Ask question

Ask question

All categories

2 years ago

10

Mae sold raffle tickets to Steven and to Theo. Each ticket costs k dollars. Steven bought 10 raffle tickets. Theo bought 15 raff

le tickets. Which expression must be equal to the difference between how many dollars Theo spent and how many dollars Steven spent

2 answers:

morpeh [17]2 years ago

8 0

Steven:10k=x and Theo:15k=x. Then you subtract Theo's or the highest number by the smallest number, or Steven

zhenek [66]2 years ago

8 0

Went ahead and answered it before. Just wanted to make sure. I sent you my work to show you the three possible ways of getting 5k.

You might be interested in

Half angle tan 5pi/8

Bond [772]

The half-angle formula for tangent is:

tan(a/2) = (sin a / (1 + cos a)) = ((1 - cos a) / sin a)

Now we can plug in values:

tan(5π/8) = (sin(5π/4) / (1 + cos(5π/4)) = ((1 - cos(5π/4)) / sin(5π/4)

tan(5π/8) = (-√2/2) / (1 + (-√2/2)) = (1 - (-√2/2)) / (-√2/2)

tan(5π/8) = ((-√2/2)) / ((2 - √2)/2) = ((2 + √2)/2) / (-√2/2)

Now we can solve the first half:

(-√2/2)(2 / (2 - √2))
(-√2/2)((4 + 2√2) / 2)
(-√2/2)(2 + √2)
(-2√2 - 2)/2
-√2 - 1

tan(5pi/8) = -√2 - 1

4 0

2 years ago

The owner of a chain of supermarkets notices that there is a positive correlation between the sales of beer and the sales of ice

Dmitry_Shevchenko [17]

Answer:

D. the sale of beer and ice cream may both be affected by another variable such as the outside temperature.

Step-by-step explanation:

A. There is no evidence to indicate that the positive correlation observed is an error.

B. Even though there is a positive correlation between beer and ice cream sales, there is no evident cause and consequence relationship.

C. The relationship isn't necessarily linear.

D. It is plausible to assume that the sales of beer and ice cream are both affected by another variable like temperature. Both of the products are usually consumed cold and should see an increase in sales during warmer seasons and a decrease in sales during colder seasons.

4 0

2 years ago

g Assume that the distribution of time spent on leisure activities by adults living in household with no young children is norma

OLga [1]

Answer:

"<em>The probability that the amount of time spent on leisure activities per day for a randomly selected adult from the population of interest is less than 6 hours per day</em>" is about 0.8749.

Step-by-step explanation:

We have here a <em>random variable</em> that is <em>normally distributed</em>, namely, <em>the</em> <em>time spent on leisure activities by adults living in a household with no young children</em>.

The normal distribution is determined by <em>two parameters</em>: <em>the population mean,</em> $\\ \mu$ , and <em>the population standard deviation,</em> $\\ \sigma$ . In this case, the variable follows a normal distribution with parameters $\\ \mu = 4.5$ hours per day and $\\ \sigma = 1.3$ hours per day.

We can solve this question following the next strategy:

Use the <em>cumulative</em> <em>standard normal distribution</em> to find the probability.
Find the <em>z-score</em> for the <em>raw score</em> given in the question, that is, <em>x</em> = 6 hours per day.
With the <em>z-score </em>at hand, we can find this probability using a table with the values for the <em>cumulative standard normal distribution</em>. This table is called the <em>standard normal table</em>, and it is available on the Internet or in any Statistics books. Of course, we can also find these probabilities using statistics software or spreadsheets.

We use the <em>standard normal distribution </em>because we can "transform" any raw score into <em>standardized values</em>, which represent distances from the population mean in standard deviations units, where a <em>positive value</em> indicates that the value is <em>above</em> the mean and a <em>negative value</em> that the value is <em>below</em> it. A <em>standard normal distribution</em> has $\\ \mu = 0$ and $\\ \sigma = 1$ .

The formula for the <em>z-scores</em> is as follows

$\\ z = \frac{x - \mu}{\sigma}$ [1]

Solving the question

Using all the previous information and using formula [1], we have

<em>x</em> = 6 hours per day (the raw score).

$\\ \mu = 4.5$ hours per day.

$\\ \sigma = 1.3$ hours per day.

Then (without using units)

$\\ z = \frac{x - \mu}{\sigma}$

$\\ z = \frac{6 - 4.5}{1.3}$

$\\ z = \frac{1.5}{1.3}$

$\\ z = 1.15384 \approx 1.15$

We round the value of <em>z</em> to two decimals since most standard normal tables only have two decimals for z.

We can observe that z = 1.15, and it tells us that the value is 1.15 standard deviations units above the mean.

With this value for <em>z</em>, we can consult the <em>cumulative standard normal table</em>, and for this z = 1.15, we have a cumulative probability of 0.8749. That is, this table gives us P(z<1.15).

We can describe the procedure of finding this probability in the next way: At the left of the table, we have z = 1.1; we can follow the first line on the table until we find 0.05. With these two values, we can determine the probability obtained above, P(z<1.15) = 0.8749.

Notice that the probability for the z-score, P(z<1.15), of the raw score, P(x<6) are practically the same, $\\ P(z$ . For an exact probability, we have to use a z-score = 1.15384 (without rounding), that is, $\\ P(z$ . However, the probability is approximated since we have to round z = 1.15384 to z = 1.15 because of the use of the table.

Therefore, "<em>the probability that the amount of time spent on leisure activities per day for a randomly selected adult from the population of interest is less than 6 hours per day</em>" is about 0.8749.

We can see this result in the graphs below. First, for P(x<6) in $\\ N(4.5, 1.3)$ (red area), and second, using the standard normal distribution ( $\\ N(0, 1)$ ), for P(z<1.15), which corresponds with the blue shaded area.

5 0

2 years ago

Find the cube root of 8x7x9x49x3

vodka [1.7K]

Answer:

=42

Step-by-step explanation:

The expression 8×7×9×49×3 can be written in its simplest factor form as follows.

8=2³

49=7²

9=3²

Thus the expression becomes:2³×7×3²×7²×3

Combine the indices to the same base.

2³×3³×7³

Finding the cube root involves dividing the index by three.

Thus ∛(2³×3³×7³)= 2×3×7

=42

5 0

2 years ago

Tania has a set of nesting rings. This table shows the relationship between the radius of a ring and the ring's circumference.

valentinak56 [21]

Answer:

The circumference is 59.66 cm

Step-by-step explanation:

we know that

The circumference of a circle (ring) is given by the formula

$C=2\pi r$

If the radius is

$r=9.5\ cm$

substitute in the formula

$C=2\pi (9.5)$

$C=19\pi\ cm$ ----> exact value

assume

$\pi =3.14$

substitute

$C=19(3.14)=59.66\ cm$

5 0

2 years ago