What is the volume of the following rectangular prism?

The value of the shortest of the four side lengths of the quadrilateral is 30 cm

The perimeter of a quadrilateral is the sum of all the sides.

Perimeter of the Quadrilateral = 132 centimeters

Let

The shortest side = x

Since, the sides are consecutive even integers;

Second side = (x + 2)

Third side = (x + 4)

Fourth side = (x + 6)

Perimeter of the Quadrilateral = shortest side + Second side + Third side + Fourth side

132 = x + (x + 2) + (x + 4) + (x + 6)

132 = x + x + 2 + x + 4 + x + 6

132 = 4x + 12

132 - 12 = 4x

120 = 4x

divide both sides by 4

x = 120/4

x = 30 centimeters

Therefore,

Second side = (x + 2)

= 30 + 2

= 32 cm

Third side = (x + 4)

= 30 + 4

= 34 cm

Fourth side = (x + 6)

= 30 + 6

=36 cm

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Answer:

Step-by-step explanation:

25×80%=20

so she need to get 20 questions right

Answer:

20

Step-by-step explanation:

total question: 25

marks need to pass: 80%

25-20% = 20

Step-by-step explanation:

[tex]3 : 12 \equiv \frac{3}{12} \equiv 1 : 4[/tex]

[tex] \frac{3}{5} \equiv3 : 5[/tex]

[tex]108 : 9 \equiv \frac{108}{9} \equiv12 : 1[/tex]

Answer:$ 1341.99

Step-by-step explanation: Hope its helps

Answer:

y=4x+26

Step-by-step explanation:

x intercept =( [tex]\frac{- 13}{2} \\[/tex], 0)

y intercept = (0,26)

Answer:

A. 3/4 or .75

B.  5/6 or .83333

C. 11/12 or .91667

D. 1/20 or .05

Step-by-step explanation:

A. 1/2 + 1/4 = 3/4 or .75

B. 1/2 + 1/3 = 5/6 or .83333

a. 1/4 + 2/3 = 11/12 or .91667

b. 1/4 - 1/6 = 1/20 or .05

Answer:

Axis of symmetry= 3

Step-by-step explanation:

f(x)= 2x^2 +12x-4

f(x)=ax^2+bx+c

x=12/2(2)

x=3

f(x)= 2(3)^2+12(3)-14

f(x)= 2(9)+36-14

f(x)=18+36-14

f(x)= 54-14

y=40

Answer:

Mean: 16.333333333333

Median: 18.5

Mode: 9,10,18,19,20,22

Step-by-step explanation:

Mean: Add all the terms together and divide your result by the amount of you there are. ((22+9+10+19+18+20) / 6)

Median- Organize the terms from least to greatest. When you find the middle of the terms you will get 18.5, look for what between 18 and 19.

Mode- Normally to find the mode you would order the terms from least to greatest, and then find which term occurs the most. But since all the terms occur once, it will be all of the terms.

Answer:

Step-by-step explanation:

In 12 hours, the train will travel 487.5 miles

8/325=40.625

40.625 x 12 = 487.5

Submarine must descend 17 feet in the 5th minute.

What is the average of the data?

Only numerical variables, whether continuous or discrete, can be used to calculate the mean. It is calculated by merely dividing the total number of values in a data set by the sum of all the values in the data set. A frequency table of data or raw data can both be used for the calculation.

Let the distance descended by submarine in 5th minute = x feet

Average distance descended by the submarine

= (Total distance distended/ Duration or time)

= (6 + 8 + 14 + 15 + x) / 5

= (43 + x) / 5

Statement given in the question → "Submarine must descend at an average rate of at least 12 feet per minute"

So the inequality for the statement will be,

(43 + x) / 5 ≥ 12

43 + x ≥ 60

x ≥ 17

Therefore, submarine must descend 17 feet in the 5th minute.

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Answer:

5) 1: 63

  2: 117

  3: 63

  4: 117

  5: 63

  6: 117

  7: 63

  8: 117

Step-by-step explanation:

The length of the hypotenuse will be 5√2 = 7.07

The triangle specified in the question is right-angled, one angle is mentioned to be 90°. It is also an isosceles triangle since both other angles are equal. if both angles are equal, both sides will also be equal.

So the length of both equal sides = 5 cm

Pythagoras' theorem tells us about the relationship between the three sides of a right-angled triangle. It states that the square of the hypotenuse of the right-angled triangle will be equal to the sum of squares of the other two sides. If a, b, and c are the sides

 c² = a²+ b²

  c = √(a²+b²)

According to Pythagoras' theorem, Hypotenuse = √base²+ alt²

                                                          Hypotenuse = √5²+5²

                                                                                = 5√2

                                                                               = 7.07 cm

So the length of the hypotenuse is 5√2 = 7.07 cm.

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Given:

A card is selected randomly from a standard deck of 52 cards.

To find:

The probability of each outcome.

a. a king of heart

b. a queen of spades

c. an ace of flower

d. an ace of diamond​

Solution:

In a standard deck of 52 cards.

Total number of cards = 52

13 cards of each suit (heart, diamond, club, spade).

13 cards are Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King.

a. We need to find the probability of getting a king of heart.

Number of king of heart = 1

[tex]P(\text{a king of heart})=\dfrac{\text{Number of king of heart}}{\text{Total cards}}[/tex]

[tex]P(\text{a king of heart})=\dfrac{1}{52}[/tex]

b. We need to find the probability of getting a queen of spades.

Number of queen of spades = 1

[tex]P(\text{a queen of spades})=\dfrac{\text{Number of queen of spades}}{\text{Total cards}}[/tex]

[tex]P(\text{a queen of spades})=\dfrac{1}{52}[/tex]

c. We need to find the probability of getting an ace of flower (spades).

Number of ace of flower = 1

[tex]P(\text{an ace of flower})=\dfrac{\text{Number of ace of flower}}{\text{Total cards}}[/tex]

[tex]P(\text{an ace of flower})=\dfrac{1}{52}[/tex]

d. We need to find the probability of getting an ace of diamond​.

Number of ace of diamond​ = 1

[tex]P(\text{an ace of diamond​})=\dfrac{\text{Number of ace of diamond​}}{\text{Total cards}}[/tex]

[tex]P(\text{an ace of diamond​})=\dfrac{1}{52}[/tex]

Therefore, the required probabilities for each parts are:

(a) [tex]\dfrac{1}{52}[/tex]

(b) [tex]\dfrac{1}{52}[/tex]

(c) [tex]\dfrac{1}{52}[/tex]

(d) [tex]\dfrac{1}{52}[/tex]

The probabilities for each of the given selections are;

A) 1/52

B) 1/52

C) 1/52

D) 1/52

A) Since total number of cards in the deck is 52 and there is only one king of heart, then;

Probability of selecting a king of heart = 1/52

B) Since total number of cards in the deck is 52 and there is only one queen of spades, then;

Probability of selecting a queen of spade = 1/52

C) Since total number of cards in the deck is 52 and there is only one ace of flower, then;

Probability of selecting an ace flower = 1/52

D) Since total number of cards in the deck is 52 and there is only one ace of diamond, then;

Probability of selecting am ace of diamond = 1/52

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The values of a, b, c and d are -5, -1, 3 and 5.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The given equation is y=2x+1

Substitute (-3, a) in y=2x+1, we get

a=2(-3)+1

a=-6+1

a=-5

Substitute (-1, b) in y=2x+1, we get

b=2(-1)+1

b=-1

Substitute (1, c) in y=2x+1, we get

c=2(1)+1

c=3

Substitute (2, d) in y=2x+1, we get

d=2(2)+1

d=5

Therefore, the values of a, b, c and d are -5, -1, 3 and 5.

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"Your question is incomplete, probably the complete question/missing part is:"

Use the table to work out the values a, b, c and d.

      x        y=2x+1

     -3           a

     -2           -3

      -1           b

       0            1

       1            c

       2            d

hola cómo estás yo muy bien y tu qué tal

Answer:

366.16

Step-by-step explanation:

area to paint = (10 x 6 x 2) + (10 x 2 x 2) + (6 x 2 x 2) = 184 m²

184 x 1.99 = 366.16

Options e and f is the correct answers. The distance from the top of hays' head to the end of his shadow is 7.21ft

Hays' body and his shadow are perpendicular.

So if we imagine the line from the top of his head to the end of his shadow on the ground, we have a right triangle, and the imaginary line is the hypotenuse.  

Then you can stand back and let Pythagoras figure out the length of the line for you, using c²  =  a² + b²

(Distance)²=(Hay's height)²+(length of his shadow)²

(Distance)²=(6 ft)² + (4 ft)²

(Distance)²=(36 ft²) + (16 ft²)

(Distance)=52 ft²

Distance =√(52 ft)²

Distance = 7.21 ft

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Answer:

a

Step-by-step explanation:

Answer:

a2

Step-by-step explanation:

The final equation is a polynomial of primes  [tex]2x^{4} + x^{3} - x + 2[/tex] It can't be factored. Variables are sometimes known as indeterminate in mathematics.

 An essential component of the "language" of mathematics and algebra are polynomials. They are used to express numbers that are the result of mathematical operations in almost every area of mathematics. Other types of mathematical expressions, such as rational expressions, also use polynomials as "building blocks."

given

Is a base form of a polynomial in other words is a polynomial that can't be factored.

so we have

[tex]A ) x^{3} +3x^{2} - 2x - 6 = ( x +3 ) ( x^{2} - 2 )\\B) x^{3} -2x^{2} +3x - 6 = ( x- 2 ) (x^{2} + 3)\\C)4x^{4} +4x^{3} - 2x - 2 = 2( x +1 )(2x^{2} - 1)\\D) 2x^{4} +x^{3} -x + 2[/tex]

hence, the final equation is a polynomial of primes  [tex]2x^{4} + x^{3} - x + 2[/tex] It can't be factored.

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Answer: 490.088 in2

Step-by-step explanation:

Answer:

$388.50

Step-by-step explanation:

42 tins

$9.25/tin

[tex]42*9.25=388.5[/tex]

So, they raised $388.50

Answer:

Step-by-step explanation:

We will check if 5/15 and 1/3 are in proportion or not by cross-multiplication.

5/15 = 1/3

5*3 = 15*1

15 = 15

as the left-hand side is equal to the right side. So, these fractions are in proportion.

Answer:

17%

Step-by-step explanation:

Firstly, we can establish that the tip is a percentage of the bill, excluding tips. This means that the $75.29 would be 100%, thus to find the percentage of tip received, we would take
$12.80/$75.29 × 100 = 17%

Answer: AAS

Step-by-step explanation:

AAS, because the side congruence isn't between the angles as it should be in order for it to be ASA.

Answer:

6 is 6.82% of 88

Answer:

Step-by-step explanation:

If the firstborn arrived 26 years ago, his mother's age was likely between 20 and 30 years old when she gave birth.  Her current age is likely between 46 and 56 years.

Find the area of the room by multiplying the length by the width:

Area of room = 20 x 12 = 240 square feet.

Find the area of the tile: 2x 2 = 4 square feet.

To find the number of tiles divide the area of the room by the area of a tile:

240/4 = 60

They will need 60 tiles.

Answer:

120

Step-by-step explanation:

20*12=240

240/2=120

Answer:

b: Two thousand four hundred and forty (2440)

c: 1.33 x 10^27

Step-by-step explanation:

I'm uncertain by what an ordinary number is, but to calculate the answer for part b, you need to divide the diameter of Mercury by 2, which would give the aforementioned answer.

As for part c, you will need to subtract the masses of Jupiter and Saturn:
mass of Jupiter - mass of Saturn = 1.33 ×[tex]10^{27}[/tex]

The commission on the sale would be $62.5

To find the commission on a sale, you can use the following formula:

Commission = Sale Amount x Commission Rate

Sale Amount: the total value of the sale

Commission Rate: the percentage or decimal value of the commission rate (e.g. 5% = 0.05)

The commission on a sale can be calculated by multiplying the total sale amount by the commission rate.

In this case, the commission on a 1,250 sale with a commission rate of 5% would be:

= 1,250 x 0.05

= 62.5

So the commission on the sale would be $62.5

It's also worth noting that commission rate is given as a decimal and not a percentage. 5% is 0.05 as decimal.

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