The function C(x) = 200x + 240 gives the cost for a college to offer x sections of an introductory class in CPR. The function R(x) = 280x gives the amount of revenue the college brings in when offering x sections of CPR. Find the point where the cost equals the revenue by graphing each function on the same coordinate system.

Answer:

1 can sing but cannot play keyboard.

Step-by-step explanation:

There are six members in the rock band. We need to identify how many person can sing, play guitar and play keyboard. To identify this we will find out number of member for each activity,

Total 6 members

4 can play guitar

3 can pay keyboard

All singers play guitar but one guitarist cannot sing.

There will be 1 singer who cannot play keyboard.

Answer:

(-0.5, 0)

Step-by-step explanation:

Coordinates of endpoints of segment are:

A= (-2, 1)

B= (1, - 1)

By mid-point formula:

The midpoint of [tex] \overline{AB} [/tex]

[tex] = \bigg(\frac{ - 2 + 1}{2}, \: \: \frac{1 + ( - 1)}{2} \bigg) \\ \\ = \bigg(\frac{ - 1}{2}, \: \: \frac{0}{2} \bigg)\\ \\ = \bigg(\frac{ - 1}{2}, \: \: 0 \bigg)\\ \\ = ( - 0.5, \: \: 0 )[/tex]

Answer:

sinR = 0.7184

Step-by-step explanation:

Pythagorean Theorem: a² + b² = c²

sin∅ = opposite/hypotenuse

Step 1: Find missing leg length

16² + b² = 23²

b² = 23² - 16²

b = √273

Step 2: Find sinR

sinR = √273/23

sinR = 0.718379

Answer:

Option 2

Step-by-step explanation:

Last month the change in water level was -13 mm. This month, the water level increase by 13 mm.

-13 + 13 = 0

Answer:

x=9,3

Step-by-step explanation:

x²-12x=-27

x²-12x+(12/2)²=-27+(12/2)²

x²-12x+6²=-27+36

(x-6)²=9

x-6=[tex] \frac{ + }{ - } \sqrt{9} [/tex]

x-6=+3 and x-6=-3

x=9 and 3

Answer: Apothem

Step-by-step explanation: Half of an octagon is called an apothem

The dashed line shown in the regular octagon is called an apothem.

Octagon is an eight-sided two-dimensional geometrical figure. An octagon consists of 8 interior angles and 8 exterior angles. The sum of the interior angles of an octagon is 1080°, and the sum of its exterior angles is 360°.

Given is a regular octagon, we need to determine the asked part of the given octagon is called what,

So, the part asked is called the apothem.

A line from the center of a regular polygon at right angles to any of its sides is called an apothem.

Hence, the dashed line shown in the regular octagon is called an apothem.

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Answer:

(a)[tex]D(x)=-2,500x+60,000[/tex]

(b)[tex]R(x)=60,000x-2500x^2[/tex]

(c) x=12

(d)Optimal ticket price: $12

Maximum Revenue:$360,000

Step-by-step explanation:

The stadium holds up to 50,000 spectators.

When ticket prices were set at $12, the average attendance was 30,000.

When the ticket prices were on sale for $10, the average attendance was 35,000.

(a)The number of people that will buy tickets when they are priced at x dollars per ticket = D(x)

Since D(x) is a linear function of the form y=mx+b, we first find the slope using the points (12,30000) and (10,35000).

[tex]\text{Slope, m}=\dfrac{30000-35000}{12-10}=-2500[/tex]

Therefore, we have:

[tex]y=-2500x+b[/tex]

At point (12,30000)

[tex]30000=-2500(12)+b\\b=30000+30000\\b=60000[/tex]

Therefore:

[tex]D(x)=-2,500x+60,000[/tex]

(b)Revenue

[tex]R(x)=x \cdot D(x) \implies R(x)=x(-2,500x+60,000)\\\\R(x)=60,000x-2500x^2[/tex]

(c)To find the critical values for R(x), we take the derivative and solve by setting it equal to zero.

[tex]R(x)=60,000x-2500x^2\\R'(x)=60,000-5,000x\\60,000-5,000x=0\\60,000=5,000x\\x=12[/tex]

The critical value of R(x) is x=12.

(d)If the possible range of ticket prices (in dollars) is given by the interval [1,24]

Using the closed interval method, we evaluate R(x) at x=1, 12 and 24.

[tex]R(x)=60,000x-2500x^2\\R(1)=60,000(1)-2500(1)^2=\$57,500\\R(12)=60,000(12)-2500(12)^2=\$360,000\\R(24)=60,000(24)-2500(24)^2=\$0[/tex]

Therefore:

Answer:

no solution

Step-by-step explanation:

4x+3y = 6

8x + 6y = 5

Multiply the first equation by -2

-2(4x+3y) = 6*-2

-8x -6y = -12

Add this to the second equation

-8x-6y = -12

8x + 6y = 5

---------------------

0x + 0y = -7

0 = -7

Since this is never true there is no solution

Answer:

X = 8/3, y= -14/9

Step-by-step explanation:

using elimination method:

subtract equation 1 from equation 2

8x-4x + 6y-3y = 5-6

4x+3y= -1

4x= -1-3y

divide both sides by 4

x = -1-3y÷4

substitute x = -1-3y/4 in equation 2

8(-1-3y)/4 +6y = 5

-8-24y/4+ 6y =5

-8-24y+6y/4 =5

-8-18y/4 = 5

Cross multy

-8-18y × 1 = 4×5

-8-18y = 20

collect like terms

-18y = 20+8

-18y = 28

divide both sides by-18

y = 28/-8

y = -14/9

put y = -14/9 in equation 1

4x+3(-14/9) = 6

4x-42/9 = 6

42/9 = 14/3

so, 4x=6+14/3

LCM =3

4x = 18+14/3

4x= 32/3

cross multiply

4x×3 = 32

12x = 32

divide both sides by 12

12x/12= 32/12

x = 8/3

so, x = 8/3, y = -14/9

check:

first equation:

4(8/3) + 3(-14/9)

32/3 - 14/3( 3 cancels 9 rem 3)

LCM= 3

32 - 14/3

= 18/3

= 6

Answer:

  2 1/10

Step-by-step explanation:

We suppose you want the quotient of the mixed numbers 5 3/5 and 2 2/3.

  (5 3/5)/(2 2/3) = (28/5)/(8/3) = (28/5)(3/8) = (4)(7)(3)/(5(4)(2)) = 21/10

  = 2 1/10

Answer:

A 90% confidence interval for the standard deviation of the fracture toughness distribution is [4.06, 6.82].

Step-by-step explanation:

We are given the following observations that were made on fracture toughness of a base plate of 18% nickel maraging steel below;

68.6, 71.9, 72.6, 73.1, 73.3, 73.5, 75.5, 75.7, 75.8, 76.1, 76.2,  76.2, 77.0, 77.9, 78.1, 79.6, 79.8, 79.9, 80.1, 82.2, 83.7, 93.4.

Firstly, the pivotal quantity for finding the confidence interval for the standard deviation is given by;

                             P.Q.  =  [tex]\frac{(n-1) \times s^{2} }{\sigma^{2} }[/tex]  ~ [tex]\chi^{2} __n_-_1[/tex]

where, s = sample standard deviation = [tex]\sqrt{\frac{\sum (X - \bar X^{2}) }{n-1} }[/tex] = 5.063

            [tex]\sigma[/tex] = population standard deviation

            n = sample of observations = 22

Here for constructing a 90% confidence interval we have used One-sample chi-square test statistics.

So, 90% confidence interval for the population standard deviation, [tex]\sigma[/tex] is ;

P(11.59 < [tex]\chi^{2}__2_1[/tex] < 32.67) = 0.90  {As the critical value of chi at 21 degrees  

                                                  of freedom are 11.59 & 32.67}  

P(11.59 < [tex]\frac{(n-1) \times s^{2} }{\sigma^{2} }[/tex] < 32.67) = 0.90

P( [tex]\frac{ 11.59}{(n-1) \times s^{2}}[/tex] < [tex]\frac{1}{\sigma^{2} }[/tex] < [tex]\frac{ 32.67}{(n-1) \times s^{2}}[/tex] ) = 0.90

P( [tex]\frac{(n-1) \times s^{2} }{32.67 }[/tex] < [tex]\sigma^{2}[/tex] < [tex]\frac{(n-1) \times s^{2} }{11.59 }[/tex] ) = 0.90

90% confidence interval for [tex]\sigma^{2}[/tex] = [ [tex]\frac{(n-1) \times s^{2} }{32.67 }[/tex] , [tex]\frac{(n-1) \times s^{2} }{11.59 }[/tex] ]

                                     = [ [tex]\frac{21 \times 5.063^{2} }{32.67 }[/tex] , [tex]\frac{21 \times 5.063^{2} }{11.59 }[/tex] ]

                                     = [16.48 , 46.45]

90% confidence interval for [tex]\sigma[/tex] = [[tex]\sqrt{16.48}[/tex] , [tex]\sqrt{46.45}[/tex] ]

                                                 = [4.06 , 6.82]

Therefore, a 90% confidence interval for the standard deviation of the fracture toughness distribution is [4.06, 6.82].

Answer:

The right answer is the last option, 12,12.

Step-by-step explanation:

[tex]GI^2=FI*IH\\ GI^2 = 7*21\\ GI = \sqrt{147}[/tex]

[tex]\sqrt{147} = 12,124... = 12,12[/tex]

Answer:

1.88

Step-by-step explanation:

8-2√5=3.527864045

square root of 3.527864045=1.87826090972

the question will probably want it to 2d.p (decimal places) which means the answer would be 1.88

Answer:

The square root of 8 - 2√5 is

[tex] \sqrt{4 + \sqrt{11} } \: - \sqrt{4 - \sqrt{11} } [/tex]

Step-by-step explanation:

To find the square root

8-2√5 must be in the form √a - √b where a > b

√ 8 - 2√5 = √a - √b

Square both sides

8 - 2√5 = (√a - √b)²

That's

8 - 2√5 = (a + b) - 2√ab

Since the two surd expressions are equal we can equate them

That's

8 = a + b ........ 1

a = 8 - b ........ 2

2√5 = 2√ab

Simplify

Divide both sides by 2

√5 = √ab

square both sides

We have

5 = ab ....... 3

Substitute a = 8 - b into equation 3

5 = ( 8 - b)b

5 = 8b - b²

b² - 8b + 5 = 0

After solving

b = 4 + √ 11 or 4 - √ 1

Since b is less than a

b = 4 - √11

a = 4 + √11

So the square root of 8 - 2√5 is

[tex] \sqrt{4 + \sqrt{11} } \: - \sqrt{4 - \sqrt{11} } [/tex]

Hope this helps you.

Answer:

Systematic sampling

Step-by-step explanation:

We have the following sampling technique:

-Random sampling is analogous to putting everyone's name in a hat and extracting several names. Each element of the population has the same probability of occurring.

-Systematic sampling, here the list of elements is "counted". That is, each element k is taken. This is similar to aligning everyone and listing "1,2,3,4; 1,2,3,4; etc."

-Convenience sampling, easily available data is used here. That is, the first people the surveyor meets.

-Cluster sampling is achieved by dividing the population into groups, generally geographically.

-Stratified sampling also divides the population into groups called strata. However, this time it is for some feature, not geographically

In the case of the statement it is systematic because every 30th multiple is picked up which is in a system order members

Answer:

d. t ≈ 5m

e. y ≈ 44°

f. x = 36°

Step-by-step explanation:

We'd apply the trigonometry function to solve for all missing sides and angles as follows:

d. Adjacent length = t

Hypothenuse = 11.1m

θ = 62°

Use Cos θ = adjacent/hypothenuse

Cos(62) = t/11.1

Multiply both sides by 11.1

11.1*cos(62) = t

11.1*0.4695 = t

t = 5.21 ≈ 5 m

e. Opposite = 7m

Hypotenuse = 10m

θ = y°

Use sine θ = opposite/hypotenuse

Thus,

sine θ = 7/10

sine θ = 0.7

θ = sin-¹(0.7) = 44.4

y ≈ 44° (nearest whole number)

f. Opposite = 4.2cm

Adjacent = 5.8cm

θ = x°

Use tan θ = opposite/adjacent

tan θ = 4.2/5.8

tan θ = 0.7241

θ = tan-¹(0.7241) = 35.91

θ = x ≈ 36°

Answer:

2.89

Step-by-step explanation:

just do 1.7×1.7=2.89

Answer:

Step-by-step explanation:

This is a test of 2 population proportions. Let 1 and 2 be the subscript for the men and women who own cats respectively. The population proportion of men and women who own cats would be p1 and p2 respectively.

p1 - p2 = difference in the proportion of men and women who own cats.

The null hypothesis is

H0 : p1 = p2

p1 - p2 = 0

The alternative hypothesis is

Ha : p1 ≠ p2

p1 - p2 ≠ 0

it is a two tailed test

Sample proportion = x/n

Where

x represents number of success

n represents number of samples

For men

n1 = 80

p1 = 55/100 = 0.55

x1 = p1n1 = 0.55 × 80 = 44

For women,

n2 = 100

p2 = 30/100 = 0.3

x2 = p2n2 = 0.3 × 100 = 30

The pooled proportion, pc is

pc = (x1 + x2)/(n1 + n2)

pc = (44 + 30)/(80 + 100) = 0.41

1 - pc = 1 - 0.41 = 0.59

z = (p1 - p2)/√pc(1 - pc)(1/n1 + 1/n2)

z = (0.55 - 0.3)/√(0.41)(0.59)(1/80 + 1/100) = 3.39

Test statistic = 3.39

Answer:

Step-by-step explanation:

To find the answer to Part A we can do (97 - 42) + 1 = 56. The reason we do + 1 is because 97 - 42 is just counting the numbers in between 42 and 97 but it leaves out 42 and since it's inclusive we need to include 42.

Part B: We can do (200 / 2) - 1 = 99. The reason we do - 1 is because 200 / 2 includes the endpoint of the line but since we don't want to include the endpoint of the line we do - 1.

Answer:

Part A = 56 Integers

Part B = 99 Points

Step-by-step explanation:

Part A ~ Since it's inclusive, at the end we must put n + 1 -->

97 - 42 = 55 => 55 = n => 56 Integers

Part B ~ n - 1  Since it is exclusive. so, =>

200/2 = 100, 100 = n (n-1) => 99 Points

Hope this helps!

Answer:

There is not enough evidence to support the claim that women who exercise daily have a significantly different duration of labor than all women.

Standard error sm = 1.634

Test statistic t = 1.102

P-value = 0.28

Step-by-step explanation:

This is a hypothesis test for the population mean.

The claim is that women who exercise daily have a significantly different duration of labor than all women.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=16\\\\H_a:\mu\neq 16[/tex]

The significance level is 0.05.

The sample has a size n=29.

The sample mean is M=17.8.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=√77.4=8.8.

The estimated standard error of the mean is computed using the formula:

[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{8.8}{\sqrt{29}}=1.634[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{17.8-16}{1.634}=\dfrac{1.8}{1.634}=1.102[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=29-1=28[/tex]

This test is a two-tailed test, with 28 degrees of freedom and t=1.102, so the P-value for this test is calculated as (using a t-table):

[tex]\text{P-value}=2\cdot P(t>1.102)=0.28[/tex]

As the P-value (0.28) is bigger than the significance level (0.05), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that women who exercise daily have a significantly different duration of labor than all women.

Answer:

C

Step-by-step explanation:

Tan = opposite / adjacent

= 1 / √3

= √3 / 3

Answer:

C.

Step-by-step explanation:

Tangent= opposite over adjacent.

Tangent = 1/√3

Answer:

D. 3 and -4

Step-by-step explanation:

Given the expression, x² - x - 12, let's factorise to find the value of p and q using the table, for which we would have the expression simplified as (x + p)(x + q)

From the table, let's find the values of p and q that would give us -12 when multiplied together, and would also give us -1 when summed together.

Thus, from the table given, the row containing the values of p(3) and q(-4) gives us = -1 (p+q) . p = 3, q = -4 would be our values to use to factor x² - x - 12, as multiplying both will also give us "-12".

Thus, x² - x - 12 would be factorised or simplified as (x + 3)(x - 4)

Therefore, the answer is: D. 3 and -4

Answer:

D a p e x

Step-by-step explanation:

Answer:

P [ x > 59000} = 0,6057

Step-by-step explanation:

We assume Normal Distribution

P [ x > 59000} = (x - μ₀ ) /σ/√n

P [ x > 59000} =  (59000 - 60000)/ 3800

P [ x > 59000} = - 1000/3800/√35

P [ x > 59000} = - 1000*5,916 /3800

P [ x > 59000} =  - 5916/3800

P [ x > 59000} = - 1,55

We look for p value for that z score n z-table and find

P [ x > 59000} = 0,6057

Answer and Step-by-step explanation:

The computation is shown below:

a. The economic order quantity is

[tex]= \sqrt{\frac{2\times \text{Annual demand}\times \text{Ordering cost}}{\text{Carrying cost}}}[/tex]

[tex]= \sqrt{\frac{2\times \text{6,100}\times \text{\$31}}{\text{\$8}}}[/tex]

= 217 units

b. The average inventory used is

[tex]= \frac{economic\ order\ quantity}{2}[/tex]

[tex]= \frac{217}{2}[/tex]

= 108.5 units

c. The optimal order per year

[tex]= \frac{annual\ demand}{economic\ order\ quantity}[/tex]

[tex]= \frac{6,100}{217}[/tex]

= 28 orders

d. The optima number of days is

[tex]= \frac{working\ days}{optimal\ number\ of\ orders}[/tex]

[tex]= \frac{250}{28}[/tex]

= 8.9 days

e. The total annual inventory cost is

= Purchase cost + ordering cost + carrying cost

where,

Purchase cost is

[tex]= \$6,100 \times \$101[/tex]

= $616,100

Ordering cost = Number of orders × ordering cost per order

= 28 orders × $31

= $868

Carrying cost = average inventory × carrying cost per unit

= 108.50 units × $8

= $868

So, the total would be  

= $616,100 + $868 + $868

= $617,836

Answer:

12.1 km

Step-by-step explanation:

350 * 2 = 700

200 * 2 = 400

700 + 400 = 1100

1100 * 11 = 12100

12100 / 1000 = 12.1

12.1 km

Answer:

hope it helps uh......

Step-by-step explanation:

Kaytee's total points are WX + 2S − L.  The total number of exams is W − Y + 2.  Therefore:

G = (WX + 2S − L) / (X − Y + 2)

The total number of exams is W − Y + 2.

We have given that,

In professor Hoepker's class, there are X tests and a final. At the end of the semester, the lowest Y test scores are dropped and the remaining test scores and the final (which has twice the weight of a test) are averaged to compute the average score for the entire class. The final cannot be dropped.

Going into the final, student Kaytee has an average of W on the X tests. The sum of her lowest Y test scores is L. Her final exam score is S.

The sum brings two or more numbers together to make a new total.

We have to determine her average score of G in the class in terms of X, Y, W, L, and S.

Kaytee's total points are WX + 2S − L.  

The total number of exams is W − Y + 2.

Therefore:G = (WX + 2S − L) / (X − Y + 2)

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Answer:

C

Step-by-step explanation:

We know that A is not true because we know that h(8) is 19, not 21. B is also not true because the value of h(x) can't be -1. D can't be true because x can't be 13, therefore the answer is C.

Answer:

(B ) .  34.2cm^2

Step-by-step explanation:

[tex]A = \frac{\alpha }{360} \times \pi r^2\\\alpha=20 \\r = 14\\\\A =\frac{20}{360} \times 22/7\times 14^2\\A = 1/18 \times4312/7\\A =34.2 cm^2[/tex]

Answer:

5(2a -5 + b)

Step-by-step explanation:

(10a - 25 + 5b) = 5( 2a - 5 + b)

5(b +  2a  - 5) = 5(2a - 5 + b)

Answer:

5(2a -5 + b)

Step-by-step explanation:

Answer:

D) Standard deviation, because there are no outliers that affect the center