What is the fifth term in the expansion of (3x - 3y)??
x³y4

Using the z-distribution, a sample of 609 nickels has to be weighed.

The confidence interval is:

[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]

The margin of error is:

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which:

For this problem, the parameters are:

[tex]M = 20, \sigma = 300, z = 1.645[/tex]

We solve for n to find the sample size, then:

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]20 = 1.645\frac{300}{\sqrt{n}}[/tex]

[tex]20\sqrt{n} = 1.645 \times 300[/tex]

[tex]\sqrt{n} = 1.645 \times 15[/tex]

[tex](\sqrt{n})^2 = (1.645 \times 15)^2[/tex]

n = 608.9

Rounding up, a sample of 609 nickels has to be weighed.

More can be learned about the z-distribution at https://brainly.com/question/25890103

#SPJ1

The intensity at a distance of 14 feet is 18.29 ft

The intensity (I) of a light source is inversely proportional to the square of the distance (d) from the source.

Light intensity refers to the strength or amount of light produced by a specific lamp source

The light intensity is measured in terms of lumens per square foot or lumens per square meter.

Therefore,

I ∝ 1 / d²

Hence,

I = k / d²

where

Therefore,

k = Id²

k = 16 × 16

k = 256

Hence,

I = 256 / 14

I = 18.2857142857

I = 18.29 ft

Therefore, the intensity at a distance of 14 feet is 18.29 ft

learn more on intensity here: https://brainly.com/question/25926665

#SPJ1

[tex] \huge{↬ \boxed{ \sf{ \pink{A\green{n \blue{s \color{yellow}w \red{e \orange{r}}}}}}}}[/tex]

[tex] \leadsto[/tex]According to Angle sum property of a triangle , sum of the interior angles of a triangle is 180°.

➱ ∠SPR + ∠QPR = 180° [Linear pair]

➱ 135° + ∠QPR = 180°

➱ ∠QPR = 180° - 135°

➱ ∠QPR = 45°.....(i)

➱ ∠PQT + ∠PQR = 180° [Linear pair]

➱ 110° + ∠PQR = 180°

➱ ∠PQR = 180° - 110°

➱ ∠PQR = 70°.....(ii)

➛ ∠PQR + ∠QPR + ∠PRQ = 180° [Angle sum property of a triangle]

➱ 70°+ 45° + ∠PRQ = 180° [from (i) and (ii)]

➱ ∠PRQ = 180° - 115°

➥ ∠PRQ = 65°

hope it's help u!! :D

Answer: 4.08x2

Step-by-step explanation:

Answer:

4.08x2

Step-by-step explanation:

Answer:

80

Step-by-step explanation:

1) if the number of hamburgers is 'h', number of cheesburgers is 'c', then

2) the condition 'The number of cheeseburgers sold was three times the number of hamburgers' can be written as c=3h. Also

3) the condition 'combined total of 320' can be written as h+c=320, then

4) it is possible to make up the system of equations:

[tex]\left \{ {{c=3h} \atop {c+h=320}} \right. \ = > \ \left \{ {{c=240} \atop {h=80}} \right.[/tex]

5) finally, number of hamburgers is 80.

The missing Statement and reason for the transverse line angles is; m∠YXD = 60° and  Supplementary angles sum up to 180°.

Statement 1; AB ║ CD

Reason 1; Given

Statement 2; m∠ZYB = 60°

Reason 2; Given

Statement 3; ∠YXD and ∠DXW form a linear pair

Reason 3; Definition of Linear Pair

Statement 4; m∠YXD = 60°

Reason 4; Corresponding angles have equal measure.

Statement 5; m∠DXW = 120°

Linear pairs usually sum up to 180° because they are supplementary angles. Thus;

m∠YXD = 180° - 60° = 120°

Reason 5; Supplementary angles sum up to 180°.

Read more about Congruent Angles at; https://brainly.com/question/2938476

#SPJ1

Answer:

484

Step-by-step explanation:

because a=22² , which is equal to 484

because a=22² , which is equal to 484, but a=c hence C is equal to 484

Answer:

The numbers 1 to 12 must be placed in the circles of the star shown on the right. The sums of the numbers in each row, and the sum of the numbers in the six outer circles of the star, must be equal to 26. Arrange the numbers accordingly.

Answer: -7

Step-by-step explanation:

First, lets use the functions to find the answer to f(-8) and g(4)

f(-8) is the same as asking for the value of y when x is -8

Therefore, f(-8) = -5 (according to the graph)

Using the same rule, g(4) would be the value of y when x = 4 which,

according to the graph, g(4) = 3

Plug these values back into the original equation to get:

[tex]-1*f(-8)-4*g(4)=?\\=-1*-5-4*3\\[/tex]

using the order of operations, we will multiply the values first

[tex](-1*-5)+(-4*3)\\=5+(-12)\\=5-12\\=-7[/tex]

Answer:

-7

Step-by-step explanation:

The volume of the composite figure is 655.44 unit³.

The information is incomplete. An overview will be given. Let's assume that the shape is a cylinder.

The volume of a cylinder is πr²h

Assumed radius = 7

Assumed height = 4

The volume will be:

= πr²h

= 3.14 × 7² × 4

= 615.44 unit³

Learn more about volume on:

brainly.com/question/1972490

#SPJ1

Answer:

t=20

Step-by-step explanation:

t-19=1

t-19(+19)=1+19

t=20

The function is increasing on the intervals:

(-∞, 3] and [5, ∞)

Then the correct options are a and c.

The function is increasing when, reading from left to right, we can see that the curve goes upwards.

By looking at the graph, we can see that the function increases between -∞ and 3, and also increases between 5 and ∞, then the correct options are a and c-

(-∞, 3] and [5, ∞)

If you want to learn more about increasing functions:

https://brainly.com/question/1503051

#SPJ1

The list of data points used to generate the histogram is

   x            Frequency

15-20              0

20-25             4

25-30              6

30-35              3

35-40              4

40-45              0

45-50              3

From the question, we are to write the list of data points used to generate the given histogram

The list of data points used to generate the histogram is

   x            Frequency

15-20              0

20-25             4

25-30              6

30-35              3

35-40              4

40-45              0

45-50              3

Learn more on Histogram & Data points here: https://brainly.com/question/11683216

#SPJ1

The area of the equilateral triangle is 110.9 cm

area of a triangle = 1 / 2 bh

where

Therefore,

tan 60 = opposite / adjacent

tan 60 = 8√3 / x

x =  8√3 / √3

x = 8

hence,

b = 8 + 8 = 16

Therefore,

area of a triangle =  1 / 2 × 16 × 8√3

area of a triangle = 64√3

area of a triangle = 110.851251684

area of a triangle = 110.9 cm

learn more on triangle here: https://brainly.com/question/20593575

#SPJ1

Answer:

The equation is 5x - 9 = 2x + 23.

The answer is option A.

Step-by-step explanation:

Answer:

2 : 12

Step-by-step explanation:

There are 2 blue triangles, so 2 will come first. It's then followed by the sum of blue and yellow, which is 2 + 10, which is 12. So, the ratio is 2 : 12.

Brainliest, please :)

[tex]|\Omega|=15\\|A|=7+4=11\\\\P(A)=\dfrac{11}{15}\approx73.3\%[/tex]

Answer:

RED COUNTER: 7/15

BLUE COUNTER: 4/15

Hope it helps,

for further explanation do contact me

Reflection and dilation is the transformation which will occur to map triangle ABC triangle to A^ * B^ n C^ prime.

This refers to a plane figure which has features such as three angles and three sides.

Reflection and dilation involves flipping and enlargement/reduction respectively which gives rise to the sides being changed.

Read more about Triangle here https://brainly.com/question/1058720

#SPJ1

Answer:

c. a reflection and a dilation

Step-by-step explanation:

The probability that the diameter of a randomly selected pipe will exceed 0.84 inch is 0.977

Probabilities are used to determine the chances, likelihood, possibilities of an event or collection of events

The given parameters are:

Mean = 0.8

Variance = 0.0004

Calculate Standard deviation using

σ = √σ²

This gives

σ = √0.0004

Evaluate

σ = 0.2

Calculate the z-score at x = 0.84 using

z = (x - [tex]\bar x[/tex])/σ = √σ²

This gives

z = (0.84 - 0.8)/0.02

Evaluate

z = 2

The probability is then represented as:

P(x > 0.84) = P(z > 2)

Next, we look up the value of the z table of probabilities

From the z table of probabilities, we have:

P(x > 0.84) = 0.977

Hence, the probability that the diameter of a randomly selected pipe will exceed 0.84 inch is 0.977

Read more about probability at:

https://brainly.com/question/11234923

#SPJ1

he instructions to find the LCM of 20, 35 and 40 are the next:

1. Decompose all numbers into prime factors

20 2 10 2 5 5 1

35 5 7 7 1  

40 2 20 2 10 2 5 5 1  

2. Write all numbers as the product of its prime factors

Prime factors of 20 = 22 . 5

Prime factors of 35 = 5 . 7

Prime factors of 40 = 23 . 5

3. Choose the common and uncommon prime factors with the greatest exponent

Common prime factors: 5

Common prime factors with the greatest exponent: 51

Uncommon prime factors: 2 , 7

Uncommon prime factors with the greatest exponent: 23, 71

4. Calculate the Least Common Multiple or LCM

Remember, to find the LCM of several numbers you must multiply the common and uncommon prime factors with the greatest exponent of those numbers.

LCM = 51. 23. 71 = 280

The value of m∠7, given the data from the question is 80°

Alternate angle theorem states as follow:

When two parallel lines are cut by a line (i.e transversal), then the alternate interior angles or alternate exterior angles are aqual.

From the diagram,

From the above, we can see that m∠3 and m∠7 are alternate angles.

Therefore,

m∠7 = m∠3

m∠7 = 80°

Learn more about alternate angles:

https://brainly.com/question/2656732

#SPJ1

Complete question

please see attached photo

The probability of inductees who are female will be 0.155.

Question: What proportion of inductees have been female or have included female members?

From the information, 303 groups or individuals and forty-seven of the inductees have been female or have included female members.

Therefore, the proportion will be:

= 47/303

= 0.155

Learn more about probability on:

brainly.com/question/24756209

#SPJ1

$13,000 was invested at 6% whereas $7,000 was invested at 10% using simple interest approach

What is simple interest?

Simple interest is determined as the amount invested multiplied by the interest rate and the number of years that investment lasts.

I=PRT

I=interest

P=principal

R=rate of return

T=time

Let X be the amount invested at 6%

I at 6%=6%*X*1

I=0.06X

The amount invested at 10% is 20,000-X

total interest=0.06X+0.10*(20000-X)

total interest=1,480

1480=0.06X+0.10*(20000-X)

1480=0.06X+2000-0.10X

1480-2000=0.06X-0.10X

-520=-0.04X

X=-520/-0.04

X=13,000

13,000 was invested at 6%

amount invested at 10%=20,000-X

amount invested at 10%=20,000-13,000

amount invested at 10%=7,000

Find out more about simple interest on:https://brainly.com/question/20690803

#SPJ1

Answer:

x = 34

Step-by-step explanation:

complementary angle sum to 90°

sum the 2 angles and equate to 90

x + x + 22 = 90

2x + 22 = 90 ( subtract 22 from both sides )

2x = 68 ( divide both sides by 2 )

x = 34

Answer:

undefined

Step-by-step explanation:

slope = (y_2 - y_1)/(x_2  x_1)

slope = (-3 - 4)/(6 - 6)

slope = -7/0

Since division by zero is undefined, this line has undefined slope.

The side lengths of rectangle is 3 cm and 1.75 cm  and  5.25 cm and  9 cm.

According to the statement

we have given that Rectangle A has side lengths of 6 cm  and 3.5 cm

And The side lengths of rectangle B are proportional to the side lengths of rectangle A.

And we have to Find that the What could be the side lengths of rectangle B?

A  3 cm and 1.75 cm

B  5 cm and  2.5 cm

C  7 cm and  7 cm

D  12 cm and  5 cm

E  5.25 cm  and  9 cm

Here we see that the side B are proportional to side length A of rectangle.

So,

Let say sides of rectangle B are  a  and  b  corresponding to sides  6 and 3.5 cm

=> a/6  = b/3.5

=> a/b = 6/3.5

=> a/b  = 12/7

A  3 cm and 1.75 cm    

3/1.75  = 12/7

Hence this is proportional

B  5 cm and  2.5 cm

5/2.5  = 2  ≠ 12/7

Not Proportional

C  7 cm and  7 cm

7/7 = 1 ≠ 12/7

Not Proportional

D  12 cm and  5 cm

12/5   ≠ 12/7

Not Proportional

E  5.25 cm  and  9 cm

9/5.25  = 36/21  = 12/7

Hence this is proportional

So, 3 cm and 1.75 cm   and   5.25 cm and  9 cm  could be the side lengths of rectangle B.

Learn more about Rectangles here https://brainly.com/question/18019422

#SPJ1

The preparation of the Cash Flow Statement for Nikea Inc. for the year ended December 31, 2013, is as follows:

Direct Method:

Nikea Inc.

Cash received from customers  $600,000

Cash paid to suppliers of goods (400,000)

Cash paid to vendors of servides (30,000)

Cash from operating activities    $170,000

Indirect Method:

Nikea Inc.

For the year ended December 31, 2013

Net income                                $150,000

Add non-cash expenses:

Depreciation                                 20,000

Cash from operating activities $170,000

The direct method of preparing the Cash Flow Statement starts with the operating income and adds the non-cash expenses to obtain the cash flow from operating activities.

On the other hand, the indirect method reconciles the accounts receivable and payable to extract the exact cash flows received from customers or paid to suppliers of goods and services.

Both methods of determining the cash flow from operating activities yield the same result.

Nikea’s income statement for the year 2013

Sales                          $600,000

Cost of Goods Sold   (400,000)

Gross Profit                 200,000

Operating Expenses   (30,000)

Deprecation                (20,000)

Net Income                 150,000

Learn more about the direct and indirect methods of cash flow statements at https://brainly.com/question/5256701

#SPJ1

Answer:

the number 27 is a composite

Step-by-step explanation:

Yes, since 27 has more than two factors . 1, 3, 9, 27. In other words, 27 is a composite number because 27 has more than 2 factors

Answer:

The number 27 is composite.