What is the coefficient of the term x5y7 in the expansion of (x - y)12 ?

Step-by-step explanation:

The distance traveled varies directly with the time spent in motion. If d is distance and t is time taken. Then,

[tex]d\propto t[/tex]

or

[tex]d=kt[/tex]

k is the constant of variation

If d = 150 miles and t = 4 hours

[tex]k=\dfrac{d}{t}\\\\k=\dfrac{150}{4}\\\\k=37.5\ mph[/tex]

Answer:

24 cm

Step-by-step explanation:

Assuming that the triangles are similar,

then the ratio of their sides must be the same.

in this case you are dealing with  2 longest sides and the 2 shortest sides.

We are asked to find the y (the length of the shortest side of the blue triangle)

because they are similar, we can form a ratio with their sides:

Purple Long Side / Blue Long Side = Purple Short Side / Purple Long side

100 / 80 = 30 / y

100y = (30)(80)

y = (30)(80) / 100

y = 24 cm

Answer:

y = 24

Step-by-step explanation:

Since these triangles are similar, you can set up a proportion like this:

[tex]\frac{100}{80} =\frac{30}{y}[/tex]

→Cross multiply:

[tex]\frac{100y}{2400}[/tex]

→Divide 2400 by 100:

y = 24

Answer:

D

Step-by-step explanation:

3 to 7 is about 4.

Answer:

x=0, y=8

slack is zero

surplus is 4

Step-by-step explanation:

See graph for optimal region

if x=0, y=8

15(0)+20(8)= 160

if x= 0, y=4

15(0) + 20(4)= 80

if x=10/3 , y=8/3

15(10/3) + 20(8/3)= 310/3

Slack

8(0)+ 5(8) ≤ 40

40≤40

slack is zero

0.4(0) + 8   ≥ 4

8  ≥ 4

Answer:

His overal final score is 81.2. His letter grade is a B.

Step-by-step explanation:

Weighed average:

The sum of all values multiplied by it's weight. The weight is a proportion(a value between 0 and 1).

So.

Score of 72 on the midterm, which counts 5%.

Score of 83 on the project score, which counts 25%.

Score of 91 on homework assignments, which counts 35%.

Score of 74 on the final exam, which counts 35%.

His grade is:

G = 72*0.05 + 83*0.25 + 91*0.35 + 74*0.35 = 82.1.

His overal final score is 81.2.

At least 80 but less than 90 is a​ B

So his letter grade is a B.

Answer:

Step-by-step explanation:

At the Northside assembly plant, 30% of the workers were classied as minority, while at the Southside assembly plant, 60% of the workers were classied as minority. When Northside and Southside were closed, all workers transferred to the new Eastside plant to make up its entire work force. If 40% of the 3750 employees at Eastside are minority, then how many employees did Northside and Southside have originally?

Answer:

  x - y = 0

Step-by-step explanation:

We see that in both cases, y = x. The standard-form version of this equation is ...

  x - y = 0

Answer:

(a)See attached

(b)[tex]\text{Average Weight =}\dfrac{1}{4}$ lb[/tex]

Step-by-step explanation:

The weights of the bag are given below:

[tex]1/8 lb, 1/4 lb, 1/8 lb, 1/2 lb, 1/8 lb, 1/4 lb, 1/8lb, 1/2 lb \\1/8 lb, 1/4 lb, 1/8 lb, 1/2 lb, 1/8 lb, 1/8 lb, 1/4 lb, 1/2 lb.[/tex]

When sorted, we have:

[tex]1/8 lb, 1/8 lb, 1/8lb, 1/8 lb, 1/8 lb, 1/8 lb, 1/8 lb, 1/8 lb\\ 1/4 lb,1/4 lb, 1/4 lb, 1/4 lb\\ 1/2 lb, 1/2 lb, 1/2 lb,1/2 lb,[/tex]

Part A

See attached for the Line plot

Part B

Average Weight of the bags

[tex]=\dfrac{(8X\dfrac{1}{8})+ (4X\dfrac{1}{4})+(4X\dfrac{1}{2})}{16} \\=\dfrac{1+1+2}{16}\\=\dfrac{4}{16}\\$Average Weight =\dfrac{1}{4}$ lb[/tex]

Answer:(-12,15)

Step-by-step explanation:

My Instagram: kxng_V2

Answer:

first question: 36

second question: 5

Step-by-step explanation:

for the first question, the parentheses just mean you are multiplying. so it would be 2 x 3 x 6 which equals 36.

For the second question, you would add d and g together and e and f, then subtract the sum of e and f from the sum of d and g.

(2 + 12) - (3 + 6)

14 - 9 = 5

Step-by-step explanation:

d=2

e=3

f=6

g=12

therefore , (2)×(3)×(6)

=36

2. d=2

e=3

f=6

g=12

(d+g) - (e+f)

(2+12) - (3+6)

(14) -(9)

=5.

Answer:

a. $52.20

b. [tex]z=11x+0.09y[/tex]

Step-by-step explanation:

[tex]z=7x+0.11y[/tex]

a.

x = 4

y = 220

[tex]z=(7*4)+(0.11*220)\\z=28+24.2\\z=52.2[/tex]

It costs $52.20 under those conditions.

b.

[tex]z=11x+0.09y[/tex]

If z is still how much it costs in total

If x is how many days rented

If y is how many miles driven

Answer:

x=20

Step-by-step explanation:

Let's solve your equation step-by-step.

4x−4+3x−2+2x+6=180

Step 1: Simplify both sides of the equation.

4x−4+3x−2+2x+6=180

4x+−4+3x+−2+2x+6=180

(4x+3x+2x)+(−4+−2+6)=180(Combine Like Terms)

9x=180

9x=180

Step 2: Divide both sides by 9.

9x

9

=

180

9

x=20

Answer:

x=20

Answer:

x=20

Step-by-step explanation:

im pretty sure this is right. you can't take away 4 from 4 x, so you do it like this: -4+(-2)+6 =0. 4x + 3x + 2x =9x. 180/9 = 20

Find the total minutes:

15 + 30 + 25 + 35 = 105 minutes

This is equal to 1 hour and 45 minutes

Subtract 1 hour and 45 minutes from 9:30

She woke up at 7:45 am

Answer:

The mean and standard deviation of the combined distribution is 16 and 7.192 respectively.

Step-by-step explanation:

We have given that a distribution consists of three components with frequencies 200, 250, and 300 having means 25, 10, and 15 and standard deviations 3, 4, and 5 respectively.

And we have to find the mean and standard deviation of the combined distribution.

Firstly let us represent some symbols;

[tex]n_1[/tex] = 200           [tex]\bar X_1[/tex] = 25                 [tex]\sigma_1[/tex] = 3

[tex]n_2[/tex] = 250            [tex]\bar X_2[/tex] = 10                  [tex]\sigma_2[/tex] = 4

[tex]n_3[/tex] = 300            [tex]\bar X_3[/tex] = 15                  [tex]\sigma_3[/tex] = 5  

Here, [tex]\bar X_1, \bar X_2 , \bar X_3[/tex] represent the means and [tex]\sigma_1,\sigma_2,\sigma_3[/tex] represent the standard deviations.

Now, as we know that Mean of the combined distribution is given by;

                         [tex]\bar X = \frac{n_1 \times \bar X_1+n_2 \times \bar X_2+n_3 \times \bar X_3}{n_1+n_2+n_3}[/tex]

Putting the above values in the formula we get;

                         [tex]\bar X = \frac{200 \times 25+250 \times 10+300 \times 15}{200+250+300}[/tex]

                         [tex]\bar X = \frac{5000+2500 +4500}{750}[/tex]

                         [tex]\bar X = \frac{12000}{750}[/tex]  =  16

Similarly, the formula for combined standard deviation is given by;

       [tex]\sigma = \sqrt{\frac{n_1\sigma_1^{2} + n_1(\bar X_1-\bar X)^{2}+n_2\sigma_2^{2} + n_2(\bar X_2-\bar X)^{2}+n_3\sigma_3^{2} + n_3(\bar X_3-\bar X)^{2} }{n_1+n_2+n_3} }[/tex]

       [tex]\sigma = \sqrt{\frac{(200 \times 3^{2}) + 200 \times (25-16)^{2}+(250 \times 4^{2}) + 250 \times (10-16)^{2}+(300 \times 5^{2}) + 300 \times (15-16)^{2} }{200+250+300} }[/tex]

       [tex]\sigma = \sqrt{\frac{1800 + (200 \times 81)+4000 + (250 \times 36)+7500 +( 300 \times 1) }{750} }[/tex]        

       [tex]\sigma = \sqrt{\frac{1800 + 16200+4000 + 9000+7500 +300 }{750} }[/tex]  

       [tex]\sigma = \sqrt{\frac{38800 }{750} }[/tex]  =  7.192

Hence, the mean and standard deviation of the combined distribution is 16 and 7.192 respectively.

Answer:

Surface Area: 1,200 units²

Lateral Area: 624 units²

Volume: 960 units³

Step-by-step explanation:

Surface Area is the area of all the faces of the object.

Lateral Area is the area of all the faces of the object NOT INCLUDING the base.

Volume is how much the object can hold.

Using the formula [tex]\frac{1}{2} *b*h[/tex] the area of ONE of the lateral faces of the pyramid is

0.5×24×13=

12×13=

156 units²

156 un² × 4 lateral faces =

624 un²

The lateral surface area is 624 units²

Since the lateral surface area + base is the total surface area:

The base is 24² or 576 units²

624 un²+576 un²=

1,200 units² is the total surface area.

Volume formula for a pyramid is [tex]\frac{1}{3} *b*h[/tex]

We know the base is 576 units².

We don't know the height yet.

We can use the Pythagorean Theorem to find the height of our pyramid.

a²+b²=c²

Half of 24 is 12

12²+b²=13²

144+b²=169

Subtract 144 from both sides.

b²=25

Square root both sides.

b=[tex]\sqrt{25}[/tex]

b=5

The height of our pyramid is 5.

[tex]\frac{1}{3} *576*5=\\\\192*5=\\\\960[/tex]

Our volume for the pyramid is 960 units³

Hope you understand more!

Answer:

4:14 or 2:7

Step-by-step explanation:

there are 4 girls and 14 boys

the ratio is 4:14

correct me if this is wrong

Answer:

2/7

Step-by-step explanation:

two find the answer you need to reduce 4 and 14 into the lowest common denominator.

Answer:

Step-by-step explanation:

They closed the 200 mile distance in 2.5 hours, so the sum of their speeds was ...

  (200 mi)/(2.5 h) = 80 mi/h

If s is the speed of the slower one, then ...

  s + (s+20) = 80

  2s = 60

  s = 30

The slower wander's speed was 30 mph; the faster one's was 50 mph.

Answer:

The maximum value is +√21 and the minimum value is -√21

Step-by-step explanation:

f(x,y,z) = x² + y² + z². Let g(x,y,z) = x⁴ + y⁴ + z⁴ - 7 = 0

Using Lagrange multipliers,

df/dx = λg/dx, df/dy = λg/dy. and df/dz = λg/dz

df/dx = 2x, df/dy = 2y, df/dz = 2z

dg/dx = 4x³, dg/dy = 4y³, dg/dz = 4z³

So, df/dx = λg/dx ⇒ 2x = 4λx³     (1)

df/dy = λg/dy ⇒ 2y = 4λy³           (2)

df/dz = λg/dz ⇒ 2z = 4λz³           (3)

From (1) 4λx³ - 2x = 0

2λx³ - x = 0

x(2λx² - 1) = 0

solving, x = 0 or (2λx² - 1) = 0 ⇒ 2λx² = 1 ⇒ x = ±1/√(2λ) since x ≠ 0

From (2) 4λy³ - 2y = 0

2λy³ - y = 0

y(2λy² - 1) = 0

solving, y = 0 or (2λy² - 1) = 0 ⇒ 2λy² = 1 ⇒ y = ±1/√(2λ) since y ≠ 0

From (3) 4λz³ - 2z = 0

2λz³ - z = 0

z(2λz² - 1) = 0

solving, z = 0 or (2λz² - 1) = 0 ⇒ 2λz² = 1 ⇒ z = ±1/√(2λ) since z ≠ 0

g(x,y,z) = x⁴ + y⁴ + z⁴ - 7 = 0

(1/√(2λ))⁴ + (1/√(2λ))⁴ + (1/√(2λ))⁴ - 7 = 0

3 (1/√(2λ))⁴ = 7

(1/√(2λ))⁴ = 7/3

1/√(2λ) = ⁴√7/3

√(2λ) = ⁴√3/7

2λ = √3/7

λ = 1/2(√3/7)

Since x = 1/√(2λ) = 1/√(2 [1/2(√3/7)]) = 1/⁴√3/7 = ±⁴√7/3

Also y = 1/√(2λ) = 1/√(2 [1/2(√3/7)]) = 1/⁴√3/7 = ±⁴√7/3

and z = 1/√(2λ) = 1/√(2 [1/2(√3/7)]) = 1/⁴√3/7 = ±⁴√7/3

Substituting x,y and z into f(x,y,z) we have

f(x,y,z) = (⁴√7/3)² + (⁴√7/3)² + (⁴√7/3)² = 3(⁴√7/3)² = 3(√7/3) = √(7 × 3) = ±√21

The maximum value is +√21 and the minimum value is -√21

Answer:

The limit leads to a determinate form.

[tex]\lim_{x \to \infty} \frac{2}{-x+3} = 0[/tex]

Step-by-step explanation:

The following are indeterminate forms.

[tex]\frac{0}{0} \ and \ \frac{\infty}{\infty}[/tex]

Given the limit of a function [tex]\lim_{x \to \infty} \frac{2}{-x+3}[/tex], to show if the given limit is determinate or indeterminate form, we will need to substitute the value of -[tex]\infty[/tex] into the function as shown,

[tex]\lim_{x \to \infty} \frac{2}{-x+3}\\= \frac{2}{-(-\infty)+3}\\= \frac{2}{\infty+3}\\= \frac{2}{\infty}\\\\Generally, \ \frac{a}{\infty} =0[/tex]

where a is any constant, therefore [tex]\frac{2}{\infty} = 0[/tex]

Since we are able to get a finite value i.e 0, this shows that the limit does exist and leads to a determinate form

Answer:

A = 55.15

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

cos theta = adjacent/ hypotenuse

cos A = 4/7

Take the inverse cos of each side

cos^-1 cos A = cos^-1 (4/7)

A = 55.15009542

To the nearest hundredth

A = 55.15

Step-by-step explanation:

we have diameter and volume

and volume function is : v=(3.14)(r^2)h

so : h = 196/112

Approximately 3.6

:) Hope this helps

Answer:

  C.  38°

  D.  30°

Step-by-step explanation:

The relevant relation in both cases is the inscribed angle measures half the measure of the arc it intercepts.

__

C. Angle TSQ intercepts arc TQ, so the measure of arc TQ is 2(86.5°) = 173°. The measure of arc TR is the difference between the measures of arcs TQ and RQ, so is ...

  arc TR = 173° -135° = 38°

__

D. Inscribed angle PQR intercepts arc PR, so is half its measure.

  angle PQR = 60°/2 = 30°

Answer:

The team ordered 7 black T-shirts.

The team ordered 14 red T-shirts.

Step-by-step explanation:

The team ordered 140 T-shirts.

How many black T-shirts did the baseball team order?

Of those, 5% are black.

0.05*140 = 7

The team ordered 7 black T-shirts.

How many red T-shirts?

Of those, 10% are red.

0.1*140 = 14

The team ordered 14 red T-shirts.

Answer:

llolololol

Step-by-step explanation:

Answer:80 grams

Step-by-step explanation:

Answer:

A.

Step-by-step Explanation:

P(A or B) = P(A)+P(B)-P(A and B)

Now

Putting the givens

0.68 = 0.2 + P(B) - 0.12

P(B) = 0.68 - 0.2 +0.12

P(B) = 0.6

Note: This is the correct table format.

Flour type                   z                      Mean                            StDev

No DBS                       00                      552                                 18

5% DBS                       00                      525                                 23

15% DBS                     00                      485                                  24

Answer:

5. ANOVA for several means

Step-by-step explanation:

In this question, three different means of the data are compared. ANOVA is used for comparing between two or more means to test for differences. It extends the z and t test that are only used for comparing two means.

Since three means are compared, the inference procedure to be used is ANOVA.

Answer:

1.88

Step-by-step explanation:

From Trigonometry Identity;

Cos 20° = AC/ CB

AC = Cos 20° × CB

= Cos 20° × 2

= 1.879

= 1.88 ( to the nearest hundredth)

Answer:

a) The null and alternative hypothesis are:

[tex]H_0: \mu=35.1\\\\H_a:\mu< 35.1[/tex]

b) The 95% confidence interval for the mean stocks traded in 2014 in millions is (21.13, 29.07).

c)  D. Reject the null hypothesis because μ= 35 1 million shares does not fall in the confidence interval.

Step-by-step explanation:

The claim is that 2014 stock volumes are significantly different from 2011 stock volumes (35.1 millions).

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=35.1\\\\H_a:\mu< 35.1[/tex]

We can test this by calculating a 95% confidence interval for the mean.

The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.

The sample mean is M=25.1.

The sample size is N=40.

When σ is not known, s divided by the square root of N is used as an estimate of σM:

[tex]s_M=\dfrac{s}{\sqrt{N}}=\dfrac{12.4}{\sqrt{40}}=\dfrac{12.4}{6.32}=1.961[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=40-1=39[/tex]

The t-value for a 95% confidence interval and 39 degrees of freedom is t=2.023.

The margin of error (MOE) can be calculated as:

[tex]MOE=t\cdot s_M=2.023 \cdot 1.961=3.966[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=M-t \cdot s_M = 25.1-3.966=21.13\\\\UL=M+t \cdot s_M = 25.1+3.966=29.07[/tex]

The 95% confidence interval for the mean is (21.13, 29.07).

The value 35.1 is not included in the interval, so we can conclude that there is significant difference from the 2011 stock volume.

Answer:

r = 3cm

Step-by-step explanation:

Use the formula for the surface area of a cylinder and solve to obtain r=3cm

Hence radius of base is 3 cm of right circular cylinder.

The cylinder is known as a right circular cylinder when the axis (one of the rectangle's sides) is perpendicular to the radius ((r)). The base and top of the right circular cylinder are both round and parallel to one another. The general formula for the total surface area of a cylinder is T. S. A. =[tex]2\pi rh+2\pi r^{2} .[/tex]

Given total surface area of right circular cylinder =84[tex]\pi cm^{2}[/tex]

Using formula for right circular cyinder =.[tex]2\pi rh+2\pi r^{2} .[/tex]=84

and height=11 cm

[tex]2\pi r11+2\pi r^{2} =84.\pi[/tex]

⇒[tex]11r+ r^{2} =84/2[/tex]

⇒[tex]11r+ r^{2} =42[/tex]

⇒[tex]r^{2} +11r-42=0[/tex]

⇒r = [tex]\frac{-11+-\sqrt{11^{2}-4(1)42 } }{2}[/tex]

⇒r=[tex]\frac{-11+-17}{2}[/tex]

⇒r=3,-1

Hence radius of base is 3 cm as value can't be negative .

Learn more about surface area of cylinder https://brainly.com/question/12763699

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