What is the volume of this rectangular prism?

Answer:

Step-by-step explanation:

i) The union of the two sets is the list of elements that are in either. Duplicates are listed only once.

  U = {1, 2, 3, 4, 5, 10, 11, 12}

  A' = U - A = {10, 11, 12}

  A'∪B' = {10, 11, 12}∪{1, 2, 4} = {1, 2, 4, 10, 11, 12}

__

ii) A has 5 elements, so has 2^5 = 32 subsets, including the empty set and the whole set.

Answer:

No, all of her work is correct.

Step-by-step explanation:

Answer:

No, all of her work is correct.

Step-by-step explanation:

All of her work is correct.

The first step is showing factorization of √50

The second step is simplifying the factorization

The third step is simplifying the entire radical.

When you take a square root of a square, they cancel out, so:

√5² = 5

We multiply it with our leftover √2 and we get:

5√2

Answer:

Step-by-step explanation:

Domain of a function represents the set of x-values (input values) and y-values (output values) of the function represent the Range of the function.

Given function is,

[tex]y=-\frac{2}{3}x+7[/tex]

If Domain (input values) of this function is,

{-12, -6, 3, 15}

Table for the input-output values of this function,

x        -6         3        15       -12

y        11         5         -3        15

Answer:

Step-by-step explanation:

Answer:

20100

Step-by-step explanation:

To find the sum of:

[tex]1 + 2 + 3+ 4+ ...... +200[/tex]

As per the trick of Gauss, let us divide the above terms in two halves.

[tex]1+2+3+4+\ldots+100[/tex] and

[tex]101+102+103+104+\ldots+200[/tex]

Let us re rewrite the above terms by reversing the second sequence of terms.

[tex]1+2+3+4+\ldots+100[/tex]  (it has 100 terms) and

[tex]200+199+198+197+\ldots+101[/tex] (It also has 100 terms)

Adding the corresponding terms (it will also contain 100 terms):

1 + 200 = 201

2 + 199 = 201

3 + 198 = 201

:

:

100 + 101 = 201

The number of terms in each sequence are 100.

So, we have to add 201 for 100 times to get the required sum.

Required sum = 201 + 201 + 201 + 201 + . . . + 201  (100 times)

Required sum = 100 [tex]\times[/tex] 201 = 20100

Answer:

Linear f(x) = 2·x + 3

Quadratic f(x) = x² + 2·x - 3

Exponential f(x) = 3ˣ - 2

Step-by-step explanation:

1) Linear function

The general form of the linear equation is of the form, f(x) = y = m·x + c

Where;

m = The slope

c = y-intercept (Constant)

The linear function is therefore, f(x) = 2·x + 3

2) Quadratic function

The general form of the quadratic function is f(x) = a·x² + b·x + c

Where;

a, and b are the coefficients of x² and x respectively and c is the constant term

Therefore,  f(x) = x² + 2·x - 3, is a quadratic function, with a = 1, b = 2, and c = -3

3) Exponential function

The general form of the exponential function is f(x) = a·bˣ + k

Where;

a = The initial

b = The multiplier (growth or decay value)

k = vertical shift

Therefore, the function f(x) = 3ˣ - 2 is an exponential function with the initial = 1, b= 3, and k = -2

Answer:

Hey there!

20^2+25^2=c^2

400+625=c^2

1025=c^2

Square root 1025 is the correct answer, so option C.

Let me know if this helps :)

Answer: B

Step-by-step explanation:

Answer:

6500 rupees

Step-by-step explanation:

We are given a rectangular garden is the dimensions of:

Length = 400 m

Breadth = 150 m

Perimeter of a rectangle = 2(L + B)

= 2(400 + 150)

= 2(650)

= 1300m

We are told that the cost of fencing a rectangular garden per meter is rupees 5

1 m = 5 rupees

1300m =

Hence, the cost to fence the entire garden = 1300 × 5 rupees

= 6500rupees

Answer: Hi!

First, we will use inverse operations to remove the 7. Subtract 7 on both sides:

7 - 7 = 0

4 - 7 = -3

Our equation now looks like this:

-11b = -3

Now we will use inverse operations to isolate the b. Divide -11 on both sides:

-11b ÷ -11 = b

-3 ÷ -11 = 3/11

Our equation now looks like this:

3/11 = b

3/11 is equal to b. This is your answer!

Hope this helps!

Answer:

x=2

y=3

Step-by-step explanation:

x/2+y/3=2   so      

3x/6+2y/6=12/6

then multiply by 6

3x+2y=12    

equation number 2

x/3+y/2=13/6

2x/6+3y/6=13/6

multiply by 6

2x+3y=13

so the system is now

3x+2y=12  

2x+3y=13

from the first equation 2y=12-3x,  y=6 -  3x/2

then put  y in  the second equation

2x+3*(6-3x/2)=13

2x+18-9x/2=13

2x-9x/2=13-18

4x/2-9x/2=-5

-5x/2=-5

*(-1/5)    *(-1/5)

x/2=1

*2    *2

x=2

so y=6-3*2/2=6-3

y=3

Step-by-step explanation:

Given that:

(1/2x)+(1/3y) = 2 --------(1)

(1/3x)+(1/2y) = 13/6-----(2)

Put 1/x = a and 1/y = b then

(1) becomes

(a/2 )+( b/3) = 2

⇛ (3a+2b)/6 = 2

⇛ 3a+2b = 2×6

⇛ 3a+2b = 12 --------(3)

(2) becomes

(a/3)+(b/2)=13/6

⇛ (2a+3b)/6 = 13/6

⇛ 2a+3b=13----------(4)

On adding (3)&(4) then

3a+2b=12

2a+3b=13

(+)

_________

5a+5b = 25

_________

⇛ 5a+5b = 25

⇛ 5(a+b)=25

⇛ a+b=25/5

⇛ a+b=5 -------------(5)

On subtracting (3) from (4)

2a+3b=13

3a+2b=12

(-)

_________

-a+b = 1

_________

⇛ -a+b = 1

⇛ b = 1+a --------(6)

On Substituting the value of b in (5) then

a+1+a = 5

⇛2a+1 = 5

⇛ 2a = 5-1

⇛ 2a = 4

⇛ a = 4/2

⇛ a = 2

On Substituting the value of a in (6) then

b = 1+2

b = 3

Now,

a = 2

⇛ 1/x=2

⇛ “x” = 1/2

and

b= 3

⇛ 1/y = 3

⇛“y” = 1/3

Answer:- Hence, the value of x and y with be 1/2 and 1/3 respectively.

The solution for the given problem is (1/2,1/3)

Check:-

If x = 1/2 and y = 1/3 then

LHS = (1/2x)+(1/3y)

= 1/2(1/2)+1/3(1/3)

= 1/(2/2)+1/(3/3)

= (1/1)+(1/1)

= 1+1

=2

= RHS

LHS=RHS is true

and

LHS=(1/3x)+(1/2y)

⇛ 1/3(1/2)+ 1/2(1/3)

⇛ 1/(3/2)+1/(2/3)

⇛ (2/3)+(3/2)

⇛ (4+9)/6

⇛ 13/6

⇛ RHS

LHS = RHS is true

also read similar questions: Simultaneous equations: 1. 2x+2y=10 X+2y=6 2. 3x+y=18 2x+y=13 3. X+y=1 X-y=5 4. 3x+4y=29 X-4y=-17 5. 4c+3y=11 2x+y=7

https://brainly.com/question/12286263?referrer

Answer:

when two inscribed angles in one circle both equal 75°, the two angles must intercept the same arc that measures 75°.

Step-by-step Explanation:

The relationship between an intercepted arc and an inscribed angle is given as:

the measure of the intercepted arc = twice the inscribed angle that intercepts it.

Also, by virtue of this, when two inscribed angles intercepts the same arc, both inscribed angles are said to be congruent. And the measure of both angles equal the measure of the arc they both intercept.

Therefore, if the measure of an arc, that is intercepted by 2 inscribed angles, is given as 75°, both inscribed angles equal 75° as well. Thus, each of the inscribed angles is half the measure of the intercepted arc.

Therefore, the statement that is true about inscribed angles is: "when two inscribed angles in one circle both equal 75°, the two angles must intercept the same arc that measures 75°."

Answer:

The order from least to greatest is B, A, C

Step-by-step explanation:

Given

Recipe A = 3 bananas to 12 Muffins

Recipe B = 5 bananas to 24 Muffins

Recipe C = 11 bananas to 48 Muffins

Required

Order the recipe from least to greatest

To solve this, we have to divide the number of bananas by number of muffins; this will give the unit banana per muffin

Recipe A: 3 bananas to 12 Muffins

[tex]A = \frac{3}{12}[/tex]

[tex]A = 0.25[/tex]

Recipe B: 5 bananas to 24 Muffins

[tex]B = \frac{5}{24}[/tex]

[tex]B = 0.2083[/tex]

Recipe C: 11 bananas to 48 Muffins

[tex]C = \frac{11}{48}[/tex]

[tex]C = 0.229167[/tex]

By comparison;

Recipe B (0.2083) is the smallest; followed by Recipe C (0.229167) then Recipe A (0.25)

Hence; the order from least to greatest is B, A, C

Answer:

its BCA

Step-by-step explanation:

Answer:

10 centimeters.

Step-by-step explanation:

First, we need to remember what's the formula to get the volume of a rectangular solid and a cube.

The volume of the first equals:

Volume = Length x Width x Height

While the volume of the cube is:

[tex]Volume = a^{3}[/tex] where a is the edge.

We are given the measures of the rectangular solid so we can calculate its volume:

[tex]Volume= (20)(5)(10)=1000[/tex] cubic cms.

Now, we know that  both the volume of the rectangular solid and the cube are the same so we will use this information to calculate the edge of the cube.

[tex]1000=a^3 \\\sqrt[3]{1000} =\sqrt[3]{a^3} \\10=a[/tex]

Thus the length of an edge of the cube is 10 centimeters

Answer:

(a) 283 days

(b) 248 days

Step-by-step explanation:

The complete question is:

The pregnancy length in days for a population of new mothers can be approximated by a normal distribution with a mean of 268 days and a standard deviation of 12 days. ​(a) What is the minimum pregnancy length that can be in the top 11​% of pregnancy​ lengths? ​(b) What is the maximum pregnancy length that can be in the bottom ​5% of pregnancy​ lengths?

Solution:

The random variable X can be defined as the pregnancy length in days.

Then, from the provided information [tex]X\sim N(\mu=268, \sigma^{2}=12^{2})[/tex].

(a)

The minimum pregnancy length that can be in the top 11​% of pregnancy​ lengths implies that:

P (X > x) = 0.11

⇒ P (Z > z) = 0.11

⇒ z = 1.23

Compute the value of x as follows:

[tex]z=\frac{x-\mu}{\sigma}\\\\1.23=\frac{x-268}{12}\\\\x=268+(12\times 1.23)\\\\x=282.76\\\\x\approx 283[/tex]

Thus, the minimum pregnancy length that can be in the top 11​% of pregnancy​ lengths is 283 days.

(b)

The maximum pregnancy length that can be in the bottom ​5% of pregnancy​ lengths implies that:

P (X < x) = 0.05

⇒ P (Z < z) = 0.05

⇒ z = -1.645

Compute the value of x as follows:

[tex]z=\frac{x-\mu}{\sigma}\\\\-1.645=\frac{x-268}{12}\\\\x=268-(12\times 1.645)\\\\x=248.26\\\\x\approx 248[/tex]

Thus, the maximum pregnancy length that can be in the bottom ​5% of pregnancy​ lengths is 248 days.

Answer:

$38

Step-by-step explanation:

cost of ticket for adult = $22

cost of ticket for youngster = $16

______________________________

cost of ticket for John's mom = $22 as she is adult

cost of ticket for john = $16 as he is young , his age is less than 18 years

Total cost of ticket for John and his mother = $22 + $16 = $38

Answer:

11

Step-by-step explanation:

4=1

14=2

24=3

34=4

40=5

41=6

42=7

43=8

44=9

45=10

46=11

You will encounter 11 4s.

Answer:

3 - b=12

4- b=14.1

Step-by-step explanation:

Area of the bookshelf=864 square inches

the book shelf is a rectangular prism

if we have height=4b, width=3b, length=b

then the area=length * width

A=(l*w)*2 ( we have 2 shelves)

864=(b*3b)*2

864=6b²

b²=864/6=144

b=√144= 12 inches

4- to cover the sides :

(height * length)*2   ( we have 2 sides)

(4b*b)×2=1600

8b²=1600

b²=1600/8=200

b=√200=14.1

Answer:

Question #3:  b = 12 in

Question #4:  b = 14.1 in

Step-by-step explanation:

Please see in the image attached the actual proportions that the furniture manufacturer uses to build the furniture in question:

Height = 4 b

Width = 3 b

Depth = b

So for question #3, given that the customer wants a total surface of the shaded shelves to be 864 [tex]in^2[/tex]

we can write that one wants twice the area of each rectangle of width 3 b and depth b to total 864:

[tex]2\,(3b\,*\,b)=864\\6 b^2=864\\b^2=864/6\\b^2=144\\b=12\,\,in[/tex]

Question # 4:

The total lateral surface to be covered by the silk is 1600 [tex]in^2[/tex], therefore if we consider the surface of each lateral plank as:

Area of each lateral plank :

[tex](4b)\,(b) = 4\,b^2[/tex]

Then twice these is: [tex]8\, b^2[/tex]

So we can solve for be requesting that these total surface equal the amount of silk:

[tex]8\,b^2=1600\\b^2=1600/8\\b^2=200\\b=\sqrt{200} \\b\approx 14.1421\,\,in[/tex]

which rounded to the nearest tenth of an inch gives:

[tex]b\approx 14.1\,\,in[/tex]

Answer:

0

Step-by-step explanation:

Hello, do you agree that 25 * 2 = 50 ?

So, we can write that [tex]50 = 25 * \boxed{2} + \boxed{0}[/tex]

the remainder is 0.

Thank you

Answer:

number 4 on edge

Step-by-step explanation:

Answer:

a. 92 minutes b. 7:56am

Step-by-step explanation:

He should leave at 7:56 so he gets to the bus at 8:05,

he gets to Coventry at 9:37 with enough time to walk 12 minutes to get to work before 10am.

false. range of [tex] \cos^{-1}(x)[/tex] is $[0,\pi]$

Answer:

TI-Nspire models automatically detect most points of interest such as x and y-intercepts, maximum values, and minimum values when you are in trace mode. TI-84 Plus models require you to use a series of left and right bounds and guesses to find those same values.

Answer:

$200

Step-by-step explanation:

We know that she already has $20. And we know that every week, for three weeks she gets $10.

20+3(10)+150=m

We add all of this up, and we find that at the end of 3 weeks Sarah has $200 saved.

Answer:

Pregunta 1: Opcion D. 8

Pregunta 2: Opción A. 19 (aunque lo correcto es decir que son 20)

Pregunta 3: 28 años (no está como opción)

Pregunta 4: Opción D. 1/3

Step-by-step explanation:

Las fracciones irreductibles son aquellas que después de dividirlas por un común divisor, una vez que no se pueden dividir más se dice que son irreducibles, por lo tanto no existe ningún número que sea divisor común del numerador y del denominador más que 1.

Fracciones irreductibles con común denominador 24.

Como máximo divisor tenemos el 24 y como mínimo el 1

entre 1/24 y 1 estarán nuestras fracciones o sea:

1/24 < x/24 < 1. Ahora convertimos el 1 en fracción de 24, lo que sería 24/24 para igualar el numerador en ambos lados de la ecuación, para poder determinar x

1/24 < x/24 < 24/24

Como vemos que x tiene que estar entre 1 y 24, las respuestas serán:

2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22 y 23

Eliminamos los números divisores de 24, aquellos pares, y nos focalizamos en los que no podriamos dividir por nada con 24, o sea los números primos

5, 7, 11, 13, 17, 19, 23. Como nos falta el 1, obtenemos un total de 8 fracciones: 1/24, 5/24, 7/24, 11/24, 13/24, 17/24, 19/24, 23/24

Mismo procedimiento para el 25:

1/25 es una de las fracciones irreductibles. Pensamos en los valores de x

1/25 < x/25 < 25/25

2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25

Los números divisibles por 25, son los multiplos de 5, asi que esas respuestas no irían. Las fracciones irreductibles son:

1/25, 2/25, 3/25, 4/25, 6/25, 7/25, 8/25, 9/25, 11/25, 12/25, 13/25, 14/25, 16/25, 17/25, 18/25, 19/25, 21/25, 22/25, 23/25 y 24/25 haciendo un total de

20. Por alguna razón está mal formulada la pregunta, son 20 pero no está como opción y como te piden fraccion impropia (numerador > denominador), contamos a partir de 26. FIjate que hasta el proximo entero que sería 50/25, también son 20 fracciones (irreductibles e impropias)

26/25, 27/25, 28/25, 29/25, 31/25, 32/25, 33/25, 34/25, 36/25, 37/25, 38/25, 39/25, 41/25, 42/25, 43/25, 44/25, 46/25, 47/25, 48/25, 49/25

Próxima pregunta:

Miguel tiene 4/5 de la edad de la novia, y ambas edades suman 63.

Plantiemos la siguiente ecuacion donde x es la edad de la novia

4/5x + x = 63

9/5x = 63

x = 63 . 5/9 (como 9/5 pasa al otro lado de la igualdad dividiendo, damos vuelta la fraccion multiplicandola)

x = 35

Si la novia tiene 35 años y la edad de Miguel es 4/5 de esa edad

4/5 .35 = (35 .4) /5 = 28

Es raro porque no está la respuesta como tal.

Próxima pregunta:

Al ser las 8 am, quiere decir que han pasado 8 horas de que empezó el día

y el día tiene 24 horas.

8 horas transcurridas / 24 horas totales = 1/3

Answer:

13

Step-by-step explanation:

Basically, we have to plug in 4 for r into g(r). Doing so gives us g(4) = 25 - 3 * 4 = 25 - 12 = 13.

Some more examples:

g(6) = 25 - 3 * 6 = 25 - 18 = 7

g(1) = 25 - 3 * 1 = 25 - 3 = 22

Answer:g(4)=13

Step-by-step explanation:

g(4)=25-3r

25-3(4)

25-12

g(4)=13

Answer:

Step-by-step explanation:

Yes you can just write them with denominator 1,

So 3 = 3/1 and -6 = -6/1.

Answer:

Yes.

Step-by-step explanation:

ALL real numbers can be written as fractions, and since integers fall under the category of real numbers, it is official that they can be written as fractions.

I am joyous to assist you at any time.

Answer:

see below

Step-by-step explanation:

4.2 x 10^6 − 1.2 x 10^5 − 2.5 x 10^5

All exponent have to have the same number

42 x 10^5 − 1.2 x 10^5 − 2.5 x 10^5

Subtract the number

42 - 1.2 - 2.5 = 38.3

Add back the exponent

38.3 * 10 ^5

This is not in scientific notation

Move the decimal one place to the left and add one to the exponent

3.83 * 10^6

3.3 x 10^9 + 2.6 x 10^9 + 7.7 x 10^8

All exponent have to have the same number

3.3 x 10^9 + 2.6 x 10^9 + .77 x 10^9

Add the numbers

3.3+2.6+.77 =6.67

Add back the exponent

6.67*10^9

This is in scientific notation

8.0 x 10^4 − 3.4 x 10^4 − 1.2 x 10^3

All exponent have to have the same number

8.0 x 10^4 − 3.4 x 10^4 − .12 x 10^4

Subtract

8.0 - 3.4 - .12 = 4.48

Add back the exponent

4.48* 10^4

This is in scientific notation

Answer:

F = -16

Step-by-step explanation:

F/4-5=-9

Add 5 to each side

F/4-5+5=-9+5

F/4=-4

Multiply each side by 4

F/4 *4=-4*4

F = -16

Answer:

[tex]\boxed{4 units}[/tex]

Step-by-step explanation:

Hey there!

Well if the base is 4 and we use the formula,

b*h / 2

4*4 = 16

16/2 = 8

So x is 4.

Hope this helps :)

Answer:

Step-by-step explanation:

Area of a triangle is given by

base × height

[tex] A = \frac{1}{2} base × height[/tex]

From the question

Area = 4 units²

height = 4 units

let x represent the base

We have

[tex]4 = \frac{1}{2} \times x \times 4[/tex]

4 = 2x

Divide both sides by 2

Hope this helps you

Answer:

196.496

Step-by-step explanation:

0.152x726+0.128x673

110.352+86.144

=196.496

Answer:

1.) 10044

2.) 100.44

Step-by-step explanation:

Since n is a number of five-digit positive integers which are divisible by 36, start multiplying 36 by number. Starting from 278.

Five digits numbers start from multiplying 36 by 278. Any multiplication below 278 by 36 will give four digits numbers.

36 × 278 = 10,008

36 × 279 = 10,044

10,044 tens digit and unit digit equal. Therefore n = 10044

To find n/100, divide 10044 by 100

10044 / 100 = 100.44

Problem 1

a^2+b^2 = 25^2+20^2 = 225+400 = 625

c^2 = 25^2 = 625

We get the same output of 625.

This shows that a^2+b^2 = c^2 is true for (a,b,c) = (15,20,25). We have a pythagorean triple and this is a right triangle. This is also scalene as all three sides are different lengths.

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

Problem 2

a^2+b^2 = 3^2+3^2 = 18

while c^2 = 1^2 = 1

So a^2+b^2 = c^2 is not a true equation for this a,b,c set of values. We do not have a right triangle. Instead we have an acute triangle based on these rules below

We see that we have the form a^2+b^2 > c^2 since 18 > 1.

This acute triangle is also isosceles because a = b.

Answer:

Triangle A is a scalene triangle.

Triangle B is an isosceles triangle

Exaplanation for the 1st Answer:

A scalene triangle is a triangle whose all side lengths are different.

Triangle A has the side lengths are 15, 20, 25. All these lengths are different, so this is a scalene triangle.

Explanation for the 2nd Answer:

An isosceles triangle has 2 sides lengths the same and the other side length different. Triangle B has side lengths of 3, 3, 1. Two side lengths are same, but 1 side length is different. So, this is an isosceles triangle.