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skelet666 [1.2K]
4 years ago
10

Rosie needs to buy balloons and tablecloths for her party. Each balloon costs $1.50 and each tablecloth costs $2.25. She cannot

spend more than $30.00 on balloons and tablecloths for the
party. Write an inequality to represent the possible number the balloons and tablecloths that Rosie can buy. Let'x' represent balloons and and represent the tablecloths
Mathematics
2 answers:
sammy [17]4 years ago
7 0

Answer: The inequality can be written as 1.5x + 2.25y ≤ 30

Step-by-step explanation: What Rosie needs is an expression that shows  the highest she can spend on tablecloths and balloons. If the question states that she cannot spend more than 30 dollars, then it simply means she can either spend a maximum of 30 dollars, OR any amount below 30 dollars. So what she needs is an inequality that shows her spending as being less than or equal to 30.

Let the balloons be represented by letter x and the tablecloths be represented by the letter y. If each balloons cost 1.50 dollars, then the total cost of balloons equals 1.5 times x or simply 1.5x. Likewise, if each tablecloth cost 2.25, then the total cost of tablecloths shall be 2.25y.

The possible number of balloons and tablecloths that she can buy based on the conditions given can be expressed as follows;

1.5x + 2.25y ≤ 30

Snezhnost [94]4 years ago
3 0

Answer:

1.50x + 2.25y ≤ 30

Step-by-step explanation:

Hi, let’s say that 'y' represent the tablecloths.

So, we have to write an inequality:

The product of the number of balloons (x) and the cost of each one (1.50) plus the product of the number of tablecloths (y) and the cost of each tablecloth (2.25) must be less or equal to Rosie's budget (30)

Mathematically speaking:

1.50x + 2.25y ≤ 30

Feel free to ask for more if needed or if you did not understand something  

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antoniya [11.8K]

Answer:

N(T(t)) = 1408t^2 - 385.6t - 105.52

Time for bacteria count reaching 8019: t = 2.543 hours

Step-by-step explanation:

To find the composite function N(T(t)), we just need to use the value of T(t) for each T in the function N(T). So we have that:

N(T(t)) = 22 * (8t + 1.7)^2  - 123 * (8t + 1.7) + 40

N(T(t)) = 22 * (64t^2 + 27.2t + 2.89) - 984t - 209.1 + 40

N(T(t)) = 1408t^2 + 598.4t + 63.58 -  984t - 169.1

N(T(t)) = 1408t^2 - 385.6t - 105.52

Now, to find the time when the bacteria count reaches 8019, we just need to use N(T(t)) = 8019 and then find the value of t:

8019 = 1408t^2 - 385.6t - 105.52

1408t^2 - 385.6t - 8124.52 = 0

Solving this quadratic equation, we have that t = 2.543 hours, so that is the time needed to the bacteria count reaching 8019.

4 0
4 years ago
What is the standard form of this function?
Solnce55 [7]

Answer:

D. Rx) = x2 - 4x + 10

Step-by-step explanation:

R(x)=(x-2)^2+6

R(x)=(x-2)^2+6

=(x-2)(x-2)+6

=x^2-2x-2x+4+6

=x^2-4x+10

R(x) = x^2 - 4x + 10

Option D is the answer

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4 years ago
In 2009 a survey of Internet usage found that 79 percent of adults age 18 years and older in the United States use the Internet.
Alex777 [14]

Answer:

0.025 = 2.33\sqrt{\frac{0.79*0.21}{n}}

Option d.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence level of 1-\alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which

z is the zscore that has a pvalue of 1 - \frac{\alpha}{2}.

The margin of error is:

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

79 percent of adults age 18 years and older in the United States use the Internet.

This means that \pi = 0.79

98% confidence level

So \alpha = 0.02, z is the value of Z that has a pvalue of 1 - \frac{0.02}{2} = 0.99, so Z = 2.33.

Which of the following should be used to find the sample size (n) needed?

We have to find n for which M = 0.025

So the equation is:

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

0.025 = 2.33\sqrt{\frac{0.79*0.21}{n}}

Option d.

4 0
3 years ago
A machine that produces a major part for an airplane engine is monitored closely. In the past, 10% of the parts produced would b
nata0808 [166]

Answer:

With a .95 probability, the sample size that needs to be taken if the desired margin of error is .04 or less is of at least 216.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence level of 1-\alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which

z is the zscore that has a pvalue of 1 - \frac{\alpha}{2}.

The margin of error:

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

For this problem, we have that:

p = 0.1

95% confidence level

So \alpha = 0.05, z is the value of Z that has a pvalue of 1 - \frac{0.05}{2} = 0.975, so Z = 1.96.

With a .95 probability, the sample size that needs to be taken if the desired margin of error is .04 or less is

We need a sample size of at least n, in which n is found M = 0.04.

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

0.04 = 1.96\sqrt{\frac{0.1*0.9}{n}}

0.04\sqrt{n} = 0.588

\sqrt{n} = \frac{0.588}{0.04}

\sqrt{n} = 14.7

(\sqrt{n})^{2} = (14.7)^{2}

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Answer:

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Step-by-step explanation:

The center-radius form (formally called the standard form) of a circle is

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So if we replace (h,k) with (0,0) since the center is the origin and r with 2 since the radius is 2 we get:

(x-0)^2+(y-0)^2=2^2

Let's simplify:

x^2  +  y^2   = 4

8 0
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