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3 years ago

Find the height of the pyramid.

Mathematics

1 answer:

SOVA2 [1]3 years ago

4 0

Answer:

Step-by-step explanation:

Let the height of pyramid be h

$v = \frac{1}{3} lwh$

v= 224

w= 8

l= 12

224=1/3(12)(8)(h)

224=32h

h=224/32

h=7

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.Natalie has $680 to spend at a bicycle store for some new gear and biking outfits.Assume all prices listed include tax.She buys

Vitek1552 [10]

Answer:

Writing the inequality, we have;

$420.56+32.43x\leq680$

the solution to the inequality is;

$x\leq8$

Explanation:

Given that Natalie has $680 to spend at a bicycle store for some new gear and biking outfits.

Total spending must not exceed $680

$\text{total spending }\leq680$

She buys a new bicycle for $383.33.

• She buys 2 bicycle reflectors for $7.61 each and a pair of bike gloves for $22.01.

She plans to spend some or all of the money she has left to buy new biking outfits

for $32.43 each.

let x represent the number of biking outfits she can buy.

Total spending is;

$\begin{gathered} 383.33+2(7.61)+22.01+32.43(x) \\ 420.56+32.43x \end{gathered}$

Writing the inequality, we have;

$420.56+32.43x\leq680$

we can now solve the inequality;

$\begin{gathered} 420.56+32.43x\leq680 \\ \text{subtract 420.56 from both sides;} \\ 420.56-420.56+32.43x\leq680-420.56 \\ 32.43x\leq259.44 \\ \text{divide both sides by 32.43} \\ \frac{32.43x}{32.43}\leq\frac{259.44}{32.43} \\ x\leq8 \end{gathered}$

Therefore, the solution to the inequality is;

$x\leq8$

6 0

2 years ago

The gardening club at school is growing vegetables. The club has 300 square feet of planting beds. Cucumber plants require 6 squ

nadya68 [22]

The question doesn't ask anything in particular, I will show the set of inequalities defined in the problem.

Answer:

System of inequalities:

$6c+4t\leq 300$

$c>0\\t > 0\\c+t\geq 60$

Step-by-step explanation:

Inequalities

The express relations between expressions with a sign other than the equal sign. Common relationals are 'less than', 'greater than', 'not equal to', and many others.

The gardening club at school has 300 square feet of planting beds to plant cucumber and tomato. Each cucumber plant requires 6 square feet of growing space and each tomato plant requires 4 square feet of growing space. We know the total area cannot exceed 300 square feet, so

$6c+4t\leq 300$

Being c and t the number of cucumber and tomato plants respectively.

We also know the students want to plant some of each type of plant and have at least 60 plants. This lead us to more conditions

$c>0\\t > 0\\c+t\geq 60$

Note: The set of inequalities shown is not enough to uniquely solve the problem. We need something to maximize or minimize to optimize c and t

8 0

3 years ago

A study investigated the effectiveness of meditation training in reducing trait anxiety. The study evaluated subjects trait anxi

Setler79 [48]

Answer:

The 99% confidence interval for the population mean reduction in anxiety was (1.2, 8.6).

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 27 - 1 = 26

99% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 26 degrees of freedom(y-axis) and a confidence level of $1 - \frac{1 - 0.99}{2} = 0.995$ . So we have T = 2.7787.