determine (a) the volume and (b) the surface area of the three-dimensional figure. when appropriate, use the pi key on your calculator.

a) the volume is _____
b) the surface area is ____

Answer:

a

Step-by-step explanation:

Answer:

370 mm²

Step-by-step explanation:

The area of this figure can be calculated by taking the whole figure as a full rectangle, and consider the part that is cut out from the middle of the shape as another rectangle.

Find the area of the cut-out part and subtract from the area of the full rectangular shape to get the area of the composite figure.

=>Area of full rectangular shape:

Length = 30 mm

Width = 15 mm

Area = L * B = 30*15 = 450 mm²

=>Area of the cut-out Rectangle part:

Length = 10 mm

Width = 8 mm

Area = 10*8 = 80 mm²

=>Area of composite figure = 450 mm² - 80 mm² = 370 mm²

Answer: 32 copies of hardcover version.

Step-by-step explanation: Suppose the quantity of hardcover version copies sold is H and the paperback copies is P.

1) A store sells a total of 70 copies:

H + P = 70

2) One hardcover is sold for $15 and one paperback for $11.50. In one month was charged $917:

15H + 11.5P = 917

Solving the system of equations:

H + P = 70 (I)

15H + 11.5P = 917 (II)

Since it is asked for the hardcover version, find H.

Multiply equation (I) by -11.5:

-11.5H - 11.5P = - 805 (III)

Add (II) and (III):

-11.5H - 11.5P = - 805

  15H + 11.5P = 917

  3.5H            = 112

H = 32

In one month, it was sold 32 hardcover version of a book.

Answer:

m=0.5

Step-by-step explanation:

Copy the equation.

3.6m-2.7=-1.8m

Subtract 3.6m from both sides.

-2.7=-5.4m

Divide by -5.4 on both sides.

0.5

Answer:

The 500th term is 3,517

Step-by-step explanation:

Here in this question, we are given an explicit formula to calculate the 500th term of the sequence

The formula to use is ;

a + (n-1)d

where a refers to the first term which is 24 in this case, while d is the common difference which is the difference between success terms and that is 52-45 = 45-38 = 7 and finally n is 500

Now we make a substitution into the formula and we have

24 + (500-1)7

= 24 + (499)7

= 24 + 3493 = 3,517

Answer:

Below

Step-by-step explanation:

Let x be that missing number

One third of it is x/3

One-ninth of it is x/9

Multiply x/3 and x/9

● (x/3)*(x/9) = (x^2/27)

● (x^2/27) = 108

Multiply both sides by 27

● (x^2/27)*27 = 108*27

● x^2 = 2916

● x = √(2,916) or x = -√(2,916)

● x = 54 or x = -54

So there are two possibilities 54 and -54.

a1/3×1/9=!08

if you multiply you should get 1/27a=108

in order to let a alone multiply both sides by 27

and now your a which is unknown will equal 2916.

Answer:

? = 33

Step-by-step explanation:

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

tan ? = opp / adj

tan ? = 13/20

Take the inverse tan of each side

tan ^-1 tan ? = tan ^-1 ( 13/20)

? = 33.02386756

To the nearest degree

? = 33

Answer:

33.

Step-by-step explanation:

inverse tan (13/20) = 33.023867579302

Answer:

a) 10x - 14y = -4

Step-by-step explanation:

Two equations linear dependent if you can write one as a multiple of the other. It means that the equation that is a linear dependent with -5x+7y=2 is:

10x - 14y = -4

Because it can be written as:

-2(-5x+7y) = -2(2)

So, this equation is equivalent to -5x + 7y = 2

Answer:

36

Step-by-step explanation:

9/5 = z/20

First, we have to divide what we know

9/5 = 1.8

1.8 = z/20

Next, we have to multiply both sides of the equation by 20 to cancel out the division sign

1.8•20 = z/20•20

36 = z

Answer:

6x + 2(−2x + 1) = 22

Step-by-step explanation:

Answer: The answer is 6x + 2(−2x + 1) = 22

triangle is the best answer

Answer:

Step-by-step explanation:

Answer:

-5

Step-by-step explanation:

Given the two box plots showing the number of seconds the students completes the 50-meter-dash race before and after the program, we are to determine the difference between the median value of seconds before and after the program.

Median in a box plot is represented by the vertical line that divides the rectangular box in a box plot.

Thus, the median before the program = 15 seconds

The Median after the program = 10 seconds

The median change = 10 - 15 = -5 seconds.

This means, after the program, most of the students now finish the 50-meter-dash faster, about 5 seconds less the former seconds used before the program.

Answer:

-5

Step-by-step explanation:

i did it on Imagine Math and i got it correct!

Answer:

C

Step-by-step explanation:

This is because it has a constant rate of change.

5 x 1.5 = 7.5

6 x 1.5 = 9

7 x 1.5 = 10.5

You can find this image by dividing y by x and testing this rate of change on the other y values. Thus C is correct.

Answer:

3 [tex]\pm[/tex] [tex]\sqrt{5}[/tex].

Step-by-step explanation:

x^2 = 6x - 4

x^2 - 6x + 4 = 0

Now, we can use the quadratic formula to solve.

[tex]\frac{-b\pm\sqrt{b^2 - 4ac} }{2a}[/tex], where a = 1, b = -6, and c = 4.

[tex]\frac{-(-6)\pm\sqrt{(-6)^2 - 4 * 1 * 4} }{2 * 1}[/tex]

= [tex]\frac{6\pm\sqrt{36 - 4 * 4} }{2}[/tex]

= [tex]\frac{6\pm\sqrt{36 - 16} }{2}[/tex]

= [tex]\frac{6\pm\sqrt{20} }{2}[/tex]

= [tex]\frac{6\pm2\sqrt{5} }{2}[/tex]

= 3 [tex]\pm[/tex] [tex]\sqrt{5}[/tex]

x = 3 [tex]\pm[/tex] [tex]\sqrt{5}[/tex].

Hope this helps!

Answer:

The last choice (3,2), because both lines pass through this point.

Step-by-step explanation:

For a point to be a solution to a system of linear equations, both equation's lines have to pass through that same point.

Answer: (3, 2), because both lines pass through this point

Step-by-stepexplanation:

This can be solved by substitution. The graph will show the same result.

Answer:

[tex]\boxed{ x = 23}[/tex]

Step-by-step explanation:

=> x - 15 = 8

Adding 15 to both sides

=> x - 15 + 15 = 8 + 15

=> x = 23

Answer:

A. x = 23

Step-by-step explanation:

Step 1: Write out equation

x - 15 = 8

Step 2: Add 15 to both sides (Addition Equality)

x - 15 + 15 = 8 + 15

x = 23

Answer:

9

Step-by-step explanation:

3 times the sum of 4 and 2 = 3*(4+2)

                                            = 3 * 6

                                           = 18

18 - 9 = 9

Answer: A. 51%

Step-by-step explanation:

Area of circle = [tex]\pi r^2[/tex] , where r = radius of the circle.

In the figure below, we have the complete question.

According to that,

Radius of outer circle = 7ft

Radius of inner circle = 5ft

The probability that the thumbtack will be placed on the inner circle

[tex]=\dfrac{\text{Area of inner circle}}{\text{Area of outer circle}}\\\\=\dfrac{\pi (5)^2}{\pi (7)^2}\\\\=\dfrac{25}{49}[/tex][π is canceled from numerator and denominator

in percent, [tex]\dfrac{25}{49}\times100=51.0204081633\%\approx51\%[/tex]

So, the probability that the thumbtack will be placed on the inner circle = 51%

Hence, the correct option is A. 51%.

The correlation coefficient r is always between -1 and 1, inclusive of both endpoints. We can write [tex]-1 \le r \le 1[/tex]

If r = 0, then we have no linear correlation at all. If r = 1, then we have perfect positive correlation. If r = -1, then we have perfect negative correlation.

We see that r = 0.9 is close to r = 1, so we have strong positive linear correlation going on here.

Answer:

4.5%

Step-by-step explanation:

Simple interest:

I = Prt

112.5 = 1250(r)(2)

1250r = 56.25

r = 0.045 = 4.5%

Answer: 4.5%

Answer:

Area of the composite figure = 75.25 cm²

Step-by-step explanation:

Question (4). Given figure is a composite figure having,

(1). Right triangle STU

(2). A kite PSUV

(3). A trapezoid PQRS

Now we will calculate the area of each figure.

(1). Area of the right triangle = [tex]\frac{1}{2}(\text{ST})(\text{TU})[/tex]

                                              = [tex]\frac{1}{2}(3.5)(3)[/tex]

                                              = 5.25 cm²

(2). Area of the kite PSUV = [tex]\frac{1}{2}(\text{Diagonal 1})(\text{Diagonal 2})[/tex]

                                           = [tex]\frac{1}{2}(\text{PU})(\text{SV})[/tex]

                                           = [tex]\frac{1}{2}(\text{TS+RQ})(\text{SV})[/tex]

                                           = [tex]\frac{1}{2}(3.5+7)(6)[/tex] [Since SV = 2 × 3 = 6 cm]

                                           = [tex]3\times 10.5[/tex]

                                           = 31.5 cm²

(3). Area of the trapezium = [tex]\frac{1}{2}(b_1+b_2)(h)[/tex] [Where [tex]b_1[/tex] and [tex]b_2[/tex] are the bases and h is the distance between the bases]

                                           = [tex]\frac{1}{2}[(7-3)+7](7)[/tex]

                                           = [tex]\frac{77}{2}[/tex]

                                           = 38.5 cm²

Total area of the given figure = 5.25 + 31.5 + 38.5

                                                 = 75.25 cm²

Step-by-step explanation:

An arithmetic sequence is given by relation as follows :

[tex]A(n)=-6+(n-1)\dfrac{1}{5}[/tex]

For the first term, put n = 1. So,

[tex]A(1)=-6+(1-1)\dfrac{1}{5}\\\\A(1)=-6[/tex]

For fourth term, put n = 4. So,

[tex]A(4)=-6+(4-1)\dfrac{1}{5}\\\\A(4)=\dfrac{-27}{5}\\\\A(4)=-5\dfrac{2}{5}[/tex]

For tenth term, put n = 10. So,

[tex]A(10)=-6+(10-1)\dfrac{1}{5}\\\\A(10)=-6+\dfrac{9}{5}\\\\A(10)=\dfrac{-21}{5}\\\\A(10)=-4\dfrac{1}{5}[/tex]

Hence, the correct option is (C).

Answer:

the answer in C)-6, -5 2/5, -4 1/5

[tex]x^2-2x+20=0\implies D=b^2-4ac<0\implies x_1,x_2\notin\mathbb{R}[/tex].

There are no real solutions to the quadratic equation.

Hope this helps.

Answer:

12

Step-by-step explanation:

Answer:

(7x^3+2y^3)(2x^3−7y^3)

Answer:

D is correct one

Step-by-step explanation:

The pattern consists of repeating 4 faces

1000 is fully divisible by 4

The 1000th face ends the pattern of 4

The next, 1001th one is the very first face

Correct choice is D

Answer:

The correct option is;

Both spreads are best described by the standard deviation

Step-by-step explanation:

The given information are;

,                                    College                       High School

High,                              20                               20

Low,                                6                                 3

Q₁,                                   8                                 5.5

Q₃,                                  18                                16

IQR,                                 10                                10.5

Median,                           14                                11

Mean,                              13.3                             11

σ,                                      5.2                             5.4

Checking for outliers, we have

College

Q₁ - 1.5×IQR gives 8 - 1.5×10 = -7

Q₃ + 1.5×IQR gives 18 + 1.5×10 = 33

For high school

Q₁ - 1.5×IQR gives 5.5 - 1.5×10.5 = -10.25

Q₃ + 1.5×IQR gives 16 + 1.5×10.5 = 31.75

Therefore, there are no outliers and the data is representative of the population

From the data, for the college students, it is observed that the difference between the mean, 13.3 and Q₁, 8, and between Q₃, 18 and the mean,13.3 is approximately the standard deviation, σ, 5.2

The difference between the low and the high is also approximately 3 standard deviations

Therefore the college spread is best described by the standard deviation

Similarly for the high school students, the IQR is approximately two standard deviations, the  difference between the mean, 11 and Q₁, 5.5, and between Q₃, 16 and the mean,11 is approximately the standard deviation, σ, 5.4

Therefore the high school spread is also best described by the standard deviation.

Answer:

Both spreads are best described by the standard deviation

Step-by-step explanation:

Answer:

A.

Step-by-step explanation:

Answer:

(x + 9) (x - 7)

Step-by-step explanation:

when we put x + 9 = 0 then x = -9 as it's the root of the fuction.

same thing here: x - 7 = 0 then x = 7

Answer:

x = -4/5 and x = 3/5.

Step-by-step explanation:

The coefficient of x^2 is 25, which is 5 * 5. 5 * -3 = -15, and 5 * 4 = 20. 20 - 15 = 5.

So...

25x^2 + 5x - 12 = 0

(5x + 4)(5x - 3) = 0

5x + 4 = 0

5x = -4

x = -4/5

5x - 3 = 0

5x = 3

x = 3/5

So, x = -4/5 and x = 3/5.

Hope this helps!