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1 year ago

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Tony’s class needs more than $500 for the school dance. So far, they have raised $200. They plan to have a car wash, charging $8

a car, to raise more money. Tony solved the inequality 8x + 200 Greater-than-or-equal-to 500, and determined that if they wash 37 cars, they will have enough money. Is he correct

2 answers:

adell [148]1 year ago

5 0

Answer:

38

Step-by-step explanation:

The solution to the inequality is x Greater-than-or-equal-to 37.5.

For this situation, only whole number solutions make sense.

Tony needs to round up to 38.

Orlov [11]1 year ago

4 0

Answer: no Tony is not correct It is less than 5 hundred dollars.

Step-by-step explanation: 8×37=296 +200 = 496

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Choose which statements are true about Pi. Check all that apply. Piis a whole number. Piis double the radius. Piis approximately

Ludmilka [50]

Answer:

Answer in explanation

Step-by-step explanation:

In this question, we would be examining the validity of some statements on the number π(pi)

π Is a whole number?

This is wrong, π is a fraction of 22 to 7 parts I.e 22/7

π Is double the radius?

This is wrong. It is the diameter that is double the radius

π Is approximately 3.14?

This is correct to an extent. The actual value in decimal is around 3.142857142857143 which makes the 3.14 somehow correct

π represents the ratio of the circumference of the circle to the diameter?

This is correct.

Mathematically, circumference C = π * diameter D

Hence C/D = π

π Is approximately 22/7?

This is correct. This is the ratio used for π

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1 year ago

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Jordan solved the equation −7x + 25 = 48; his work is shown below. Identify the error and where it was made. −7x + 25 = 48 Step

almond37 [142]

Answer:

Step 4 : he should have divided both sides by negative seven

Step-by-step explanation:

6 0

1 year ago

A television station plans to ask a random sample of 400 city residents if they can name the news anchor on the evening news at

hodyreva [135]

Answer:

There is an 8.38% probability that the anchor will be fired.

Step-by-step explanation:

For each resident, there is only two possible outcomes. Either they can name the news anchor on the evening news at their station, or they cannot.

This means that the binomial probability distribution will be used in our solution.

However, we are working with samples that are considerably big. So i am going to aaproximate this binomial distribution to the normal.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X), \sigma = \sqrt{V(X)}$ .

In this problem, we have that:

400 city residents are going to be asked. So $n = 400$ .

Suppose that in fact 12% of city residents could name the anchor if asked. This means that $p = 0.12$ .

So,

$\mu = E(X) = 400*0.12 = 48$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{400*0.12*0.88} = 6.5$ .

They plan to fire the news anchor if fewer than 10% of the residents in the sample can do so.

What is the approximate probability that the anchor will be fired?

10% of the residents is 0.10*400 = 40 residents.

Fewer than 10% is 39 residents. So the probability that the anchor will be fired is the pvalue of Z when $X = 39$ .

So:

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{39 - 48}{6.5}$

$Z = -1.38$

$Z = -1.38$ has a pvalue of 0.0838. This means that there is an 8.38% probability that the anchor will be fired.

5 0

2 years ago

In a completely randomized experimental design involving three assembly methods, 30 employees were randomly selected and 10 were

AnnZ [28]

Answer:

$F = \frac{MSR}{MSE} =\frac{45.89}{6.27}=7.32$

So then the best option is:

a. 7.32

Step-by-step explanation:

Previous concepts

Analysis of variance (ANOVA) "is used to analyze the differences among group means in a sample".

The sum of squares "is the sum of the square of variation, where variation is defined as the spread between each individual value and the grand mean"

If we assume that we have $3$ groups and on each group from $j=1,\dots,10$ we have $10$ individuals on each group we can define the following formulas of variation:

$SS_{total}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x)^2$

$SS_{between=Treatment}=SS_{model}=\sum_{j=1}^p n_j (\bar x_{j}-\bar x)^2$

$SS_{within}=SS_{error}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x_j)^2$

And we have this property

$SST=SS_{between}+SS_{within}$

Where SST represent the total sum of squares.

The degrees of freedom for the numerator on this case is given by $df_{num}=k-1=3-1=2$ where k =3 represent the number of groups.

The degrees of freedom for the denominator on this case is given by $df_{den}=df_{between}=N-K=30-3=27$ .

And the total degrees of freedom would be $df=N-1=30 -1 =29$

From the info given we know that $MSR=\frac{SSR}{2}=45.89$

And $MSE=\frac{SSE}{27}=6.27$

From definition the F statisitc is defined as:

$F = \frac{MSR}{MSE} =\frac{45.89}{6.27}=7.32$

So then the best option is:

a. 7.32

3 0

2 years ago

The peso is the currency of Mexico. On October 17, 2016, the exchange rate for 1 Mexican peso was $0.053 U.S. If a traveler exch

Allushta [10]

1 peso = 0.053 dollars.

x pesos = 400 US dollars.

1/x = 0.053 / 400 Cross multiply

400 * 1 = 0.053 x Divide by 0.053

400/0.053 = 0.053*x / 0.053

7547.17 pesos which rounded is

Answer: 7547 pesos

4 0

1 year ago

Read 2 more answers