Of 162 students honored at an academic awards banquet, 48 won awards for mathematics and 78 won awards for English. There are 14

Answer:

Yes, the cost in dollars and the quantity of yogurt are indeed proportional.

The relationship can be expressed as:

Step-by-step explanation:

1. If varies directly with , it can be represented as:

Here, represents the constant of proportionality.

2. We'll calculate the proportionality constant. Given that and , we have:

3. Thus, the equation becomes:

4. Now, we need to verify proportionality. Substituting , which is the quantity of yogurt purchased by Jonah, we should arrive at $0.48:

5. They are indeed directly proportional.

Hello! I'm here to assist you! To calculate interest, we apply the formula prt, which involves multiplying the principal (the amount of money initially), the rate (the interest rate), and the time (typically in years). Here are the results:

$252 at 8% over 2 years yields $40.32
$400 at 2% for a duration of 6 months results in $4
$5,000 at 3.5% for 1 year gives $175
$6,240 at 10% for 9 months amounts to $468

For period calculations, we convert months into decimals: 6 months equals 0.5 years, and 9 months equals 0.75 years. Simply multiply the principal amount by the percentage in decimal form and by the time, and that’s it!

A)
4(q - 10) = 76..... Tim earned 4 points for each correct answer, totaling 76 points. He got 10 answers right less than the total number of questions on the test.

b)
q = 10 + 76/4
q = 29

Thus, the overall number of questions on Tim's math test amounted to 29.

Answer:

The P-value ranges between 2.5% and 5% according to the t-table.

Step-by-step explanation:

A random sample of 16 students from a large university showed an average age of 25 years with a standard deviation of 2 years.

Let = true average age of all students at the university.

So, the Null Hypothesis, : 24 years {indicating the average age is less than or equal to 24 years}

Alternate Hypothesis, : > 24 years {indicating the average age is significantly greater than 24 years}

Here we employ the One-sample t-test statistics as the population's standard deviation is unknown;

                              T.S. = ~

where, = sample average age = 25 years

             s = sample standard deviation = 2 years

             n = sample size = 16

This gives us the test statistics = ~

                                     = 2

The value of the t-test statistics is 2.

Moreover, the P-value of the test-statistics can be found as follows;

P-value = P( > 2) = 0.034 {as per the t-table}

Thus, the P-value lies between 2.5% and 5% based on the t-table.

Given:
1 pack = 5 pencils and cardboard.
1 pack should weigh between 60 grams and 95 grams

60g < x < 95g; where x signifies 1 pack.

Cardboard: 15 grams.

95g - 15g = 80g represents the maximum total weight of 5 pencils.
80g / 5 = 16g is the maximum weight for a single pencil.

60g - 15g = 45g is the minimum total weight of 5 pencils.
45g / 5 = 9g is the minimum weight for a single pencil.

9 < x < 16; where x represents a single pencil in the pack.