z_{0.975}= (δ/√n)

(δ/√n)= 0.05/ 1.96 = 0.0255

(δ/√n) is the denominator in the formula, corresponds to the standard deviation of the distribution.

Now you have all values and can calculate the statistic under the null hypothesis:

Z= <u> 3.4 - 3.5 </u> = -3.92

       0.0255

And the p-value:

P(Z ≤ -3.92) = 0.000044 ⇒ My Z- table goes up to P(Z ≤ -3.00) = 0.001, so using strictly the table I can say that the probability is less than 0.001.

To calculate the exact probability I've used a statistic program.

p-value < 0.001

I hope it helps!

8 0
3 years ago
Please help me with math!!!!!
saveliy_v [14]

Answer:

We need for inforamtion like what is the volume for both of the shapes

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
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