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2 years ago

4

Dave's scale drawing of a tree outside his house is shown below. If 2 centimeters (cm) on the scale drawing equals 6 feet on the

real tree, what is the actual height of the tree?

2 answers:

loris [4]2 years ago

5 0

Answer:

The actual height of the tree is $23.4\ ft$

Step-by-step explanation:

we know that

Using proportion

see the attached figure to better understand the problem

$\frac{2}{6}\frac{cm}{ft}=\frac{7.8}{x}\frac{cm}{ft} \\ \\x=6*7.8/2\\ \\ x=23.4\ ft$

Illusion [34]2 years ago

4 0

Answer:

23.4

Step-by-step explanation:

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A case of tomato cans weighs 563 dekagrams. A case of soup cans weighs 458 dekagrams. How much do the two cases weigh together i

oee [108]

Answer:

102,100 decigrams

Step-by-step explanation:

(564 dag + 458 dag) = 1021 dag

1021 dag × 100 dg/dag = 102100 dg

The two cases together weigh 102,100 decigrams.

_____

1 dag = 10 g

1 dg = 0.1 g

6 0

2 years ago

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At a particular restaurant, each onion ring has 45 calories and each chicken wing has 65 calories. A combination meal with onion

IceJOKER [234]

Answer:

$Number\ of\ chicken\ rings=5\\\\Number\ of\ onion\ rings=10$

Step-by-step explanation:

$Let\ number\ of\ chicken\ rings=x\\\\Number\ of\ onion\ rings=Number\ of\ chicken\ rings+5=x+5\\\\$

Calories:

$Calories\ in\ 1\ chicken\ ring=45\\\\Total\ calories\ because\ of\ onion\ ring=45\times Number\ of\ onion\ ring\\\\Total\ calories\ because\ of\ onion\ ring=45\times(x+5)=45x+225\\\\Calories\ in\ 1\ onion\ ring=65\\\\Total\ calories\ because\ of\ chicken\ ring=65\times Number\ of\ chicken\ ring\\\\Total\ calories\ because\ of\ chicken\ ring=65x\\\\Total\ calories=Calories\ because\ of\ onion\ ring+Calories\ because\ of\ chicken\ ring\\\\Total\ calories=45x+225+65x\\\\Tota\ calories=110x+225$

$Given\ total\ calories=775\\\\110x+225=775\\\\110x=775-225\\\\110x=550\\\\x=5\\\\Number\ of\ chicken\ rings=5\\\\Number\ of\ onion\ rings=5+5=10$

6 0

2 years ago

A King in ancient times agreed to reward the inventor of chess with one grain of wheat on the first of the 64 squares of a chess

statuscvo [17]

Let's start by visualising this concept.

Number of grains on square:
1 2 4 8 16 ...

We can see that it starts to form a geometric sequence, with the common ratio being 2.

For the first question, we simply want the fifteenth term, so we just use the nth term geometric form:
$T_n = ar^{n - 1}$
$T_{15} = 2^{14} = 16384$

Thus, there are 16, 384 grains on the fifteenth square.

The second question begs the same process, only this time, it's a summation. Using our sum to n terms of geometric sequence, we get:
$S_n = \frac{a(r^{n} - 1)}{r - 1}$
$S_{15} = \frac{2^{15} - 1}{2 - 1}$
$S_{15} = 2^{15} - 1 = 32767$

Thus, there are 32, 767 total grains on the first 15 squares, and you should be able to work the rest from here.

6 0

2 years ago

Read 2 more answers

Mia opens a coffee shop in the first week of January. The function W(x) = 0.002x3 - 0.01x2 models the total number of customers

Len [333]

We need to know the function that models the difference in the number of customers visiting the two stores.
We know the function that models the number of customers in the cafeteria
W (x) = 0.002x3 - 0.01x2
We also know the function that models the number of customers who visit the ice cream parlor
R (x) = x2 - 4x + 13
Therefore the difference, D (x), in the number of customers visiting the two stores is:
D (x) = W (x) - R (x)
D (x) = 0.002x ^ 3 - 0.01x ^ 2 - (x ^ 2 -4x +13)
D (x) = 0.002x ^ 3 - 0.01x ^ 2 - x ^ 2 + 4x -13

D (x) = 0.002x ^ 3 - 1.01x ^ 2 + 4x -13
<span> The answer is the third option</span>

8 0

2 years ago

Read 2 more answers

Conscientiousness is a tendency to show self-discipline, act dutifully, and aim for achievement. The trait shows a preference fo

MAVERICK [17]

Answer:

a

The Null hypothesis represented as

$H_0: \mu_1 - \mu_2 = 0$

The Alternative hypothesis represented as

$H_a: \mu_1 - \mu_2 < 0$

b

p-value = P(Z < -3.37 ) = 0.000376

c

There is insufficient evidence to conclude that graduate students score higher, on average, on the HPI than undergraduate students

Step-by-step explanation:

From the question we are told that

The population size is $n= 650$

The sample size for graduates is $n_1 = 300$

The sample mean for graduates is $\= x _1 = 148$

The sample standard deviation for graduates is $\sigma_1 = 16$

The sample size for under-graduates is $n _2 = 350$

The sample mean for under-graduates is $\= x _2 = 153$

The sample standard deviation for graduates is $\sigma_2 = 21$

The Null hypothesis represented as

$H_0: \mu_1 - \mu_2 = 0$

The Alternative hypothesis represented as

$H_a: \mu_1 - \mu_2 < 0$

Where $\mu_1 \ and \ \mu_2$ are the population mean

Now the test statistic is mathematically represented as

$t = \frac{(\= x_1 - \= x_2 ) }{ \sqrt{ \frac{ (n_1 - 1 )\sigma_1 ^2 + (n_2 - 1)\sigma_2^2}{n_1 +n_2 -2} } * \sqrt{ \frac{1}{n_1} + \frac{1}{n_2} } }$

substituting values

$t = \frac{(148 - 153 ) }{ \sqrt{ \frac{ (300- 1 )16 ^2 + (350 - 1) 21^2}{300 +350 -2} } * \sqrt{ \frac{1}{300} + \frac{1}{350} } }$

$t = -3.37$

The p-values is mathematically evaluated as

p-value = P(Z < -3.37 ) = 0.000376

The above answer is gotten using a p-value calculator at (0.05) level of significance

Looking the p-value we see that it is less than the level of significance (0.05) so Null hypothesis is rejected

Hence there is insufficient evidence to conclude that graduate students score higher, on average, on the HPI than undergraduate students

6 0

2 years ago