Question
Five people, each working 8 hours a day, can assemble 400 toys in a 5-day work week. What is the average
number of toys assembled per hour, per person?

Answer:

a) 0.0749 = 7.49% probability that the student makes more than $15,000.

b) 0.227 = 22.7% probability that the student makes between $13,000 and $14,000.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Full-time Ph.D. students receive an average of $12,837 per year.

This means that [tex]\mu = 12837[/tex]

Standard deviation of $1500

This means that [tex]\sigma = 1500[/tex]

a. The student makes more than $15,000.

This is 1 subtracted by the p-value of Z when X = 15000.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{15000 - 12837}{1500}[/tex]

[tex]Z = 1.44[/tex]

[tex]Z = 1.44[/tex] has a p-value of 0.9251.

1 - 0.9251 = 0.0749

0.0749 = 7.49% probability that the student makes more than $15,000.

b. The student makes between $13,000 and $14,000.

This is the p-value of Z when X = 14000 subtracted by the p-value of Z when X = 13000.

X = 14000

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{14000 - 12837}{1500}[/tex]

[tex]Z = 0.775[/tex]

[tex]Z = 0.775[/tex] has a p-value of 0.7708.

X = 13000

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{13000 - 12837}{1500}[/tex]

[tex]Z = 0.11[/tex]

[tex]Z = 0.11[/tex] has a p-value of 0.5438.

0.7708 - 0.5438 = 0.227

0.227 = 22.7% probability that the student makes between $13,000 and $14,000.

7.49% of the student makes more than $15,000, while 23.85% of the student makes between $13,000 and $14,000

Z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:

z = (raw score - mean) / standard deviation

Given that:

Mean = $12837, standard deviation = $1500

a) For >15000:

z = (15000 - 12837)/1500 = 1.44

P(z > 1.44) = 1 - P(z < 1.44) = 1 - 0.9251 = 0.0749

b) For >13000:

z = (13000 - 12837)/1500 = 0.11

For <14000:

z = (14000 - 12837)/1500 = 0.78

P(0.11 < z < 0.78) = P(z < 0.78) - P(z < 0.11) = 0.7823 - 0.5438 = 0.2385

7.49% of the student makes more than $15,000, while 23.85% of the student makes between $13,000 and $14,000

Find out more on z score at: https://brainly.com/question/25638875

Answer:

6.286;

0.0165

0.976

0.1995

Step-by-step explanation:

Given that :

Mean, μ = 243. 4

Standard deviation, σ = 35

Sample size, n = 31

1.)

Standard Error

S. E = σ / √n = 35/√31 = 6.286

2.)

P(x < 230) ;

Z = (x - μ) / S.E

P(Z < (230 - 243.4) / 6.286))

P(Z < - 2.132) = 0.0165

3.)

P(x > 231)

P(Z > (231 - 243.4) / 6.286))

P(Z > - 1.973) = 0.976 (area to the right)

4)

P(x < 248)

P(Z < (248 - 243.4) / 6.286))

P(Z < 0.732) = 0.7679

P(x < 255)

P(Z < (255 - 243.4) / 6.286))

P(Z < 1.845) = 0.9674

0.9674 - 0.7679 = 0.1995

Step-by-step explanation:

Answer is in attached image...

hope it helps

Answer:

its a

Step-by-step explanation:

just did it

Answer:

Tedyxhcj eydyfhxrstetdhsawe

Answer:

40% depreciation over the 4 years

10% depreciation per year

Step-by-step explanation:

The number of years between buying and selling is:

2020 - 2016 = 4

4 years

The amount of depreciation in the 4 years is:

AED 1,500 - AED 900 = AED 600

The percent depreciation for the 4 years is:

(1500 - 900)/1500 * 100% = 40%

The percent depreciation per year is:

40%/4 = 10%

Answer:

[tex]\displaystyle a = \frac{1}{3} \text{ and } b = \frac{2}{3}[/tex]

Step-by-step explanation:

We can use the definition of inverse functions. Recall that if two functions, f and g are inverses, then:

[tex]\displaystyle f(g(x)) = g(f(x)) = x[/tex]

So, we can let j be the inverse function of h.

Function h is given by:

[tex]\displaystyle h(x) = y = 3x-2[/tex]

Find its inverse. Flip variables:

[tex]x = 3y - 2[/tex]

Solve for y. Add:

[tex]\displaystyle x + 2 = 3y[/tex]

Hence:

[tex]\displaystyle h^{-1}(x) = j(x) = \frac{x+2}{3} = \frac{1}{3} x + \frac{2}{3}[/tex]

Therefore, a = 1/3 and b = 2/3.

We can verify our solution:

[tex]\displaystyle \begin{aligned} h(j(x)) &= h\left( \frac{1}{3} x + \frac{2}{3}\right) \\ \\ &= 3\left(\frac{1}{3}x + \frac{2}{3}\right) -2 \\ \\ &= (x + 2) -2 \\ \\ &= x \end{aligned}[/tex]

And:

[tex]\displaystyle \begin{aligned} j(h(x)) &= j\left(3x-2\right) \\ \\ &= \frac{1}{3}\left( 3x-2\right)+\frac{2}{3} \\ \\ &=\left( x- \frac{2}{3}\right) + \frac{2}{3} \\ \\ &= x \stackrel{\checkmark}{=} x\end{aligned}[/tex]

Answer:

25 cm.

Step-by-step explaination:

Given,

Two sides of a triangle:

a = 7cm

b = 24 cm

To find,

Third side:

c = ?

By Pythagorean Theorem;

a² + b² = c²

[where c is the longest side,hypotenuse]

Putting the value of a and b;

we get,

7² + 24² = c²

49 + 576 = c²

625 = c²

25² = c² (square root)

25 = c

c = 25

Therefore, the length of the third side will be equal to 25 cm.

The lengths of two sides of the right triangle ABC shown in the illustration given

a= 7cm and b= 24cm

> a= 7cm

> b= 24cm

Side c (third side)

Using Pythagoras theorem,

▶️ a² + b² = c

▶️ 7cm ² + 24cm² = c²

▶️ 49cm + 576cm = c²

▶️ 625cm = c²

▶️ 25² = c² (25×25 = 625)

▶️ c = 25

The value of c is 25 cm.

bxf-mgii-whr

Step-by-step explanation:

come I will teach

9514 1404 393

Answer:

  20

Step-by-step explanation:

A whole can be divided into two pieces that are each 1/2 of the whole.

 (10 wholes) × (2 pieces per whole) = 20 pieces

Step-by-step explanation:

4x + 19 + 3x = - 5

4x + 3x + 19 = - 5 collect the like terms

7x + 19 = - 5

7x = - 5 - 19 bring 19 to the right

7x/ 7x = - 24/ 7

x = - 3.4

I hope this answers your question

Answer:

(3,1) is the midpoint

Step-by-step explanation:

To find the x coordinate of the midpoint, average the x coordinates of the endpoints

(7+-1)/2 = 6/2 =3

To find the y coordinate of the midpoint, average the y coordinates of the endpoints

(10+-8)/2 = 2/2 = 1

(3,1) is the midpoint

Answer:

(3, 1)

Step-by-step explanation:

We can use the formula [ (x1+x2)/2, (y1+y2/2) ] to solve for the midpoint.

7+(-1)/2, 10+(-8)/2

6/2, 2/2

3, 1

Best of Luck!

Answer:

There are 60 permutations.

Step-by-step explanation:

Arrangements formula:

The number of possible arrangements of n elements is given by:

[tex]A_n = n![/tex]

With repetition:

For each element that repeats, with [tex]n_1, n_2, ..., n_n[/tex] times, the formula is:

[tex]A_n^{n_1,n_2,...,n_n} = \frac{n!}{n_1!n_2!...n_n}[/tex]

In this question:

Apple has 5 letters.

P appears two times. So

[tex]A _5^{2} = \frac{5!}{2!} = 60[/tex]

There are 60 permutations.

Damaris needs to save 10.46% of his net pay each week to purchase the new pair of shoes by the end of his break.

Given:

To find: The percentage of his net pay that Damaris needs to save each week to purchase the shoes by the end of his break

Let us assume that Damaris needs to save x% of his net pay each week to buy the shoes by the end of his break.

Then, savings per week is x% of $167.30, that is,

[tex]\frac{x}{100}\times 167.30[/tex]

Then, his savings for 10 weeks is,

[tex]10 \times \frac{x}{100}\times 167.30[/tex]

Since the summer break is for 10 weeks, Damaris' savings for the entire summer break is,

[tex]10 \times \frac{x}{100}\times 167.30[/tex]

Damaris wants to buy the new pair of shoes by then end of the break. Then, his savings for the entire summer break should equal the cost of the new pair of shoes.

It is given that the cost of the new pair of shoes is $175.

Then, according to the problem,

[tex]10 \times \frac{x}{100}\times 167.30 =175[/tex]

[tex]x=\frac{175\times 100}{10\times167.30}[/tex]

[tex]x=10.460251[/tex]

Rounding to the nearest hundredth, we have,

[tex]x=10.46[/tex]

Thus, Damaris needs to save [tex]10.46[/tex]% of his net pay each week to buy the shoes by the end of his break.

Learn more about percentage here:

https://brainly.com/question/22400644

Answer:

B: I think

Step-by-step explanation:

correct me if im wrong

The line PQ is an angle bisector because it divides the angle P into two equal half option (B) angle bisector is correct.

When two lines or rays converge at the same point, the measurement between them is called a "Angle."

We have a triangle shown in the picture.

As we know,  

in terms of geometry, the triangle is a three-sided polygon with three edges and three vertices. The triangle's interior angles add up to 180°.

From the figure the segment PQ divides the angle into two equal half.

From the definition of the angle bisector, the angle bisector can be defined as a line segment that divides the angle into two half.

Angle P = 40 + 40 = 80 degrees

Thus, the line PQ is an angle bisector because it divides the angle P into two equal half option (B) angle bisector is correct.

Learn more about the angle here:

brainly.com/question/7116550

#SPJ5

here's the answer to your question

Answer:

BONANA MY NANA

Step-by-step explanation:

Answer:

hmm i thought abt it and i think the answer is no

Step-by-step explanation:

Answer:

it is 2 te he

Step-by-step explanation:

ONCE THE 5 6 = 7 10 .. ?% =1 x 7 =2 te he

Answer:

b x=5

Step-by-step explanation:

20x+10=110

20x+10-10=110-10

20x/20=100/20

x=5

Answer:

x=5

Step-by-step explanation:

20x + 10 = 110

Subtract 10 from each side

20x +10-10 = 110-10

20x = 100

divide by 20

20x/20 =100/20

x= 5

Graph is attached below ;

Answer:

Unit rate = 12 computers per day

Step-by-step explanation:

To obtain the unit rate of computers sold per day using the graph, we need to obtain the slope of the graph, which is the change in y per change in x

That is ; the gradient ;

Slope = change in y / change in x

Slope = (y2 - y1) / (x2 - x1)

y2 = 60 ; y1 = 36 ; x2 = 5 ; x1 = 3

Slope = (60 - 36) / (5 - 3) = 24 / 2 = 12

Slope = 12

Unit rate = 12 computers per day

Answer:

The probability that Nadia gets just caramel, butterscotch sauce, strawberries, and hot fudge is P =  1/32 = 0.03125

Step-by-step explanation:

There are up to 5 toppings, such that the toppings are:

caramel

whipped cream

butterscotch sauce

strawberries

hot fudge

We want to find the probability that,  If the server randomly chooses which toppings to add, she gets just caramel, butterscotch sauce, strawberries, and hot fudge.

First, we need to find the total number of possible combinations.

let's separate them in number of toppings.

0 toppins:

Here is one combination.

1 topping:

here we have one topping and 5 options, so there are 5 different combinations of 1 topping.

2 toppings.

Assuming that each topping can be used only once, for the first topping we have 5 options.

And for the second topping we have 4 options (because one is already used)

The total number of combinations is equal to the product between the number of options for each topping, so here we have:

c = 4*5 = 20 combinations.

But we are counting the permutations, which is equal to n! (where n is the number of toppings, in this case is n = 2), this means that we are differentiating in the case where the first topping is caramel and the second is whipped cream, and the case where the first topping is whipped cream and the second is caramel, to avoid this, we should divide by the number of permutations.

Then the number of different combinations is:

c' = 20/2! = 10

3 toppings.

similarly to the previous case.

for the first topping there are 5 options

for the second there are 4 options

for the third there are 3 options

the total number of different combinations is:

c' = (5*4*3)/(3!) = (5*4*3)/(3*2) = 10

4 toppings:

We can think of this as "the topping that we do not use", so there are only 5 possible toppings to not use, then there are 5 different combinations with 4 toppings.

5 toppings:

Similar to the first case, here is only one combination with 5 toppings.

So the total number of different combinations is:

C = 1 + 5 + 10 + 10 + 5 + 1 = 32

There are 32 different combinations.

And we want to find the probability of getting one particular combination (all of them have the same probability)

Then the probability is the quotient between one and the total number of different combinations.

p = 1/32

The probability that Nadia gets just caramel, butterscotch sauce, strawberries, and hot fudge is P =  1/32 = 0.03125

Answer:

Neal

Step-by-step explanation:

13.01 < 13.89

Answer:

Kindly check explanation

Step-by-step explanation:

Given the data :

Car 1 Car 2

214 220

245 221

239 244

224 225

220 258

295 259

Ordered data:

Car 1 : 214, 220, 224, 239, 245, 295

Sample mean = ΣX/ n ; n = sample size = 6

Sample mean = 1437 / 6 = 239.5

Median = 1/2(n+1)th term = 1/2(7) = 3.5th term

Median = (3rd + 4th) /2 = (224 + 239) /2 = 231.5

Sample standard deviation; √(Σ(x - xbar)²/n-1 ) = 29.60 (using calculator)

Car 2 : 220, 221, 225, 244, 258, 259

Sample mean = ΣX/ n ; n = sample size = 6

Sample mean = 1427 / 6 = 237.833

Median = 1/2(n+1)th term = 1/2(7) = 3.5th term

Median = (3rd + 4th) /2 = (225 + 244) /2 = 234.5

Sample standard deviation; √(Σ(x - xbar)²/n-1 ) = 18.21 (using calculator)

Diameter=d=2ft

We know

[tex]\boxed{\sf Lateral\:Surface\:Area=2πrh}[/tex]

[tex]\\ \sf\longmapsto Lateral\: Surface\:Area=2\times 3.14\times 2\times 1[/tex]

[tex]\\ \sf\longmapsto Lateral\;Surface\:Area=4(3.14)[/tex]

[tex]\\ \sf\longmapsto Lateral\:Surface\:Area=12.56ft^3[/tex]

[tex]\begin{gathered} {\underline{\boxed{ \rm { \purple{Surface \: \: area \: = \: 2 \: \pi \: r \: h \: + \: 2 \: \pi \: {r}^{2} }}}}}\end{gathered}[/tex]

[tex]\large{\bf{{{\color{navy}{h \: = \: 2 \: ft. }}}}}[/tex]

[tex]\bf \large \longrightarrow \: \: r \: = \: \frac{Diameter}{2} [/tex]

[tex]\bf \large \longrightarrow \: \: r \: = \: \frac{2}{2} \\ [/tex]

[tex]\bf \large \longrightarrow \: \: r \: = \: \cancel\frac{2}{2} \: ^{1} \\ [/tex]

[tex]\large{\bf{{{\color{navy}{r \: = \: 1 \: ft. \: }}}}}[/tex]

[tex]\bf \hookrightarrow \: \: \: 2 \: \times \: 3.14 \times \: 1 \: ft \: \times \: 2 \: ft \: + \: 2 \: \times \: 3.14 \: \times \: {(1 \: ft)}^{2}[/tex]

[tex]\bf \hookrightarrow \: \: \:6.28 \: ft \: \times \: 2 \: ft\: \: + \: 6.28 \: ft[/tex]

[tex]\bf \hookrightarrow \: \: \:12.56 \: {ft}^{2} \: + \: 6.28 \: ft[/tex]

[tex]\bf \hookrightarrow \: \: \:18.84 \: {ft} \: ^{2} [/tex]

Hence , the surface area of cylinder is 18.84 ft²

Round to the nearest 10 of 18.84 is 18.8

Answer:

z = √3

Step-by-step explanation:

sin (30°) = z / 2√3

z = sin (30°) 2√3

z = √3

Hi,

AxB = 0 means A=0. or B=0

so 2 solutions :

4x-3= 0

4x=3

x = 3/4

and x+2 = 0.

x= -2

solutions are : -2 +and 3/4

2 answers

1) -2

2) -3/4

Answer:

For any rectangle, the one with the largest area will be the one whose dimensions are as close to a square as possible.

However, the dividers change the process to find this maximum somewhat.

Letting x represent two sides of the rectangle and the 3 parallel dividers, we have 2x+3x = 5x.

Letting y represent the other two sides of the rectangle, we have 2y.

We know that 2y + 5x = 750.

Solving for y, we first subtract 5x from each side:

2y + 5x - 5x = 750 - 5x

2y = - 5x + 750

Next we divide both sides by 2:

2y/2 = - 5x/2 + 750/2

y = - 2.5x + 375

We know that the area of a rectangle is given by

A = lw, where l is the length and w is the width. In this rectangle, one dimension is x and the other is y, making the area

A = xy

Substituting the expression for y we just found above, we have

A = x (-2.5x+375)

A = - 2.5x² + 375x

This is a quadratic equation, with values a = - 2.5, b = 375 and c = 0.

To find the maximum, we will find the vertex. First we find the axis of symmetry, using the equation

x = - b/2a

x = - 375/2 (-2.5) = - 375/-5 = 75

Substituting this back in place of every x in our area equation, we have

A = - 2.5x² + 375x

A = - 2.5 (75) ² + 375 (75) = - 2.5 (5625) + 28125 = - 14062.5 + 28125 = 14062.5

Step-by-step explanation:

Answer:

x = 65

Step-by-step explanation:

x = √(25×(25+144))

x = √(25×169)

x = 5×13

x = 65

Answered by GAUTHMATH

Answer:

13.99 x 2 = 27.98 dollars

now if they were 14 dollars exactly and you doubled that it would be 28 dollars so the difference would be 0.02 cents

Step-by-step explanation: