1. Bailey withdrew $135 from her checking account. Write an algebraic expression that describes Bailey's action.

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:

(CX3)+10

Step-by-step explanation:

Answer:

c×3+10= j

Step-by-step explanation:

Answer:

48

Step-by-step explanation:

You are doubling 2 dimensions, so you just multiply the volume by 2 each time. Since you are doing it twice, you multiply the volume by 4. 12*4=48. You could also brute force it and just do 24*36*12/216(the volume of the 6 inch cube).

Given that, a box in the shape of a rectangular prism, with dimensions 12 inches by 18 inches by 12 inches, can hold exactly 12 cubes measuring 6 inches on each side.

We need to find that how many cubes it holds if the length and width of the base are doubled,

We know that,

Volume of a rectangular prism = length × width × height

Volume of the new rectangular prism, = 2length × 2width × height

= 4(length × width × height)

= 4(12·12·18)

= 4×2592

= 10,368

Volume of the cube = side³

= 6³ = 216

The number of cube that the new rectangular prism can hold = Volume of the rectangular prism / Volume of the cube

= 10,368 / 216

= 48

Hence, the new rectangular prism, can hold 48 cubes.

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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:

2.89

Step-by-step explanation:

just do 1.7×1.7=2.89

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:

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:

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:

-$3576

Step-by-step explanation:

Depreciation using double declining method=100%/useful life*2

Depreciation using double declining method=100%/10*2=20%

2017 depreciation=$60,000*20%=$12000

2018 depreciation=($60,000-$12000)*20%=$9600

2019 depreciation=($60,000-$12000-$9600 )*20%=$7680

2020 depreciation=($60,000-$12000-$9600-$7680 )*20%=$6144

carrying value in 2021=$60000-$12000-$9600 -$7680-$6144 =$24576

Loss on disposal of machine=$21,000-$24576  =-$3576

Answer:

the correct answer is 2x

Answer:

D. 2x

Step-by-step explanation:

20x² : 1, 2, 4, 5, 10, 20, x

14x : 1, 2, 7, 14, x

The greatest common factor of the polynomial is 2x.

2x(10x² - 7)

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:

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:

P = 1/2

Step-by-step explanation:

If the tourist spends more than 275$, they must not arrive in Chicago by bus.

( 150 + 60 < 275, 150 + 40 < 275)

The total options the tourist can make:

3 x 2 = 6

(1st leg: 3 possible options, 2nd leg: 2 possible options)

The number of options the tourist can make after excluding bus option:

2 x 2 = 4

(1st leg: 2 remaining possible options, 2nd leg: 2 possible options)

The number of options the tourist can make after excluding the bus option and spend more than 275$:

4 - 1 = 3

(excluding the case of selecting train and cab, because 225 + 40 < 275)

=> The probability that the tourist will spend more than 275$ on these 2 legs of the trip:

P = 3/6 = 1/2

Probability helps us to know the chances of an event occurring. The probability that a tourist will spend more than $275 on these 2 legs of the trip is 0.5.

Probability helps us to know the chances of an event occurring.

[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]

Given that Tourists have three choices for how to travel from New York to Chicago. They can take an aeroplane for $350, a bus for $150, or a train for $225. Also, when they arrive in Chicago, they can travel by van to their hotel for $60 or take a cab for $40. Therefore, the cost of different routes is,

As it can be seen that there are 3 cases where a tourist will spend more than $275, while the total number of cases is 6. Therefore, the probability that a tourist will spend more than $275 on these 2 legs of the trip is,

Probability = 3/6 = 1/2 =0.5z

Hence, the probability that a tourist will spend more than $275 on these 2 legs of the trip is 0.5.

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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:

The probability that a truck drives between 86 and 125 miles in a day.

P(86≤ X≤125) = 0.5890 miles

Step-by-step explanation:

Step(i):-

Given mean of the Population = 100 miles per day

Given standard deviation of the Population = 23 miles per day

Let 'X' be the normal distribution

Let x₁ = 86

[tex]Z_{1} = \frac{x_{1} -mean}{S.D} = \frac{86-100}{23} =-0.61[/tex]

Let x₂= 86

[tex]Z_{2} = \frac{x_{2} -mean}{S.D} = \frac{125-100}{23} = 1.086[/tex]

Step(ii):-

The probability that a truck drives between 86 and 125 miles in a day.

P(86≤ X≤125) = P(-0.61 ≤ Z≤ 1.08)

                      = P(Z≤ 1.08) - P(Z≤ -0.61)

                      = 0.5 +A(1.08) - ( 0.5 - A(-0.61))    

                      = A(1.08) + A(0.61)             ( A(-Z)=  A(Z)

                      = 0.3599 + 0.2291

                     = 0.5890

Conclusion:-

The probability that a truck drives between 86 and 125 miles in a day.

P(86≤ X≤125) = 0.5890  miles per day

Answer:

B. Multiply 6 by 3

Step-by-step explanation:

Do the opposite order of what Hannah did. The last step that she did was divide by 3, so you would multiply the result (6) with 3:

B. Multiply 6 by 3

Your step by step for getting the number Hannah started with:

First, multiply 6 with 3:

6 x 3 = 18

Next, subtract 4:

18 - 4 = 14

Next, divide by 2:

14/2 = 7

Hannah started with the number 7.

~

Answer: Hannah started with 7.

B. Multiply 6 by 3

Explanation:

Let the number be y

2 × y = 2y

(2y + 4)/3 = 6

2y + 4 = 6×3 = 18

2y + 4 = 18

2y = 18 - 4 = 14

y = 14/2 = 7

To solve the problem backward, the first step is to multiply 6 by 3.

Answer:

(A)Only f(x) and h(x) have y-intercepts.

(C)The minimum of h(x) is less than the other minimums.

(E)The maximum of g(x) is greater than the other maximums.

Step-by-step explanation:

From the table

f(0)=0 and h(0)=0, therefore, Only f(x) and h(x) have y-intercepts. (Option A)

Therefore, the minimum of h(x) is less than the other minimums. (Option C).

Maximum of f(x)=14

Maximum of g(x)=49

Maximum of h(x)=0

Therefore, the maximum of g(x) is greater than the other maximums. (Option E)

Answer: It's B,C, and E

Step-by-step explanation:

Answer:  [tex]\bold{S_{\infty}=\dfrac{3125}{2}=1562.5}[/tex]

Step-by-step explanation:

  a₁,  375,  a₃,   a₄,  81

First, let's find the ratio (r). There are three multiple from 375 to 81.

[tex]375r^3=81\\\\r^3=\dfrac{81}{375}\\\\\\r^3=\dfrac{27}{125}\qquad \leftarrow simplied\\\\\\\sqrt[3]{r^3} =\sqrt[3]{\dfrac{27}{125}}\\ \\\\r=\dfrac{3}{5}[/tex]

Next, let's find a₁

[tex]a_1\bigg(\dfrac{3}{5}\bigg)=375\\\\\\a_1=375\bigg(\dfrac{5}{3}\bigg)\\\\\\a_1=125(5)\\\\\\a_1=625[/tex]

Lastly, Use the Infinite Geometric Sum Formula to find the sum:

[tex]S_{\infty}=\dfrac{a_1}{1-r}\\\\\\.\quad =\dfrac{625}{1-\frac{3}{5}}\\\\\\.\quad =\dfrac{625}{\frac{2}{5}}\\\\\\.\quad = \dfrac{625(5)}{2}\\\\\\.\quad = \large\boxed{\dfrac{3125}{2}}[/tex]

Answer:

P ≈ 317.08 m

Step-by-step explanation:

Circumference: C = πd

Step 1: Find circumference of both domes

C = π(50)

Since it's a dome, we divide by 2

50π/2 = 25π

Since we have 2 domes, we simply multiply by 2 again

25π(2) = 50π

Step 2: Find perimeter of track

50π + 80(2)

P = 50π + 160

P = 317.08 m

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:

69.5309950592 cm²

Step-by-step explanation:

Area of Square:

Area = [tex]Length * Length[/tex]

Area = 18*18

Area = 324 square cm

Area of circle:

Diameter = 18 cm

Radius = 9 cm

Area = [tex]\pi r^2[/tex]

Area = (3.14)(9)²

Area = (3.14)(81)

Area = 254.469004941 square cm

Area of Shaded area:

=> Area of square - Area of circle

=> 324 - 254.469004941

=> 69.5309950592 cm²

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:

V ≈ 1436.03 cm³

Step-by-step explanation:

The formula for the volume of a sphere is [tex]\frac{4}{3}[/tex]πr³. r represents the radius, which is 7 cm since the diameter is 14 cm, so plug 7 into the equation as r. Also remember that the question states to use 3.14 for pi/π.

V = [tex]\frac{4}{3}[/tex] (3.14)(7)³

V ≈ 1436.03 cm³

The correct answer is The line will be less steep because the rate will be slower

Explanation:

The rate of the graph is defined by the number of gallons filled vs the time; this relation is shown through the horizontal axis (time) and the vertical axis (gallons). Additionally, there is a constant rate because each hour 2,500 gallons are filled, which creates a steep constant line.

However, if the rate decreases, fewer gallons would be filled every hour, and the line will be less steep, this is because the number of gallons will not increase as fast as with the original rate. For example, if the rate is 1,250 gallons per hour (half the original rate), after 8 hours the total of gallons would be 1000 gallons (half the amount of gallons); and this would make the line to be less steep or more horizontal.

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:

z= 56°

hope u understood it...

Answer:

Z=56

Step-by-step explanation:

Because i said so

Answer:

m∠3  = 115 degrees

Step-by-step explanation:

angle 6 and angle 8 are on a straight line

we know that sum of angles on straight line is 180

therefore

m∠8 = x+5

m∠6 +  m∠8 = 180

2x - 5 + x+5 = 180

=> 3x = 180

=> x = 180/3 = 60

Thus,

m∠6 = 2x-5 = 2*60 -  5 = 115

we know that for two parallel lines cut by a transversal

alternate opposite angles are equal

m∠6  and m∠3 are alternate opposite angles

thus

m∠6  = m∠3  = 115 (answer)

Answer:

2/10 for Rebecka and either 2/9 or 1/9 for Aaron depending on if Rebecka selects a poodle or not.

Step-by-step explanation:

do some math

Answer:

It's written as

[tex]89.7 \times {10}^{9} [/tex]

Or

[tex]8.97 \times {10}^{10} [/tex]

Hope this helps you

Answer:

8.97 * 10 ^10

Step-by-step explanation:

We want one nonzero digit to the left of the decimal

8.97

We moved the decimal 10 places to the left

The exponent is positive 10 since we moved 10 places to the left

8.97 * 10 ^10

Question:

A silver coin is dropped from the top of a building that is 64 feet tall. the position function of the coin at time t seconds is represented by

s(t) = -16t² + v₀t + s₀

Determine the position and velocity functions for the coin.

Answer:

position function: s(t) = (-16t² + 64) ft

velocity function: v(t) = (-32t) ft/s

Step-by-step explanation:

Given position equation;

s(t) = -16t² + v₀t + s₀                ---------(i)

v₀ and s₀ are the initial values of the velocity and position of the coin respectively.

(a) Since the coin is dropped, the initial velocity, v₀, of the coin is 0 at t = 0. i.e

v₀ = 0.  

Also since the drop is from the top of a building that is 64 feet tall, this implies that the initial position, s₀, of the coin is 64 ft at t=0. i.e

s₀ = 64ft

Substitute the values of v₀ = 0 and s₀ = 64 into equation (i) as follows;

s(t) = -16t² + (0)t + 64    

s(t) = -16t² + 64

Therefore, the position function of the coin is;

s(t) = (-16t² + 64) ft

(b) To get the velocity function, v(t), the position function, s(t), calculated above is differentiated with respect to t as follows;

v(t) = [tex]\frac{ds(t)}{dt}[/tex]

v(t) = [tex]\frac{d(-16t^2 + 64)}{dt}[/tex]

v(t) = -32t + 0

v(t) = -32t

Therefore, the velocity function of the coin is;

v(t) = (-32t) ft/s