All categories

1 month ago

Justify each step. x/3-7=11 x/3=18 x=6

1 answer:

8 0

Here are the steps to solve for the value of x in the equation: x/3 - 7 = 11. We start by moving 7 to the opposite side of the equation, changing its sign from negative to positive, resulting in x/3 = 11 + 7, or x/3 = 18. To isolate x, multiply both sides of the equation by 3, yielding x alone on one side. Thus, we find x = 54. If the equation were instead expressed as 3x - 7 = 11, the solution would give x = 6.

You might be interested in

Find a parametrization, using cos(t) and sin(t), of the following curve: The intersection of the plane y= 5 with the sphere

Svet_ta [12734]

Answer:

The parametrization of the specified curve is $x = 10 cos(t) \ \,z = 10 sin(t)$

Step-by-step explanation:

From the provided problem statement, we derive the function

$x^2 + y^2 + z^2 = 125$

When y = 5

$x^2 + 5^2 +z^2 =125$

$x^2 + z^2 = 100$

$x^2 + z^2 = 10^2$

Converting the above to a polar equation yields

$x = 10 cos(t) \ \,z = 10 sin(t)$

6 0

29 days ago

What is the relative frequency of the revenue earned by B&B Motors from sales of mini trucks compared to the total sales rev

Inessa [12570]

Answer: 0.46

Step-by-step explanation:

B&B Motors' mini trucks yield 0.59; all four companies combined yield 0.39; mini trucks yield 0.13. Hence, 0.59 - 0.13 equals 0.46.

3 0

1 month ago

Read 2 more answers

A major department store chain is interested in estimating the mean amount its credit card customers spent on their first visit

Inessa [12570]

Answer: D) $\$50\pm\$11.08$

Step-by-step explanation:

Based on the provided information, we have

Sample size: n= 15

sample mean: $\overline{x}=\$50.50$

Sample standard deviation: s= $20

Since the population standard deviation is not known, we utilize a t-test.

For a significance level of 95% confidence: $\alpha=1-0.95=0.05$

Critical t-value : $t_{n-1, \alpha/2}=t_{014,0.025}=2.145$ [Using the Student's t-value table]

The required 95% confidence interval yields:-

$\overline{x}\pm t_{n-1, \alpha/2}\dfrac{s}{\sqrt{n}}\\\\ =\$50.50\pm(2.145)\dfrac{\$20}{\sqrt{15}}\\\\\approx \$50\pm\$11.08$

Thus, the sought-after 95% confidence interval for the mean amount spent by credit card customers during their initial visit to the new store in the mall, assuming normal distribution of the spending amounts, is:

$\$50\pm\$11.08$

5 0

22 days ago

A snack stand sold hot dogs and chips at a recent game. The hot dogs cost $2.50 and the snacks cost $0.75. After the game, they

lawyer [12517]

Let x represent the hot dogs

and y represent the snacks

The equation x + y = 175

Rewrite x as 175 - y

And the second equation: 2.50x + 0.75y = 262.50

Substitute to get 2.50(175 - y) + 0.75y = 262.50

Which simplifies to 437.50 - 2.50y + 0.75y = 262.50

Rearranging gives -1.75y = -175

Hence, solving for y results in y = -175 / -1.75 = 100

Thus, 100 snacks and 75 hot dogs were sold

7 0

11 days ago

Read 2 more answers

You’re working in a pharmacy, and are making a table to help with dosage amounts for a certain drug. The recommended dosage is 4

lawyer [12517]

Answer: Children who weigh 10 pounds require 12 teaspoons, those at 15 pounds need 18 teaspoons, and for 30 pounds, it is necessary to have 36 teaspoons.

Step-by-step explanation:

We have a recommended dose of 40 mg per 2.2 pounds of weight, given in three doses throughout the day every 8 hours.

Thus, for a single pound, the daily required dosage is calculated as $\dfrac{40}{2.2}=18.18\ ml$ .

Each individual dose corresponds to $\dfrac{18.18}{3}=6.06\ ml$ of the drug.

This means for one pound, the dosage needed per dose is 6.06 ml.

Thus, for 10 pounds, the calculation is 10 x 6.06 ml = 60.6 ml

To convert ml to teaspoons, knowing that 1 teaspoon equals 5 ml, we find: (60.6 ml ÷ 5) = 12.12 ≈ 12 teaspoons.

For a weight of 15 pounds, the drug requirement is 15 x 6.06 ml = 90.9 ml.

This translates to (90.9 ml ÷ 5) = 18.18 ≈ 18 teaspoons.

For the weight of 30 pounds, it is calculated as 30 x 6.06 ml = 181.8 ml.

Converting this gives us (181.8 ml ÷ 5) = 36.36 ≈ 36 teaspoons.

Therefore, children weighing 10 pounds need 12 teaspoons, those at 15 pounds require 18 teaspoons, and those at 30 pounds need 36 teaspoons.

7 0

1 month ago