Lionel sells to two groups of customers – 50% of its sales are to wholesalers and 50% to retailers. All sales to retailers are cash sales. Collections from wholesalers are follows: 75% in the month of sale and 25% in the month following sale. ii) 60% of direct material purchases are paid in cash in the month of purchase, and the balance is paid in the month following the purchase. iii) All other expenses are paid in the month incurred. iv) Manufacturing overhead includes monthly depreciation of $15,000. v) Sales: March, $320,000. vi) Purchases of direct materials: March, $175,000. vii) Other receipts: April – Donation received, $2,000 May – Sale of used office furniture, $4,000. viii) Other disbursements: May – Purchase of Ice Cream Mixer, $10,000. ix) Repays loan: April, $30,000. x) Cash balance on April 1, is expected to be $50,000.

Answer:

b) Then z(s) is in the rejection region for H₀. We reject H₀. The p-value is smaller than α/2

c)CI 95 %  =  ( 0.00002 ;  0.09998)

Step-by-step explanation: In both cases, the size of the samples are big enough to make use of the approximation of normality of the difference of the proportions.

Recent Sample

Sample size    n₁  =  1000

Number of events of people with financial fitness more than fair

x₁  =  410

p₁ =  410/ 1000  =  0.4     then q₁ = 1 - p₁    q₁ =  1 -  0.4    q₁  = 0.6

Sample a year ago

Sample size    n₂ =  1200

Number of events of people with financial fitness more than fair

x₂  =  420

p₂  =  420/1200     p₂ = 0.35   q₂  =  1 - p₂    q₂  = 1 - 0.35   q₂ = 0.65

Test Hypothesis

Null Hypothesis                                  H₀              p₁  =  p₂

Alternative Hypothesis                      Hₐ              p₁  ≠  p₂

CI  95 % then significance level  α  =  5%   α  = 0.05    α/2  = 0.025

To calculate p-value:

SE  =  √ (p₁*q₁)/n₁  +  (p₂*q₂)/n₂

SE  =  √ 0.4*0.6/1000 +  0.65*0.35/1200

SE  =  √ 0.00024 + 0.000189

SE = 0.021

z(s) =  ( p₁ - p₂ ) / SE

z(s) = ( 0.4 - 0.35 )/0.021

z(s) = 0.05/ 0.021

z(s) =  2.38

We find p-value from z-table to be   p-value = 0.00842

Comparing

p-value with  α/2   = 0.025

α/2 >  p-value  

Then z(s) is in the rejection region for H₀. We reject H₀

CI 95 %  =  ( p₁  -  p₂ )  ±  2.38*SE

CI 95 %  =  ( 0.05 ± 2.38*0.021 )

CI 95 %  =  ( 0.05 ± 0.04998)

CI 95 %  =  ( 0.00002 ;  0.09998)

CI 95 % does not contain the 0 value affirming what the hypothesis Test already demonstrate

Answer: 3x - 2

Step-by-step explanation:

First to solve this, we need to know some basic information such as:

1. (-) × (-) = +

2. (+) × (-) = -

3. (+) × (+) = +

Therefore, 6x-(3x+2)​

= 6x - 3x - 2

= 3x - 2

The answer to the question after removing the bracket will be 3x - 2.

Answer:

Step-by-step explanation:

The difference of years:

The difference in profit over 6 years:

Average rate of change:

It has been 6 years,

The main difference in profit over 6 years between 1999 and 2005 is,

→ 206000 - 173000

→ 33000

Then the average rate of change is,

→ 33000/6

→ 5500

Hence, $ 5500 is the correct option.

Answer:

Who was the first president of United States?

Answer:

using 2 below points to draw:

(0, 7)

(3.5, 6)

Step-by-step explanation:

using

Hello,

[tex]\widehat{A}=180^o-24.4^o-103.6^o=52^o\\\\\dfrac{sin(24.4^o)}{37.3} =\dfrac{sin(103.6^o)}{c} \\\\\\c=87.760246\approx{87.8}\\\\\\\dfrac{sin(52^o)}{a} =\dfrac{sin(24.4^o)}{37.3} \\\\\\a=71.1510189...\approx{71.2}\\[/tex]

Answer:

0.0677 = 6.77% probability that they will all be nonfiction

Step-by-step explanation:

The books are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x successes is given by the following formula:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this question:

10 + 12 = 22 books.

She chooses 4 books, which means that [tex]n = 4[/tex]

12 nonfiction, which meas that [tex]k = 12[/tex]

What’s the probability that they will all be nonfiction?

This is P(X = 4). So

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 4) = h(4,22,4,12) = \frac{C_{12,4}*C_{10,0}}{C_{22,4}} = 0.0677[/tex]

0.0677 = 6.77% probability that they will all be nonfiction

Answer:

i think that $19980 is the answer

Step-by-step explanation:

i hope it will help u

Answer:

x = 3.5

Step-by-step explanation:

Triangle to the right:

4^2 + x^2 = 8^2

16 + x^2 = 64

y^2 = 48

Triangle to the left:

x^2 + 6^2 = 48

x^2 + 36 = 48

x^2 = 12

x = sqrt(12)

x = 3.5

Answer: The answer would be D

Step-by-step explanation:

Answer:

45°

Step-by-step explanation:

<lmk=90°

angles in a triangle add up to 180

45+90+<o=180

<o=180-135

<o=45

Answer:

∠ O = 45°

Step-by-step explanation:

The angle between the tangent and the radius at the point of contact is 90°

The sum of the 3 angles in Δ OML is 180° , then

∠ O = 180° - (90 + 45)° = 180° - 135° = 45°

Answer:

There exists a relationship between interpersonal violence and health.

Step-by-step explanation:

The relationship between interpersonal violence and health :

The null hypothesis will be ; the is no relationship between interpersonal violence and health while the alternative will negate the Null ;

If no relationship exists, correlation Coefficient = 0 and if a relationship exists, then correlation Coefficient is not = 0

H0 : ρ = 0

H1 : ρ ≠ 0

α = 0.05

Reported Pvalue = 0.016

Decison region :

Reject H0 ; If Pvalue < α

Therefore, Since Pvalue < α ; we reject H0 and conclude that there exists a relationship between interpersonal violence and health.

1. Volume of pyramid= One third× volume of rectangular prism, V= l×w×h

So for pyramid, V= 1/3 (l×w×h) = (l×w×h) ÷ 3.

2. The volume of the cylinder is three times the volume of the cone or the volume of the cone is one third that of the cylinder.

3. Volume of the cone = One third of volume of the cylinder.

4. Sphere's volume is 2/3 of the Cylinder's volume.

Answered by GAUTHMATH

Answer:

-15m^10 -38m8+57m^6+98m^4-30m^2

Answer:

jere is your answer i hope it will help u

Answer:

[tex]9x - 3 = 78 \\ 9x - 3 + 3 = 78 + 3 \\ 9x = 81 \\ \frac{9x}{9} = \frac{81}{9} \\ x = 9[/tex]

Answer:

[tex]9x - 3 = 78 \\9 x = 78 + 3 \\ 9x = 81 \\ x = \frac{81}{9} \\ x = 9[/tex]

Answer:

900 at 12%

2100 at 10%

Step-by-step explanation:

Let x= amount invested at 12%

let y= amount invested at 10%

with that being said we can write the two equation

Equation 1: x+y=3000

Equation 2: 3000*.106=.12x+.1y

isolte x from equation 1

x= 3000-y

plug this into equation 2

318=.12(3000-y)+.1y

318=360-.12y+.1y

-42= -.02y

y= 2100

Plug this into equation 1

x+2100=3000

x=900

she should invest $900 into the account earning 12% interest and $2100 into the account earning 10% interest.

Let's denote the amount of money Hattie invests at 12% as \(x\) dollars, and the amount she invests at 10% as \(\$3000 - x\) dollars.

The formula for calculating interest is: \(\text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time}\).

For the 12% account:

Interest_12% = \(x \times 0.12 \times 1\) (1 year)

For the 10% account:

Interest_10% = \((3000 - x) \times 0.10 \times 1\) (1 year)

Hattie wants to earn 10.6% interest on the total investment, so we can set up the equation:

\(\text{Total Interest} = \text{Interest}_12% + \text{Interest}_10%\)

\(3000 \times 0.106 = x \times 0.12 + (3000 - x) \times 0.10\)

Now, solve for \(x\):

\(318 = 0.12x + 300 - 0.10x\)

\(318 = 0.02x + 300\)

\(18 = 0.02x\)

\(x = 900\)

Hattie should invest $900 at 12% and \(3000 - 900 = 2100\) at 10%.

Therefore, she should invest $900 into the account earning 12% interest and $2100 into the account earning 10% interest.

Learn more about interest at https://brainly.com/question/29451175

#SPJ3

Answer:

prove that The given system of equations is redundant is attached below

Step-by-step explanation:

System of equations

x1 +x2 −3x3 = 7

−2x1 +x2 +5x3 = 2

 3x2 −x3 = 16

To prove that the system is redundant we will apply the Gaussian elimination ( pivot operation )

attached below is the solution

Answer:

42 degrees

Step-by-step explanation:

We already have the two angles for the triangle, we just need the third. For triangles, the can only add up to 180 degrees. 101+37=138 degrees, now we subtract 138 from 180.

180-138=42.

Answer:

(a) Cylinder, R = 5 in, H = 7 in

(b) Volume = 549.5 cubic inches

Step-by-step explanation:

length, L= 7 in

width, W = 5 in

(a) The solid is cylinder.

Radius, R = 5 in

(b) Height = 7 in

Volume of the cylinder

[tex]V = \pi r^2 h\\\\V = 3.14 \times 5 \times 5\times 7\\\\V = 549.5 in^3[/tex]

Answer:

20%?

Step-by-step explanation:

Answer:

10mg

Step-by-step explanation:

We have a proportional relationship.

We know that there are 5mg in 2ml of liquid medication.

Now we want to know how many mg there are in 4 ml of medication.

First, we can rewrite it as:

4ml = 2ml + 2ml

And we know that, in every 2 ml of medicine, there are 5mg.

Then if we have two times 2ml of medicine, we have two times 5mg.

This is:

2*5mg = 10mg

Hi there!

[tex]\large\boxed{p(x) = 7x + 7x^2 + \frac{7}{2}x^3 + \frac{7}{6}x^4}[/tex]

Recall a Taylor series centered at x = 0:

[tex]p(x) = f(0) + f'(0)(x) + \frac{f''(0)}{2}x^{2} + \frac{f'''(0)}{3!}x^{3} + ...+ \frac{f^n}{n!}x^n[/tex]

Begin by finding the derivatives and evaluate at x = 0:

f(0) = 7(0)e⁰ = 0

f'(x) = 7eˣ + 7xeˣ   f'(0) = 7e⁰ + 7(0)e⁰ = 7

f''(x) = 7eˣ + 7eˣ + 7xeˣ  f''(0) = 7(1) + 7(1) + 0 = 14

f'''(x) = 7eˣ + 7eˣ + 7eˣ + 7xeˣ    f'''(0) = 21

f⁴(x) = 7eˣ + 7eˣ + 7eˣ + 7eˣ + 7xeˣ   f⁴(0) = 28

Now that we calculated 4 non-zero terms, we can write the Taylor series:

[tex]p(x) = 0 + 7x + \frac{14}{2}x^2 + \frac{21}{3!}x^3 + \frac{28}{4!}x^4[/tex]

Simplify:

[tex]p(x) = 7x + 7x^2 + \frac{7}{2}x^3 + \frac{7}{6}x^4[/tex]

Answer:

a) The margin of error for a 98% confidence interval is of 3.388 people.

b) The 98% confidence interval for the population mean is between 20.61 people and 27.39 people.

Step-by-step explanation:

We have the standard deviation for the sample, which means that the hypergeometric 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 = 15 - 1 = 14

98% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 14 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.98}{2} = 0.99[/tex]. So we have T = 2.624

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 2.624\frac{5}{\sqrt{15}} = 3.388[/tex]

In which s is the standard deviation of the sample and n is the size of the sample. This means that the answer to question a is of 3.388.

Question b:

The lower end of the interval is the sample mean subtracted by M. So it is 24 - 3.39 = 20.61 people

The upper end of the interval is the sample mean added to M. So it is 24 + 3.39 = 27.39 people.

The 98% confidence interval for the population mean is between 20.61 people and 27.39 people.

Answer:

7.07 units

Step-by-step explanation:

Given

[tex]A = (-3,6)[/tex]

[tex]B = (2,1)[/tex]

[tex]C = (9,5)[/tex]

See comment for complete question

Required

Side length AB

To do this, we make use of the following distance formula;

[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]

So, we have:

[tex]d = \sqrt{(-3 - 2)^2 + (6 - 1)^2}[/tex]

[tex]d = \sqrt{(-5)^2 + 5^2}[/tex]

[tex]d = \sqrt{25 + 25}[/tex]

[tex]d = \sqrt{50}[/tex]

[tex]d = 7.07[/tex]

Answer:

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