Each week a person works from 8.00 a.m. to 12:30 p.m. on 6 days and from 2 p.m. to 5:30 p.m. on four days the rate of pay is 595 Naira per hour what is the person's total weekly wage.​

Answer:

2 units.

Step-by-step explanation:

In this question we use the Pythagorean theorem which is shown below:

Given that

The right triangle OMP

The hypotenuse i.e OM is the circle radius =5 units.

The segment MP = 4 units length

Therefore

[tex]OP^2 + MP^2 = OM^2[/tex]

[tex]OP^2 + 4^2 = 5^2[/tex]

[tex]OP^2 + 16 = 25[/tex]

So OP is 3

Now as we can see that ON is also circle radius so it would be 5 units

And,

ON = OP + PN

So,

PN is

= ON - OP

= 5 units - 3 units

= 2 units

Answer:

2

Step-by-step explanation:

Answer:

(a) Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \leq[/tex] $600

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > $600

(b) When H0 cannot be rejected, we conclude that the manager's claim is correct.

(c) When H0 can be rejected, we conclude that the manager's claim is wrong.

Step-by-step explanation:

We are given that the manager of the Danvers-Hilton Resort Hotel stated that the mean guest bill for a weekend is $600 or less.

The accountant will use a sample of weekend guest bills to test the manager's claim.

Let [tex]\mu[/tex] = population mean guest bill for a weekend

(a) Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \leq[/tex] $600

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > $600

Here null hypothesis states that the mean guest bill for a weekend is $600 or less.

On the other hand, alternate hypothesis states that the mean guest bill for a weekend is more than $600.

(b) When the null hypothesis ([tex]H_0[/tex]) cannot be rejected, then the correct conclusion would be: We conclude that the mean guest bill for a weekend is $600 or less which means that the manager's claim is correct.

(c) When the null hypothesis ([tex]H_0[/tex]) can be rejected, then the correct conclusion would be: We conclude that the mean guest bill for a weekend is more than $600 which means that the manager's claim is wrong.

Answer:

Length=17 yds, Width=14 yds

Step-by-step explanation:

62=x+x+(x+3)+(x+3)

4x+6=62

4x=56

x=14

x+3=17

Answer:

270 tiles.

Step-by-step explanation:

The kitchen is 15 x 18 feet. If we multiply we find the area is 270 square feet. one square foot is a 12 x 12 inch square, so we can fit one tile per square foot, giving us 270 tiles.

Answer:

If we have a growing exponential relation, we can write it as:

f(x) = A*r^x

Where A is the initial amount, r is the rate of growth, in this case, r > 1 (because is a growing exponential relation)

Now, the "slope" of the graph in x, is equal to the derivate of f(x) in that point, and we have:

f'(x) = A*(r^x)*ln(r)

Now, remember that r > 1, then ln(r) > 0.

then, f'(x) is a growing function as x grows, and f'(x) grows exponentially, this means that the slope of the graph also grows exponentially as x grows.

Answer:

w=25 degrees, x= 155 degrees, y= 155 degrees, z=155 degrees

Step-by-step explanation:

Angle W and angle I are equal because they are located on same line with PARALLEL lines A and C

Angle X and angle I need to add up to 180 degrees because they together are a strait line, so angle X is 155 because 155+25 =180

Angle Y and angle I are equal because they are exactly the same but lower on the line

Angle Z is same as angle X explenation just a different strait line

Answer:

W=25 degrees

X=155 degrees

Y =155 degrees

Z= 155 degrees

Step-by-step explanation:

Answer:

V lies in the exterior of <STU.

Step-by-step explanation:

V lies in the exterior of <STU.

Answer:

64 degrees

Step-by-step explanation:

Answer:

Factoring is a useful skill in real life. Common applications include: dividing something into equal pieces, exchanging money, comparing prices, understanding time, and making calculations during travel.

Sorry if this is a little wordy, I can get carried away with this sort of thing

anyway, hope this helped and answered your question :)

Answer:

The answer to this equation is 3 5/6

Step-by-step explanation:

in order to solve this problem, we must first turn these fractions into improper fractions. We can do this by multiplying the base number with the denominator and adding the numerator to that number.

6 1/2 = 13/2

2 2/3 = 8/3

Now, set up your equation.

13/2 - 8/3

Change the denominators to the same number so it will be easier to subtract.

39/6 - 16/6

Now subtract.

23/6 = 3 5/6

Answer:

3 5/6

Step-by-step explanation:

6 1/2 - 2 2/3 = 13/2 - 8/3

(39 - 16)/6 = 23/6 = 3 5/6

True.

Integration is also called anti-differentiation, mathematically its an inverse function of differentiation.

For example, one of the first equalities learned is:

[tex]f(x)=g'(x)\Longleftrightarrow\int g'(x)dx=f(x)[/tex].

Which explains that if you differentiate a function (get its derivative) and then integrate the derivative you will obtain the original function.

Hope this helps.

Answer:

Mean = 30, Median = 29.5, Range = 9 and Mid-range = 29.5.

Step-by-step explanation:

We are given that a local doctor’s office logged the number of patients seen in one day by the doctor for ten days.

Arranging the given data in ascending order we get;

24, 25, 27, 27, 28, 31, 33, 35, 35, 35.

(a) Mean is calculated by using the following formula;

         Mean, [tex]\bar X[/tex]  =  [tex]\frac{\text{Sum of all values}}{\text{Total number of observations}}[/tex]

                          =  [tex]\frac{27+ 31+ 27+ 35+ 35+ 25+ 28+ 35+ 33+ 24}{10}[/tex]

                          =  [tex]\frac{300}{10}[/tex]  = 30

So, the mean of the given data is 30.

(b) For calculating the median, we have to first have to observe that the number of observations (n) in the data is even or odd.

                     Median  =  [tex](\frac{n+1}{2})^{th} \text{ obs.}[/tex]

                     Median  =  [tex]\frac{(\frac{n}{2})^{th} \text{ obs.}+ (\frac{n}{2}+1)^{th} \text{ obs.} }{2}[/tex]

Here, the number of observations is even, i.e. n = 10.

So,  Median  =  [tex]\frac{(\frac{n}{2})^{th} \text{ obs.}+ (\frac{n}{2}+1)^{th} \text{ obs.} }{2}[/tex]

                     =  [tex]\frac{(\frac{10}{2})^{th} \text{ obs.}+ (\frac{10}{2}+1)^{th} \text{ obs.} }{2}[/tex]

                     =  [tex]\frac{(5)^{th} \text{ obs.}+ (6)^{th} \text{ obs.} }{2}[/tex]

                     =  [tex]\frac{28+31}{2}[/tex]

                     =  [tex]\frac{59}{2}[/tex]  =  29.5

So, the median of the data is 29.5.

(c) The range of the data is given by = Highest value - Lowest value

                                                        = 35 - 24 = 9

So, the range of the data is 9.

(d) Mid-range of the data is given by the following formula;

                   Mid-range  =  [tex]\frac{\text{Highest value}+\text{Lowest value}}{2}[/tex]

                                      =  [tex]\frac{35+24}{2}[/tex] = 29.5

Answer:

x = 25

Step-by-step explanation:

you just work out all of the degrees in the other triangles first

Answer:

  x = 2.4

Step-by-step explanation:

We assume you intend ...

  [tex]\sqrt{x^2+49}=x+5\\\\x^2+49=x^2+10x+25\qquad\text{square both sides}\\\\24=10x\qquad\text{subtract $x^2+25$}\\\\\boxed{2.4=x}\qquad\text{divide by 10}[/tex]

Answer:

x= 2.25

y=6.5

Step-by-step explanation:

2x+5y=37 y=11-2x

2x+5(11-2x)=37

2x+55-10x=37

-8x+55=37

-55       -55

-8x=-18

÷-8   ÷-8

x= 2.25

y=11-2x

y=11-2(2.25)

y=11-4.5

y=6.5

Answer: x= 18/8 y = 13/2

Step-by-step explanation:

We know that y = 11-2x

So, you want to do the substitution method.

The equation states : 2x+5y  = 37

So, you would substitute the y in the equation for 11-2x

2x+5(11-2x) = 37

2x+55-10x = 37  (combine like terms)

-8x +55 = 37 (subtract 55 from each side)

-8x = -18 ( divide -8 from each side)

x = 18/8

Now, we need to solve for y. For that, we just need to substitute the x in the y equation.

It would look like this: 11-2(18/8) =y

Now we solve.

11-18/4 = 13/2 (6.5)

So, y equals 13/2. Now to check , plug in each for the equation and see if it is correct.  

Answer:

The simple interest is Prt

The simple interest on the money will be $24300

Step-by-step explanation:

The complete question is shown below

The principal P is borrowed at simple interest rate r for a period of time t. Find the simple interest owed for the use of the money. Assume 360 days in a year. P=$18,000, r=7.5%, t=18 months

Principal = P

Interest rate = r

Time period = t

simple interest owed for the use of the money will be gotten as below

The percentage of the principal that will be owed per unit period is the rate r

The total rate that it will be involved in this time period will be the product of the rate and the time = r x t = rt

Finally, to know the amount of interest that this rate will result to, we multiply the total rate in the time period by the original principal borrowed

Total interest = Prt

For a simple interest on the principal P = $18,000,

the interest rate = 7.5% = 7.5/100 = 0.075,

time period = 18 months

we assume the interested is calculated on a monthly basis

Simple interest = Prt

==> 18000 x 0.075 x 18 = $24300

Answer:

[tex] P(Head) = \frac{65}{100}=0.65[/tex]

[tex] P(Tail) = \frac{35}{100}=0.35[/tex]

And for this case the probability that in the next flip we will get a tail would be:

[tex] P(Tail) = \frac{35}{100}=0.35[/tex]

Step-by-step explanation:

For this case we know that a coin is toss 100 times and we got 65 heads and 35 tails.

We can calculate the empirical probabilities for each outcome and we got:

[tex] P(Head) = \frac{65}{100}=0.65[/tex]

[tex] P(Tail) = \frac{35}{100}=0.35[/tex]

And for this case the probability that in the next flip we will get a tail would be:

[tex] P(Tail) = \frac{35}{100}=0.35[/tex]

Answer:

[tex]Shorter\ side=4-2\times 0.845=2.31\ m\\Longest\ side=8-2\times 0.845=6.31\ m\\Height=0.845\ m[/tex]

Step-by-step explanation:

Given that , dimension of the cardboard is 4 m by 8 m.

Lets the dimensions of the square is x m by x m.

The volume after cutting the equal size of square from all the four corners is given as

[tex]V=x\times (4-2x)\times (8-2x)\\V=x\times (32-16x-8x+4x^2)\\V=x\times (4x^2-24x+32)\\V=4x^3-24x^2+32x\\[/tex]

For the maximum volume

[tex]\dfrac{dV}{dx}=12x^2-48x+32=0\\3x^2-12x+8=0\\[/tex]

For maximum value of volume , the value of x will be 0.845

x= 0.845

Therefore the dimensions will be

[tex]Shorter\ side=4-2\times 0.845=2.31\ m\\Longest\ side=8-2\times 0.845=6.31\ m\\Height=0.845\ m[/tex]

The volume of a shape is the amount of space in the shape.

The dimensions that produce the largest volume are: 2.31 m by 6.31 m by 0.845 m

The dimensions of the cardboard is given as:

[tex]\mathbf{Length = 4m}[/tex]

[tex]\mathbf{Width = 8m}[/tex]

Assume the cut-out is x.

So, the dimension of the box is:

[tex]\mathbf{Length = 4 - 2x}[/tex]

[tex]\mathbf{Width = 8 - 2x}[/tex]

[tex]\mathbf{Height = x}[/tex]

So, the volume of the box is:

[tex]\mathbf{V = (4 - 2x)(8 - 2x)x}[/tex]

Expand

[tex]\mathbf{V = 32x -24x^2 + 4x^3}[/tex]

Differentiate

[tex]\mathbf{V' = 32 -48x + 12x^2}[/tex]

Set to 0

[tex]\mathbf{32 -48x + 12x^2 = 0}[/tex]

Divide through by 4

[tex]\mathbf{8 -12x + 3x^2 = 0}[/tex]

Rewrite as:

[tex]\mathbf{3x^2-12x +8 = 0}[/tex]

Using a calculator, we have:

[tex]\mathbf{x = 0.845,\ 3.155}[/tex]

3.155 is greater than the dimension of the box.

So, we have:

[tex]\mathbf{x = 0.845}[/tex]

Recall that:

[tex]\mathbf{Length = 4 - 2x}[/tex]

[tex]\mathbf{Width = 8 - 2x}[/tex]

[tex]\mathbf{Height = x}[/tex]

So, we have:

[tex]\mathbf{Length = 4 - 2 \times 0.845 = 2.31}[/tex]

[tex]\mathbf{Width = 8 - 2 \times 0.845 = 6.31}[/tex]

[tex]\mathbf{Height = 0.845}[/tex]

Hence, the dimensions that produce the largest volume are: 2.31 m by 6.31 m by 0.845 m

Read more about volumes at:

https://brainly.com/question/15918399

Answer:

the answer is D

Step-by-step explanation:

leshawna should've won season 1 PERIODT

6.51 × [tex]10^{-2}[/tex] oz grain of spice weighs more than the particle of unobtainium.

Given that, the weight of a particle of unobtainium is [tex]2.66\times10^{-6}[/tex] oz and the weight of a grain of spice is [tex]9.17\times10^{-4}[/tex] oz.

We need to find how much more grain of spice weighs than the particle of unobtainium.

To determine the power or exponent of 10, let us understand how many places we need to move the decimal point after the single-digit number.

Now,  [tex]9.17\times10^{-4}[/tex] - [tex]2.66\times10^{-6}[/tex]

=9.17-2.66 × [tex](10^{-4}-10^{-6})[/tex]

=6.51 × [tex]10^{-2}[/tex]

Therefore, 6.51 × [tex]10^{-2}[/tex] oz grain of spice weighs more than the particle of unobtainium.

To learn more about a scientific notation visit:

https://brainly.com/question/18073768.

#SPJ2

Answer:

a. the probability of a type II  error is 0.5319

b. the required sample size to satisfy and the type II error probability  is 59.4441

Step-by-step explanation:

From the information given; we have:

sample size n = 25

Population standard deviation [tex]\sigma[/tex] = 4

true average lifetime = Sample Mean [tex]\bar X[/tex] = 62

We can state our null hypothesis and alternative hypothesis as follows:

Null hypothesis:

[tex]\mathbf{H_o : \mu = 60}[/tex]

Alternative hypothesis

[tex]\mathbf{H_1 : \mu \neq 60}[/tex]

Where ;

∝ = 0.01

From the standard normal tables at critical value ∝ = 0.01 ; the level of significance is -2.575 lower limit and 2.575 upper limit

The z statistics for the lower limit is:

[tex]lower \ limit = \dfrac{\bar X - \mu }{\dfrac{\sigma}{\sqrt {n}}}[/tex]

[tex]-2.575= \dfrac{\bar x - 60 }{\dfrac{4}{\sqrt 25}}}[/tex]

[tex]-2.575= \dfrac{\bar x - 60 }{0.8}}}[/tex]

[tex]-2.575*0.8= {\bar x - 60 }{}}}[/tex]

[tex]-2.06= {\bar x - 60 }{}}}[/tex]

[tex]\bar x = 60-2.06[/tex]

[tex]\bar x = 57.94[/tex]

The z statistics for the upper limit is:

[tex]lower \ limit = \dfrac{\bar X - \mu }{\dfrac{\sigma}{\sqrt {n}}}[/tex]

[tex]2.575= \dfrac{\bar x - 60 }{\dfrac{4}{\sqrt 25}}}[/tex]

[tex]2.575= \dfrac{\bar x - 60 }{0.8}}}[/tex]

[tex]2.575*0.8= {\bar x - 60 }{}}}[/tex]

[tex]2.06= {\bar x - 60 }{}}}[/tex]

[tex]\bar x = 60-(-2.06)[/tex]

[tex]\bar x = 60+2.06[/tex]

[tex]\bar x = 62.06[/tex]

Thus; the probability of a type II error is determined as follows:

β = P (  [tex]57.94 < \bar x < 62.06[/tex] )

[tex]= P ( \dfrac{57.94 -62 }{\dfrac{4}{\sqrt{25}}}<\dfrac{62.06 -62 }{\dfrac{4}{\sqrt{25}}})[/tex]

[tex]= P ( \dfrac{-4.06 }{0.8}}<\dfrac{2.06 }{0.8})[/tex]

= P ( -5.08 < Z < 0.08 )

= P ( Z < 0.08) - P ( Z < - 5.08)

Using Excel Function: [ (=NORMDIST (0.08)) - (=NORMDIST(-5.08)) ] ; we have:

= 0.531881372 - 0.00000001887

= 0.531881183

≅ 0.5319

b.

What is the required sample size to satisfy and the type II error probability of b(62) = 0.1

Recall that:

The critical value of ∝ = 2.575  ( i. e   [tex]Z_{1 - \alpha/2 } = 2.575[/tex]  )

Now ;

the critical value of β is :

[tex]Z _{1- \beta} = 1.28[/tex]

The  required sample size to satisfy and the type II error probability  is therefore determined as :

[tex]n = [\dfrac{(Z_{1 - \alpha/2} + Z_{1 - \beta} ) \sigma }{\delta}]^2[/tex]

[tex]n = [\dfrac{(2.575+1.28 ) 4 }{2}]^2[/tex]

[tex]n = [\dfrac{(3.855 ) 4 }{2}]^2[/tex]

[tex]n = [\dfrac{(15.42 ) }{2}]^2[/tex]

n = 7.71 ²

n= 59.4441

Thus; the required sample size to satisfy and the type II error probability  is 59.4441

A)

In order to calculate the Type II Error, we proceed with stating the factors:

Hypothesized Mean is given as  =  μ[tex]_{0} [/tex]        = 60

True Mean  is given as                 =  μa        = 62

Standard Deviation  is given as  = σ           = 4

Sample Size                                   = n           = 25

Standard error of mean                = σx          =σ/[tex]\sqrt{\\} [/tex]σ               =  0.80

given 0.01 level and two tailed test critical value Zσ             ±  2.58 or approximately 3

Acceptance region is

given as:   = μ - Z∝ * σx ≤ Π ≤ μ+Z∝⇄            =57.9360 ≤x≤   62.0640

Type II Error = probability of not rejecting β    = P(57.94-μa/σx))     <Z< (62.064-μa)/σx))

                                      = P (-5.08   <Z<    0.08)
                                      = 0.5319-0)

                                      = 0.532

B

Hypothesized mean                        = μ₀             =        60

True Mean                                        =μₐ               =       62          

Standard Deviation                          =σ                 =      4

for 0.01 level and two-tailed test critical value Z∝/2              ± 2.58

for 0.01 level of type II error critical value Z[tex]\beta [/tex]                         = 1.28

Required sample size    = n                                       = ([tex]Z_{\alpha /2} [/tex] + [tex]Z_{\beta } [/tex])²σ²/(μ₀-μ₀)²
                                                                                    = 60


See the link below for more about two-sided tests:
https://brainly.com/question/8170655

Answer:

1,050 workers

Step-by-step explanation:

25% = 0.25

0.25 × 1400 = 350

1400 - 350 = 1050

Hope this helps.

Answer: 12600

Step-by-step explanation:

We are given the function that f(x) = 12000 * 1.05x

the x in f(x) is the amount of years that passed in the city of Peachwood, and the f(x) is the total population of Peachwood

These are two key elements in this function,

Therefore after 1 year the equation would be f(1) = 12000*1.05(1)

or f(1) = 12600

Answer

h = 5m

Step-by-step explanation:

area of a parallelogram is b * h

base = 14 m

h = ?

Area = 70 m²

Area = b * h

70 = 14 * h

h = 70 / 14

h = 5 m

Answer:

Option D is the right option

solution,

[tex]3x - 9 = - 33 \\ or \: 3x = - 33 + 9 \\ or \: 3x = - 24 \\ or \: x = \frac{ - 24}{3} \\ x = - 8[/tex]

Hope this helps...

Good luck on your assignment..

Answer:

-8

Step-by-step explanation:

3x-9=-33

transpose 9 to RHS

->3x=-33+9=> 3x=-24

transposing 3 to RHS

=> x=-24÷3

=> x=-8

Answer:

D -price of car wash keeps getting higher

Answer: The price of a car wash keeps getting higher

Step-by-step explanation:

Answer:

(2.x) + (2.7) = 36

Step-by-step explanation:

Solving the given equation with the distributive property,

 A(B + C) = (A.B) + (A.C)

So that,

2(x+7) = 36

(2.x) + (2.7) = 36

2x + 14 = 36

2x = 36 - 14

2x = 22

x = 11

From the given expressions, the option that is the correct first step to solving this equation is;

(2.x) + (2.7) = 36

Answer:

Here you go

Step-by-step explanation:

Answer:

https://brainly.com/question/8847227

Step-by-step explanation:

Answer:

Hydro static force is =18377 N

Step-by-step explanation:

The hydro static force is equals to the hydro static pressure times the area.

The hydro static pressure of a fluid increases as the depth of the fluid increases and the formula of it is given below.

Hydro static Pressure, P = d·g·ρ

Where, d is the depth of the object

g is the gravitational constant

ρ is the density of the fluid

Density of water   ρ = [tex]1000 kg/m3[/tex]

=1000 kg/m^3 * 9.8m/s^2 which is √(3/2).a below the water level.

Side of the plate  x = 10 m

The hydrostatic force = the pressure at the center x the area =[tex][sqrt(3)/2 m][1000 kg/m^3 * 9.8m/s^2][/tex][tex][(1/2)(3)(8)(sqrt(3)/2) m^2][/tex]=18377 N

Answer:

x" means that the value of y depends upon the value of x, so: y can be written in terms of x (e.g. y = 3x ). If f(x) = 3x, and y is a function of x (i.e. y = f(x) ), then the value of y when x is 4 is f(4), which is found by replacing x"s by 4"s . this should help I asked my brother for the answer and he told me to put this happy to help :0

Answer:

Step-by-step explanation:

8P3=8*7*6=336