16
Select the correct answer.
If function g is defined by the equation Y-3X = -14, which equation represents the function in function notation?
OA. gx) = 3X - 14
OB. gx) = -3X - 14
OC. g(x) = 3X + 14
OD. gx) = -3X + 14
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Answer:

£32 in total for the top and two trousers

Step-by-step explanation:

The price for a top In the "cloth for you" shop= £10

The price for a bermuda trouser In the "cloth for you" shop= £12

There is a 20% discount on tops

The price If I bought one top and would trouser will be

(10-(0.2*10)) for the top

2(12) for the trouser

Total= (10-(0.2*10))+ 2(12)

Total = 10-2+24

Total = £32

So I spent £32 in total for the top and two trousers

Answer:

  25/4 square inches

Step-by-step explanation:

The area of a sector of a circle is given by the formula ...

  A = (1/2)r²θ

where r is the radius and θ is the central angle in radians.

For your sector, the area is ...

  A = (1/2)(5 in)²(1/2) = 25/4 in²

Answer:

d. 27 cubic feet

Step-by-step explanation:

volume of cube = s^3 = B * s

volume of pyramid = (1/3) * B * h

The volume of a pyramid is 1/3 of the area of the base multiplied by the height. The volume of a cube is the area of the base multiplied by the height. Since the volume of a pyramid has the fraction 1/3 and the volume of the cube does not, then the volume of a cube is 3 times greater than the volume of a pyramid that fits inside and has the same base area.

volume of pyramid = 9 cu ft

volume of cube = 3 * 9 cu ft = 27 cu ft

Answer: d. 27 cubic feet

Answer:

27 ft^3 (Answer d)

Step-by-step explanation:

Here the volume of the pyramid is (1/3) the volume of the cube:

Letting s represent the length of one side of the base,

(1/3)(s)^2(s) = 9 ft^3, equivalent to  s^3 = 27.

Solving for s, we get s = 3 ft.

Thus, the volume of the cube is V = s^3 = (3 ft)^3 = 27 ft^3 (Answer d)

Answer:

Full question is:

Find equations of the tangent plane and the normal line to the given surface at the specified point. x + y + z = 7[tex]e^{xyz}[/tex] at a specified point (0, 0, 7)

Step-by-step explanation:

If we have a level surface, then it will give us

f(x,y,z) = x+y+z = 7[tex]e^{xyz}[/tex]. where f is the function of the x, y, and z coordinates.

Now let us calculate the ∇ gradient of f at point (0,0,7):

∇[tex]f|_{(0,0,7)}[/tex] = (fx,fy,fz) = (1−7yz[tex]e^{xyz}[/tex],1−7xz[tex]e^{xyz}[/tex],1−7xy[tex]e^{xyz}[/tex])[tex]|_{(0,0,7)}[/tex]

= (1, 1, 1)

We get the equation for the tangent plane A:

A: 1(x−0) + 1(y−0) + 1(z−7)=0

This can also be written as:

x+y+z = 7 ------------------------------------------------------------------(a)

The equation for the normal line B gives us :

L: (x,y,z) = (0,0,7) + t(1, 1, 1), t ∈ R --------------------------------(b)

Answer:

3 1/4

Step-by-step explanation:

Hey there!

Well if Cedarburg to Westford is 8 3/4 miles and Oxford to Westford is 5 1/2 miles, we can make the following,

CO = CW - OW

CO = 8 3/4 - 5 1/2

Make the denominators the same,

5 1/2

improper

11/2

*2

22/4

Proper

5 2/4

8 3/4 - 5 2/4

3 1/4 miles

Hope this helps :)

I suppose you're supposed to convert 100111 from base 2 to base 10. We have

[tex]100111_2=2^5+2^2+2^1+2^0=32+4+2+1=39_{10}[/tex]

so the missing number is 39.

Answer:

b = - 3.7

Step-by-step explanation:

here are the data values:

x   y          XY        X²

14 46         644       196

15 49         735       225

16 37          592      256

17 42          714        289

18 37          666      324

19 31           589      361

20 25         500      400

21 23          483       441

22 20         440       484

23 15          345       529

24 12         288       576

now we are required to find the summation (total) of all values of X, Y, XY and X².

∑X = 209

∑Y = 337

∑XY = 5996

∑X² = 4081

The formular for finding b is given as:

b = n∑XY - (X)(Y) / n∑X² - (∑X)²

= 11(5996) - (209)(337) / 11(4081) - (209)²

= 65956 - 70433 / 44891 - 43681

= -4477/ 1210

= -3.7

The question asked us to find the value of b but we can  go further to find the equation of the regression line:

a = ∑Y - b∑X / n

= 337 - (-3.7)(209)/  11

=1110.3/11

= 100.94

the equation is:

Y = 100.94 - 3.7X

I hope you find my solution useful!

=

Answer:

The probability is 2,010,580/13,378,456

Step-by-step explanation:

Here is a combination problem.

We want to 7 cards from a total of 52.

The number of ways to do this is 52C7 ways.

Also, we know there are 12 face cards in a standard deck of cards.

So we are selecting 3 face cards from this total of 12.

So also the number of cards which are not face cards are 52-12 = 40 cards

Out of all these 40, we shall be selecting exactly 4. The number of ways to do this 40C4

Thus, the required probability will be;

(40C4 * 12C3)/52C7 = (91,390 * 220)/133,784,560

= 20,105,800/133,784,560 = 2,010,580/13,378,456

Answer:

Expression = 2n³ - 20n

Step-by-step explanation:

Find:

Expression

Computation:

Assume given number is 'n'

Cube of number = n³

Twice of cube = 2n³

Subtract number = 20n

Expression = 2n³ - 20n

Answer: 0.0993

Step-by-step explanation:

Since the jar contains 18 red marbles and 38 blue marbles, the total marbles will be:

= 18 marbles + 38 marbles

= 56 marbles

When 2 marbles are pull out at random at the same time, the probability that both are red will be:

= (18/56) × (17/55)

= 0.3214 × 0.3091

= 0.0993

Answer:

$800

Step-by-step explanation:

Let the original price be $x.

75% reduction ----- 100% -75%= 25%

25%x= 200

[tex] \frac{25}{100} x = 200 \\ x = 200 \div \frac{25}{100} \\ x = 200 \times \frac{100}{25} \\ x = 800[/tex]

Thus, the original price of the clothes dryer is $800.

Answer:

$800

Step-by-step explanation:

Let the original price be x.

Final price=100%-75%

                  =25%

x-75%=200

x=200 x 100/75

x=8 x 100

x=800

Thank you!

Answer:

On the map:

0.8 mile / 1.5 inches

=  0.533 mile / 1 inch

Total distance on the map:

0.6 inches

distance travelled in miles:

0.6 * 0.533 = 0.32 miles

please mark brainly if you want

Answer:

The answer is A = 0.3 mile

Step-by-step explanation:

I got it right in 2021.

Answer:

Step-by-step explanation:

Perimeter of a rectangle = 2l + 2w

Area of rectangle = l × w

where

l is the length

w is the width

From the question

The length is twice its width is written as

l = 2w

Substitute this into the formula for finding the area of the rectangle

Area = 200 yd²

200 = 2w²

Divide both sides by 2

w² = 100

Find the square root of both sides

width = 10cm

Substitute this value into l = 2w

That's

l = 2(10)

length = 20cm

Perimeter of the rectangle is

2(20) + 2(10)

= 40 + 20

Hope this helps you

Answer: Please Give Me Brainliest, Thank You!

2

Step-by-step explanation:

There are two variables here, X and Y

Answer:

C = pi sqrt(x)

Step-by-step explanation:

The area of a square is x

A = s^2 where s is the side length

x = s^2

Take the square root of each side

sqrt(x) = s

This would be the diameter of the inscribed circle

The circumference of a circle is given by

C = pi d

C = pi sqrt(x)

Answer:

See below.

Step-by-step explanation:

Assign the variable n to be the sides of the square.

Since a square has four equal sides, the area of the square is n^2 or x.

Therefore:

[tex]n=\sqrt{x}[/tex]

The largest circle that can be inscribed in the square will have the largest possible diameter. The largest possible diameter will be straight across the center of the circle. So, the largest possible diameter will be the side length, n.

Therefore, the radius will be n/2.

The circumference of a circle is:

[tex]C=2\pi r[/tex]

Plug in n/2 for the radius:

[tex]C=2\pi (\frac{n}{2})\\ C=n\pi[/tex]

Now, substitute n for the square root of x:

[tex]C=\pi\sqrt{x}[/tex]

=========================================

Explanation:

Subtracting a negative is the same as adding. Example: 2-(-3) = 2+3 = 5.

So (x+y)-(-z) is the same as x+y+z. We can group up terms inside parenthesis and it won't change the result. Meaning that x+y+z is the same as any of the following below

We could also swap the order of either x, y or z, and still have the same result.

He must do a 8,00,000 sales to make total of 75000 for the year.

For salesman base salary = 35000, Salary to be atained is 75000. Having commission of 5% on every sales. Sales to be determine so the salesman attained 75000 for year.

In mathematics it deals with numbers of operations according to the statements.

Here, according to the statement.
Let x be sales,
35,000 + 5%x = 75,000
0.05x = 75000-35000
x = 40000/0.05
x = 8,00,000

Thus, he must do a 8,00,000 sales to make total of 75000 for the year

Learn more about arithmetic here:

brainly.com/question/14753192

#SPJ2

Answer:

The percentage of patients whose cholesterol is between 198 mg/dL and 207 mg/dL is 33.73%

Step-by-step explanation:

To calculate this proportion, we follow the probability route, using the z-score statistics

Mathematically;

z-score = (x-mean)/SD

from the question, mean = 200 and SD = 10

So for 198

z-score = (198-200)/10 = -2/10 = -0.2

For 207

z-score = (207-200)/10 = 7/10 = 0.7

So the probability we want to calculate is;

P(-0.2<z<0.7)

Mathematically this can be calculated as;

P(z<0.7) - P(z<-0.2)

We can calculate the required probability using the standard normal distribution table

P(-0.2<x<0.7) = 0.3373 from the standard distribution table

So it is this 0.3373 that we now convert to percentage and that is 33.73%

Answer:

D

Step-by-step explanation:

Let's first find the mean and median of each class.

Class 1:

The mean is simply all the numbers added up and then divided by the number of elements. There are 9 students in Class 1. Thus, we add all the ages up and then divide by 9. Thus:

[tex]\text{Class 1 Mean }= \frac{14+15+15+16+16+16+17+17+18}{9} \\=144/9=16[/tex]

The median is simply the middle number when the data sets are placed in order. The median of Class 1 is 16, the number in the middle.

Class 2:

Again, Class 2 has 9 students. Add up all the ages and then divide:

[tex]\text{Class 2 Mean }= \frac{13+14+15+16+16+17+18+18+19}{9}\\ =146/9\approx16.2222[/tex]

The median is the middle number of the data set. The median of Class 2 is 16.

Therefore, the mean of Class 2 is larger than the mean of Class 1. The medians of the two classes are equivalent.

Of the answer choices given, only D is correct.

Answer:

The mean of class II is larger and the median is the same

Step-by-step explanation:

Class I

14,15,15,16,16,16,17,17,18

The mean is

(14+15+15+16+16+16+17+17+18)/9

144/9 = 16

The median is the middle number

14,15,15,16,    16,    16,17,17,18

median = 16

Class II

13,14,15,16,16,17,18,18,19

The mean is

(13+14+15+16+16+17+18+18+19)/9

146/9 = 16.2repeating

The median is the middle number

13,14,15,16    ,16,       17,18,18,19

median = 16

Answer:

a. True

b. true

c. false

d. false

e. false

Step-by-step explanation:

a. true

polutation = 25% = 0.25

sample = n= 12

n x p

= 12 x o. 25 = 3 and 3 is less than 10

12(1 - p)

= 12 x 0.75

= 9 and is less than 10

b. True

the sample distribution of the population is normal when

sample size x population > or equal to 10

40 x 0.75

= 30 and 30 is greater than 10

c. false

50 x 0.25 = 12.5

50 x 0.20 = 10

z = 10 - 12.5/sqrt(12.5)

= -2.5/3.54

= -0.70

H0: Young american family who delayed

H1: young american family who did not delay

p(z = -0.70)

0.2420>0.005

therefore we accept the null hypothesis

d. false

150 x 0.20 = 30

150 x 0.75 = 37.5

z = 30 - 37.5/sqrt(37.5) = -7.5/6.12 = -1.22

p(z = -1.22) = 0.1112 > 0.05

therefore we do not reject the null hypothesis

e. false

se1 = sqrt(p(1-p)/n

se2 = sqrt(p(1-p)/3n

se2 = 1/sqrt(3)se2

Answer:

Step-by-step explanation:

Hello, this is pretty straight forward. Let me remind you the following.

The standard equation of a parabola is

[tex]y=ax^2+bx+c[/tex]

But the equation for a parabola can also be written in "vertex form":

[tex]y=a(x-h)^2+k[/tex]

In this equation, the vertex of the parabola is the point (h,k) .

So, here the vertex is the point (2, -25) and the axis of symmetry is x = 2

Thank you

Answer:

if anyone still needs the answer I added a pic

Step-by-step explanation:

Find the circumference:

Circumference = 2 x PI x radius:

Circumference = 2 x 3.14 x 16 = 100.48 inches.

A full circle is 360 degrees, a 45 degree angle is 1/8 of a full circle.

Arc length = 100.48 / 8 = 12.56 inches.

Answer:

B.

Step-by-step explanation:

10c + 5 ≤ 45

10c ≤ 40

c ≤ 4

Since the inequality uses the less than or equal to sign, we use a shaded circle on the number line. Since c is less than or equal to 4, your answer will be B, since the line extends infinitely to the left of 4.

Hope this helps!

Answer:

B

Step-by-step explanation:

To get the answer, you need to simplify or re-write the equation given:

Next, group the like terms together:

Now, we can apply algebra to simplify the equation further:

Now, look at your options. Only option B matches our equations. Therefore, B is the correct answer.

Answer:

A. y + 2= x

Step-by-step explanation:

Which equation is represented by the graph shown in the image?

A. y + 2= x

B. y + 1= x

C. y - 1= x

D. y - 2= x

Please show ALL work! <3

The graph shown has a slope of +1 and a y intercept of -2.

All given answer choices have a slope of +1, so that's not the problem.

We need one that has a y-intercept of -2, or the equation should be

y = x-2, or equivalently y+2 = x

which corresponds to answer choice A.

Answer:

5443

Step-by-step explanation:

Order of Operations: BPEMDAS

Always left to right.

Step 1: Add 68 and 5042

68 + 5042 = 5110

Step 2: Add 5110 and 333

5110 + 333 = 5443

And we have our answer!

This is equivalent to x^2+8x+13

======================================================

Explanation:

The vertex of f is at (0,0). The vertex of g is at (-4, -3). The vertex has moved 4 units to the left and 3 units down.

To shift to the left, we replace x with x+4. So we have f(x) = x^2 turn into f(x+4) = (x+4)^2 so far.

Then we subtract off 3 to move everything 3 units down. We have

g(x) = (x+4)^2-3

---------------------

Optionally we can expand things out like so

g(x) = (x+4)^2-3

g(x) = (x+4)(x+4)-3

g(x) = x(x+4)+4(x+4)-3

g(x) = x^2+4x+4x+16-3

g(x) = x^2+8x+13

Showing that (x+4)^2-3 is equivalent to x^2+8x+13

Answer:

The sum is represented by the polynomial:

[tex]5\,x^9+2 \,x^7+13\,x+4[/tex]

Step-by-step explanation:

Recall that polynomials are added by combining like terms. The only like terms in this addition are: 5 x and 8 x  which added render: 13 x. therefore, the addition of these polynomials renders;

[tex]5\,x^9+2 \,x^7+13\,x+4[/tex]

Answer:

The tree grows 33cm per year

Step-by-step explanation:

Here in this question, we are interested in knowing how fast the growth of the tree is.

This is easily obtainable from the equation for the height of the tree.

Mathematically, the equation is given as;

H = 210 + 33t

Interpreting this, we can have 210 as the original height of the tree when Renata moved in, while the term 33 represents the growth per year.

So we can say the tree adds a height of 33 cm each year and this translates to the yearly growth of the tree

Answer:

I hope you are searching for this......

Answer:

x =  12      ( two points shots )

y =  7       ( three points shots )

Step-by-step explanation:

Let´s call  "x" two points shots,  and  "y" three points shots, then

x  +  y  =  19

2*x  +  3*y  =  45

We have to solve a two-equation system for x and y

y =  19  - x

2*x  +  3 * ( 19 - x ) = 45

2*x  +  57  -  3*x   =  45

- x   =  45 - 57

-x   =  - 12

x  = 12

And     y  =  19  -  12

y  = 7