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1 year ago

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The cost of making a chair is $28 correct to the nearest dollar. Calculate the lower and upper bounds for the cost of making 450

chairs

1 answer:

Anna71 [15]1 year ago

3 0

Answer:

$12,375

$12820.50

Step-by-step explanation:

To obtain a rounded value of $28 (to nearest dollar) the lowest and highest possible value before rounding will be : 27.50 and 28.49

Hence,

Lower bound = $27.50

Upper bound = $28.49

Therefore. Cost of making 450 chairs ;

27.50 * 450 = $12,375 (lower bound)

28.49 * 450 $12820.50 (upper bound)

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Twenty-one boys and eight girls go on a camping trip. In how many ways can a group of six be selected to gather firewood, given

lorasvet [3.4K]

(a) there are 8C2 = 28 ways of picking 2 girls from 8
And there are 21C4 = 5985 ways of picking 4 boys

Required number of ways for 2g / 4b = 28 * 5985 = 167,580

(b) at least 2 girls means combinations of 2g/4b , 3g,3b , 4g/2b , 5g 1b or
6 girls.

2g/4b = 167,580 ways
3g/3b = 8C3 * 21C3 = 56 * 1330 = 74,480
4g/2b = 8C4* 21C2 = 70 * 210 = 14,700
5g 1b = 8C5* 21 = 56*21 = 1176
6 girls = 8C6 = 28

adding these up we get the answer to (b) which is 257,964

6 0

1 year ago

Members of a school club are buying matching shirts. They know at least 25 members will get a shirt. Long-sleeved shirts are $10

charle [14.2K]

Answer:

Maximum number of long sleeved shirt that can be purchase is, 8

and

Minimum number of long sleeved shirt that can be purchased is, 0

Step-by-step explanation:

let y represents the number of short sleeves and x represents the number of long sleeves.

As per the given condition:

Members of a school club are buying matching shirts. They know at least 25 members will get a shirt.

we have;

$x+y\geq 25$ or

$y\geq 25 -x$ ....[1]

Since, long sleeves shirt are $ 10 each and short sleeves shirt are $ 5 each.

then;

Total cost of long sleeves is 10x and

the total cost of short sleeves is 5y

Also; the club can spend no more than $ 165

then;

$10x+5y\leq 165$

$5y\leq 165 -10x$ or

$y\leq 33-2x$ ......[2]

Solving the inequality equation with the graph :

Plot equation [1] and [2]; we get the maximum at point (8 , 17)

so, x= 8.

If we take minimum value of x =0 then y is between 25 and 33.

so, the solution area is between the lines to the left of where the lines intersect.

Therefore, the maximum number of long sleeved shirts can be purchased is 8 and the minimum number of long sleeved shirt can be purchased is 0

6 0

2 years ago

Read 2 more answers

Find the surface area of the triangular prism. A triangular prism. The base is a right triangle with base 1 foot, height 2 feet

mylen [45]

Answer:

<h2>17.6ft²</h2>

Step-by-step explanation:

The formula for calculating the surface area of a triangular prism is expressed as shown below:

SA= bh + pH

b= base of the triangle

h- height of the triangle

p= perimeter of the triangle

H= height of the prism

Given b = 1foot

h = 2feet

perimeter of the triangle = sum of all its sides = 1ft + 2ft + 2.2ft

p = 5.2ft

H = 3ft

Substituting the values into the formula for finding the surface area:

SA = 1(2)+5.2(3)

SA = 2+15.6

SA = 17.6ft²

The surface area of the triangular prism is 17.6ft²

3 0

2 years ago

Suppose you are an expert on the fashion industry and wish to gather information to compare the amount earned per month by model

Ann [662]

Answer:

(1) The degrees of freedom for unequal variance test is (14, 11).

(2) The decision rule for the 0.01 significance level is;

If the value of our test statistics is less than the critical values of F at 0.01 level of significance, then we have insufficient evidence to reject our null hypothesis.

If the value of our test statistics is more than the critical values of F at 0.01 level of significance, then we have sufficient evidence to reject our null hypothesis.

(3) The value of the test statistic is 0.3796.

Step-by-step explanation:

We are given that you are an expert on the fashion industry and wish to gather information to compare the amount earned per month by models featuring Liz Claiborne's attire with those of Calvin Klein.

The following is the amount ($000) earned per month by a sample of 15 Claiborne models;

$3.5, $5.1, $5.2, $3.6, $5.0, $3.4, $5.3, $6.5, $4.8, $6.3, $5.8, $4.5, $6.3, $4.9, $4.2 .

The following is the amount ($000) earned by a sample of 12 Klein models;

$4.1, $2.5, $1.2, $3.5, $5.1, $2.3, $6.1, $1.2, $1.5, $1.3, $1.8, $2.1.

(1) As we know that for the unequal variance test, we use F-test. The degrees of freedom for the F-test is given by;

$\text{F}_(_n__1-1, n_2-1_)$

Here, $n_1$ = sample of 15 Claiborne models

$n_2$ = sample of 12 Klein models

So, the degrees of freedom = ( $n_1-1, n_2-1$ ) = (15 - 1, 12 - 1) = (14, 11)

(2) The decision rule for 0.01 significance level is given by;

If the value of our test statistics is less than the critical values of F at 0.01 level of significance, then we have insufficient evidence to reject our null hypothesis.

If the value of our test statistics is more than the critical values of F at 0.01 level of significance, then we have sufficient evidence to reject our null hypothesis.

(3) The test statistics that will be used here is F-test which is given by;

T.S. = $\frac{s_1^{2} }{s_2^{2} } \times \frac{\sigma_2^{2} }{\sigma_1^{2} }$ ~ $\text{F}_(_n__1-1, n_2-1_)$

where, $s_1^{2}$ = sample variance of the Claiborne models data = $\frac{\sum (X_i-\bar X)^{2} }{n_1-1}$ = 1.007

$s_2^{2}$ = sample variance of the Klein models data = $\frac{\sum (X_i-\bar X)^{2} }{n_2-1}$ = 2.653

So, the test statistics = $\frac{1.007}{2.653 } \times 1$ ~ $\text{F}_(_1_4,_1_1_)$

= 0.3796

Hence, the value of the test statistic is 0.3796.

3 0

1 year ago

The length of the shadow of a pole on level ground increases by 90m when the angle of elevation of the sun changes from 58° to 3

viva [34]

Answer:

119.45 m

Step-by-step explanation:

Given:

When angle of elevation of the sun changes from 58° to 36° the length of shadow of a pole increases by 90 m.

To find:

Length of pole = ?

Solution:

Kindly refer to the attached image.

$\triangle ABC$ represents the 1st angle of elevation of sun i.e. 58°

$\triangle ABD$ represents the 2nd angle of elevation of sun i.e. 36°

Change in shadow is represented by CD = 90 m

Let height of pole, AB = $h$ m

Let side BC = $x$ m

Now, let us apply tangent rules in $\triangle ABC, \triangle ABD$ one by one:

$tan\theta = \dfrac{Perpendicular}{Base}\\\Rightarrow tan58^\circ=\dfrac{AB}{BC}\\\Rightarrow tan58^\circ=\dfrac{h}{x}\\\Rightarrow x = 0.624h ..... (1)$

$tan36^\circ = \dfrac{h}{x+90}$

Putting value of $x$ using equation (1):

$tan36^\circ = \dfrac{h}{0.624h+90}\\\Rightarrow 0.726\times 0.624h+0.726\times 90 = h\\\Rightarrow h-0.453h =65.34\\\Rightarrow \bold{h = 119.45\ m}$

119.45 m is the height of pole.

7 0

2 years ago