Simplify this expression.
3a/9(a + b)
Enter the correct answer.

Answer:

10 books.

Step-by-step explanation:

(b) To estimate the mean we take the mean value of books for each bar.

So for 0-4 books we use 4/2 = 2, for 5-9 we use (9-5)/ 2 + 5 = 7 and so on for each bar.  So the estimate for the first bar is 2 * 9 = 18 books.

So the required mean = total estimate of books bought / number of students

= (9 *2 + 10*7 + 12*13 + 17*2 + 22*6) / 40

= 410 / 40

= 10.25

Answer:

m < S = 55°

Step-by-step explanation:

Based on tangent theorem, a tangent line is said to be perpendicular to a radius of a circle when they intercept. The point at which they meet is said to be at 90°.

Therefore, in the ∆PQS, given, m < P = 90°.

m < Q = 35°

m < S = 180° - (90° + 35°) (sum of the angles in a triangle)

m < S = 180° - 125°

m < S = 55°

Answer:

The slope of p is also - 3 .

Since p and q are parallel their slope are also the same.

Hope this helps

Answer:

The slope of line p is also -3

Step-by-step explanation:

Recall that parallel lines have the property of carrying the exact same slope (that is why they don't intersect). Therefore if the slope of line q is -3, the slope of line p must also be -3.

Answer:

Cup A

Step-by-step explanation:

Cup A

Salt: Water = 3:22

Expressed as a percentage

[tex]\dfrac{3}{22} \times 100 = 13.6\%[/tex]

Proportion of Salt =13.6%

Cup B

Salt: Water = 1:8

Expressed as a percentage

[tex]\dfrac{1}{8} \times 100 = 12.5\%[/tex]

Proportion of Salt =12.5%

Cup C

Proportion of Salt = 12.75%

Therefore, Cup A has the greatest proportion of salt.

Answer:

y = (-x - 6)/2

Step-by-step explanation:

x + 2y = -6

2y = -x - 6

y = (-x - 6)/2

Answer:

to earn a $7180 annual income from the investments, the bank needs to invest $10,000 into the bonds.

Step-by-step explanation:

Let the mortgage investment be X

The Bond to be Y

and the CDs to be Z

Thus;

X+Y+Z = 86000 ------- (1)

Y + Z = X       ------------(2)

10X + 9Y + 6Z = 7180 × 100 ------ (3)

So;we now have:

X+Y+Z = 86000 ------- (1)

Y + Z = X       ------------(2)

10X + 9Y + 6Z = 718000 ------ (3)

Let ; replace X with Y+Z in equation (1) and (3)

Y+Z + Y+Z = 86000

2Y + 2Z = 86000

Divide both sides by 2

Y+Z = 43000      ------ (4)

From equation (3)

10X + 9Y + 6Z = 718000

10(Y+Z) + 9Y + 6Z = 718000

10Y +10Z + 9Y +6Z = 718000

19Y + 16Z = 718000    -----(5)

Y+Z = 43000      ------ (4)

19Y + 16Z = 718000    -----(5)

Using elimination method; multiply (-16) with equation (4) and (5) ; so, we have:

 -16 Y -16 Z = -688000

 19Y + 16Z =    718000          

 3Y  + 0     =    30000            

3Y = 30000

Y = 30000/3

Y = 10000

From (4);

Y+Z = 43000  

So; replace Y with 10000; we have:

10000 + Z = 43000

Z = 43000 - 10000

Z = 33000

From (1) ;

X+Y+Z = 86000

X + 10000  + 33000 = 86000

X + 43000 = 86000

X = 86000 - 43000

X = 43000

Since we assume the bond to be Y and Y = $10000;

Thus; to earn a $7180 annual income from the investments, the bank needs to invest $10,000 into the bonds.

Answer:

A. -55

Step-by-step explanation:

f(x)=-2x^2+4x-7

f(-4)= -2(-4)^2+4(-4)-7

= -2(16)-18-7

= -32-16-7

= -55

Answer:

-55

Step-by-step explanation:

f(x) = −2x^2 + 4x − 7

Let x = -4

f(-4) = −2(-4)^2 + 4(-4) − 7

      = -2 (16) -16 -7

      = -32 -16 -7

      =-55

Answer:

I believe it is 18 + the square root of 26.

Step-by-step explanation:

The slope of line BC should be 5/1 because it goes up 5 times and to the right once. If you square root 26 you get 5.09.

Step-by-step explanation:

Area: bh

The shape is a square in which the side lengths are the same, so we multiply the number squared.

A = 6.25(6.25)

A = 39.06

Volume: lwh

6.25^3 = V

V = 244.14

Hope this helps:)

Step-by-step explanation:

Area: bh

The shape is a square in which the side lengths are the same, so we multiply the number squared.

A = 6.25(6.25)

A = 39.06

Volume: lwh

6.25^3 = V

V = 244.14

I hope I contributed

Answer:

15

Step-by-step explanation:

mean means add all the numbers and divide them by how many there are

plot 1: 63 divided by 9 equals 7

plot 2: 330 divided by 15 equals 22

so now we need to subtract 22 minus 7 equals 15

hope this helps

Answer:

15

Step-by-step explanation: you have to add all of the numbers and then divide the answer by the number of numers you added

Answer:

Fraction = 5/10 = 1/2

Decimal = 0.5

Step-by-step explanation:

Answer:

fraction-5/10 decimal-0.5

plz give brainiest

Step-by-step explanation:

Answer:

you can pick any of them

Step-by-step explanation:

Answer: Any are right

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Assuming the figure to be a parallelogram, then

The consecutive angles are supplementary, that is

∠ D + ∠ C = 180°

145° + ∠ C = 180° ( subtract 145° from both sides )

∠ C = 35° → D

Answer:

138 : 269

Step-by-step explanation:

Last year, the number of bicyclists that showed up was 1345.

This year, there were 690 bicyclists.

The ratio of the number of bicyclists that showed up for the past two years is the ratio of those that showed up this year to those that showed up last year:

690 : 1345

Let us put it in simplest terms:

138 : 269

Answer:

  16

Step-by-step explanation:

(f - g)(5) = f(5) -g(5)

From the tables, ...

  f(5) = 29

  g(5) = 13

Your desired function is ...

  f(5) -g(5) = 29 -13 = 16

Hey there! :)

Answer:

V = 3408 units³

Step-by-step explanation:

Given:

r = 12

h = 71

Volume of a cone: V = 1/3 (bh) where b = πr²

Calculate the area of the base:

A = 12²π

A = 144π units²

Plug this into the formula for the volume of a cone:

V = 1/3 (144π · 71)

V = 1/3 (10224)

V = 3408 units³

Answer:

B . 3408 π  units^3

Step-by-step explanation:

[tex]h = 71\\r = 12\\V =?\\V = \frac{1}{3} \pi r^2 h\\V = \frac{1}{3} \pi \times 12^2 \times 71\\V = \frac{1}{3} \pi \times 144 \times 71\\V = 3408 \pi -units^3[/tex]

Answer:

[tex]\frac{5}{5+2}(3-1)+ 1[/tex]

Step-by-step explanation:

To find the coordinate of the point that divides a line segment AB with point A at ([tex]x_1,y_1[/tex]) and point B at [tex](x_2,y_2)[/tex] in the proportion c:d, the formula used to find the location of the point is:

[tex]x-coordinate:\\\frac{c}{c+d}(x_2-x_1)+x_1 \\\\While \ for\ y-coordinate:\\\frac{c}{c+d}(y_2-y_1)+y_1[/tex]

Therefore the y coordinate that divides line segment CD with point C at ([tex]-4,1[/tex]) and point D at [tex](3,3)[/tex] in the proportion 5:2 is given by:

[tex]for\ y-coordinate:\\\frac{c}{c+d}(y_2-y_1)+y_1\\=\frac{5}{5+2}(3-1)+ 1\\=\frac{5}{7}(2)+1=\frac{17}{7}[/tex]

Answer:

{5/7}(3-1)+1

Step-by-step explanation:

Answer:

f(10) =13

Step-by-step explanation:

f(x) =x/2+8,

Let x = 10

f(10) =10/2+8,

      = 5+8

       = 13

Answer:

x = 9 (first odd number)

x + 2 = 11 (second odd number)

Step-by-step explanation:

Let

x =first odd number

x + 2=second odd number

given:

1/x - 1/(x + 2) = 2/99

Find the LCM

(x+2)-x / x(x+2)=2/99

x+2-x / x(x+2)=2/99

common denominator x( x + 2)

2 / x(x + 2) = 2/99

Take the reciprocal of both sides

1/2x(x + 2) = 99/2

multiply both by 2

x(x +2) = 99

Expand the left side

x^2 + 2x = 99

add 1 to both sides

x^2 + 2x + 1 = 100

express the left side as a square

(x + 1)^2 = 100

Square root of both sides

x + 1 = 10 or x + 1 = -10

taking the positive root only

x = 9 (first odd number)

x + 2 = 11 (second odd number)

check:

1/9 - 1/11 = 2/99

11/99 - 9/99 = 2/99

2/99 = 2/99

Answer:

one half of two fifths of x would be equivalent to one fifth of x

Answer:

Simply create a scatter plot then write in a line of best fit.

Step-by-step explanation:

Answer:

create a scatter plot then write in a line of best fit.

Step-by-step explanation:

Answer: B. False

Step-by-step explanation:

It does not follow the Pythagorean Theorem (a^2 + b^2 = c^2)

The sum of the two legs (shorter sides) squared would have to equal the hypotenuse (longest side) squared in order to form a right triangle.

5^2 = 25

6^2 = 36

25 + 36 = 61

8^2 = 64

61 < 64

Answer:

The perimeter of the triangle ABC is 17 cm.

Step-by-step explanation:

Consider the Isosceles triangle ABC.

The sides CA and CB are equal with measures, 5 cm.

The base angles are assumed to be x° each. Hence, the angle ACB is 2x°.

The altitude CP divides the base AB into two equal halves and the angle ACB is also cut into halves.

Consider the right angled triangle ACP.

The sum of all the angles in a triangle is 180°.

Determine the value of x as follows:

x° + x° + 90° = 180°

2x° = 90°

x° = 45°

Compute the length of side AP as follows:

[tex]cos\ 45^{0}=\frac{AP}{CA}[/tex]

      [tex]\frac{1}{\sqrt{2}}=\frac{AP}{5}[/tex]

     [tex]AP =\frac{5}{\sqrt{2}}\\\\AP=3.5[/tex]

Then the length of side AB is:

AB = AP + PB

     = 3.5 + 3.5

     = 7 cm

The perimeter of triangle ABC is:

Perimeter = AB + CA + CB

                = 7 + 5 + 5

                = 17

Thus, the perimeter of the triangle ABC is 17 cm.

Step-by-step explanation:

The correct answer is the vertical change divided by the horizontal change between two points on a line. We can find the slope of a line on a graph by counting off the rise and the run between two points. If a line rises 4 units for every 1 unit that it runs, the slope is 4 divided by 1, or 4.

Answer:

Calculate the rise over the run/the change in y over the change in x

Step-by-step explanation:

In order to find the rate of change on a graph from a slope, you need to look at how many units up and how many units to the right. Find a solid point on the graph for both the x and y directions. Count how many units go up and how many go right. Divide how many units go up by how many go to the right and that is the rate of change on the graph.

Answer:

Dimensions of the bottle

x (radius of the base ) = 3,99 cm

h (heigh of the bottle ) = 3,99 cm

Surface area  = 149,99 cm²

Volume of the bottle = 199,45 cm³

Step-by-step explanation:

The bottle volume  must be  V(b) = 100 ml     or   V(b) = 100 cm³

The shape of the bottle is cylindrical

Surface area of bottle is

S = surface area of the base + lateral area

Area of the base = π*x ²         where x is radius of circle

Lateral area is  2*π*x*h           where h is the heigh of the bottle

V(b) = π* x²*h                             (1)        

π*x²  +  2*π*x*h  < 150 cm²  we work with the limit  150

π*x²  + 2*π*x*h  = 150

h   =  (150 - π*x²) /2*x*π

Plugging that value in equation (1)

V(x) = π*x² * (150 - π*x²) /2*x*π   ⇒    V(x) = 150*π*x²/2*x*π  - π²*x⁴/2*x*π

V(x) = 75*x - π*x³/2

Taking derivatives on both sides of the equation

V´(x) =  75  - 3*π*x²/2

V´(x) = 0           75 - 3*π*x² /2  = 0

x² = 75*2 /3*π       ⇒   x²  = 15,92      ⇒  x = 3,99 cm

And  h = ( 150 -π*x² )/2*π*x

h = ( 150 - 49,98 )/25,05

h  =  3,99 cm

Dimensions of the bottle

x (radius of the base ) = 3,99 cm

h (heigh of the bottle ) = 3,99 cm

Surface area  = 149,99 cm²

Volume of the bottle = 199,45 cm³

Answer: 27cm²

Step-by-step explanation:

lets take the width as x and length as 3x( since length is 3 times the width)…

Perimeter of the rectangle is 24 cm( 2*(l+b))= 2×(3x+x):24

2×4x=24

8x=24

X( width): 24/8=3cm

Length= 3x: 3*3=9cm

Area of the rectangle: ( l*w)= 9×3: 27cm²

Answer:

Step-by-step explanation:

Answer:

2/6 for$10

Step-by-step explanation:

Answer:

5/6 lbs

Step-by-step explanation:

We can use ratios to solve

1/3 lbs             x lbs

--------------- = ------------

4 dollars           10 dollars

Using cross products

1/3 * 10 = 4x

Divide each side by 4

10/3 * 1/4 = 4x/4

10/12 = x

Simplifying

5/6 =x

Answer:

It should be 50 degrees

Step-by-step explanation:

180-80= 100 degrees

making the two bottom angles combined angles equal to 100 degrees

100 divided by 2= 50 degrees making x=50 degrees

x= 50 degrees

Answer:

50°

Step-by-step explanation:

80+x+x=180

80+2x=180

2x=180-80

2x=100

100/2=50