A patio deck in the shape of a parallelogram has three square cutouts for trees to grow through each square has a side length of 4 1/2 ft what area of wood boards is needed to cover the deck while leaving room for the square cutouts

Answer:

B. [tex]^{5} P_{5}[/tex] × [tex]^{20} P_{15}[/tex]

Step-by-step explanation:

No. of students from first grade = 15

No. of students from second grade = 5

There are 5 rows of seats

Each row contains 5 seats

Total seats = 25

No. of ways for second-grade students to occupy the first row (i.e first 5 seats) = [tex]^{5} P_{5}[/tex]

Remaining seats = 20

So, now we are left with 15 first grade students  

So, No. of ways for first-grade students occupy remaining seats = [tex]^{20} P_{15}[/tex]

Using the counting rule principle,

No. of ways for the students can be seated if all of the second-grade students occupy the first row = [tex]^{5} P_{5}[/tex] × [tex]^{20} P_{15}[/tex]

So, Option B is the correct answer

Hence, no. of ways for the students can be seated if all of the second-grade students occupy the first row is ×

There are ¹⁵P₁₅ x ¹⁰P₅ possible way to seat, if all of the second-grade students occupy the first row.

A permutation in math is the number of ways in which a set of data or objects can be ordered or arranged, where the order matters.

Given that, a school bus has 25 seats, with 5 rows of 5 seats. 15 students from the first grade and 5 students from the second-grade travel in the bus.

Since you have to place all first-grade students in the first three rows,

Therefore,

For the 15 first-graders of the first three rows (15 seats), we have ¹⁵P₁₅ since all 15 places have to be occupied by all 15 first-graders.

Then we have 10 remaining seats left to be assigned to the 5 second-graders = ¹⁰P₅

We then multiply the permutation numbers of those two arrangements to get the total ways:

¹⁵P₁₅ x ¹⁰P₅

Hence there are ¹⁵P₁₅ x ¹⁰P₅ possible way to seat, if all of the second-grade students occupy the first row.

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Answer:

a) 98,910

b) 4,620

Step-by-step explanation:

Recordar que un numero N es multiplo de A si N es divisible por A.

Entonces, decir:

Buscar N, tal que sea multiplo de A

es lo mismo que decir:

Buscar N, tal que sea divisible por A.

a) Queremos un múltiplo de 5 y de 6 mayor que 95.000

( _ 8 9 1 _ )

Sabemos que los múltiplos de 5 terminan en 0 o 5.

Y un número de 5 dígitos mayor que 95,000 requiere que el quinto digito en este caso sea 9, entonces tendremos:

98,91_

Para encontrar el dígito de las unidades, podemos probar remplazarlo por 0 y por 5, y luego dividirlo por 6.

Si el resultado es un número entero, entonces el número será un múltiplo de 6.

Probemos con 0, vamos a tener el número:

98,910

dividiéndolo por 6 obtenemos:

98,910/6 = 16,485

Entonces:

98,910 es más grande que 95,000

es múltiplo de 5 (porque termina en cero)

Y es múltiplo de 6, como acabamos de comprobar.

b) Ahora queremos un número divisible por 3, 4 y 5, que sea menor que 4,675

4,6__  

De vuelta, como tiene que ser divisible por 5, sabemos que termina en 5 o 0.

Y como también tiene que ser divisible por 4, sabemos que tiene que terminar si o si en número par, entonces podemos concluir que solo puede terminar en 0.

Así, sabemos que el número va a ser algo como:

4,6_0

Ahora podemos probar con el dígito de las decenas, de tal forma que el número sea divisible por 3, 4 y 5.

Recordar que este número tiene que ser menor que 4,675

Entonces el número faltante puede ser:

0, 1, 2, 3, 4, 5, 6, 7

Ahora también podemos recordar que un número es solo divisible por 3 si la suma de todos sus dígitos es divisible por 3.

Entonces tenemos que tener que:

4 + 6 + x + 0 = múltiplo de 3

10 + x = múltiplo de 3

Los posibles valores de x van a ser:

x = 2   (porque 12 es múltiplo de 3)

x = 5   (porque 15 es múltiplo de 3)

Ok, ahora sabemos que el número restante solo puede ser 2 o 3.

Entonces tenemos que remplazar esos valores en el número y ver si este es divisible por 4 o no.

Comenzamos con el 2.

Tendremos el número:

4,620

Probamos dividiendo esto por 4:

4,620/4 = 1,155

El resultado es entero, entonces 4,620 es divisible por 4 (y por como lo creamos, también sabemos que es divisible por 3 y por 5, y además es menor que 4,675, como queríamos)

Answer:

68

Step-by-step explanation:

Let The first number = X

& the Second one = X + 16

Sum of these two numbers = 120

X + X + 16 = 120

2X = 120 - 16

2X = 104

X = 52

So , the first number = 52

& Second one = 52 + 16 = 68

Answer:

The numbers are 52 and 68.

Step-by-step explanation:

Let x be the first number and y be the second. The question tells us that:

1) x = y + 16

2) (x + y) / 2 = 60

2 equations, 2 unknowns. Solve the system. Plug equation 1 into equation 2:

(y + 16 + y) / 2 = 60

2y + 16 = 120

y + 8 = 60

y = 52

Now plug the value of y back into either original equation. I'll use the first:

x = 52 + 16

x = 68

Answer:

[tex]1) y=-6[/tex]

[tex]2)x=3[/tex]

[tex]3) y=8[/tex]

[tex]4)a=8[/tex]

Step-by-step explanation:

[tex]4y+24=0[/tex]

subtract 24 from both sides

[tex]4y=-24[/tex]

divide both sides by 4

[tex]y=-6[/tex]

---------->>>>

[tex]15+3=6x[/tex]

combine like terms

[tex]18=6x[/tex]

divide both sides by 6

[tex]3=x[/tex]

---------->>>>

[tex]9y-72=0[/tex]

add 72 to both sides

[tex]9y+72[/tex]

divide both sides by 9

[tex]y=8[/tex]

---------->>>>

[tex]8a=75-11[/tex]

combine like terms

[tex]8a=64[/tex]

divide both sides by 8

[tex]a=8[/tex]

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

Hope this is helpful.

Given:

John had to pay a combined electric and gas bill $150.

The electric portion of the bill was $90.

To find:

The ratio of money spent on electric to that on gas.

Solution:

Let x be the amount of gas bill.

The electric portion of the bill was $90 and John had to pay a combined electric and gas bill $150.  So,

[tex]90+x=150[/tex]

[tex]x=150-90[/tex]

[tex]x=60[/tex]

The gas portion of the bill was $60.

The ratio of money spent on electric to that on gas is:

[tex]\text{Required Ratio}=\dfrac{\text{Electric bill}}{\text{Gas bill}}[/tex]

[tex]\text{Required Ratio}=\dfrac{90}{60}[/tex]

[tex]\text{Required Ratio}=\dfrac{3}{2}[/tex]

[tex]\text{Required Ratio}=3:2[/tex]

Therefore, the ratio of money spent on electric to that on gas is 3:2.

Answer:

y = 2

Step-by-step explanation:

horizontal lines are parallel to the x-axis

The horizontal line through (3, 2) is

y = 2

Answer:

(3, 5.5)

Step-by-step explanation:

Given the line segment AB with endpoints A(6, 4) and B(2, 6). If the coordinates of the point divide the line segment directed from A to B in the ratio of 1:3, then;

M(X, Y) = {(ax1+bx2)/a+b, ay1+by2/a+b}

X = ax1+bx2/a+b

X = 1(6) + 3(2)/1+3

X = 6+6/4

X = 12/4

X = 3

Similarly;

Y = ay1+by2/a+b

Y = 1(4)+3(6)/1+3

Y = 4+18/4

Y = 22/4

Y = 5.5

Hence the required coordinate is (3, 5.5)

Answer:

12.94811641 =x

Step-by-step explanation:

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

cos theta = adj/ hyp

cos 44 = x /18

18 cos 44 =x

12.94811641 =x

Answer:

12.9

Step-by-step explanation:

cos(44) = x/18

x = cos(44) * 18

x = 12.9

An

Step-by-step explanation:

Answer:

Adult=4, Student=6

Step-by-step explanation:

a=adult, s=student

3a+8s=60 equation 1

10a+8s=88 equation 2

-3a-8s=-60 multiply equation 1 by -1

 7a = 28 add above 2 equations

     a=4

solve for s by inserting a value into either equation

3a+8s=60

3(4)+8s=60

12+8s=60

8s=48

s=6

Answer:

Probability[Selected ball is a white ball without replacement (W)] = 5 / 22

Step-by-step explanation:

Given:

Number of white ball in jar = 5

Number of black ball in jar = 6

Find;

Probability[Selected ball is a white ball without replacement (W)]

Computation:

Probability of an event = Number of favorable outcomes / Total number of outcomes

Probability of 1st white ball = 5 / [5 + 6]

Probability of 1st white ball = 5 / 11

Probability of 2nd white ball [without replacement] = 5 / [11 - 1]

Probability of 2nd white ball [without replacement] = 5 / 10

Probability[Selected ball is a white ball without replacement (W)] = [5/11][5/10]

Probability[Selected ball is a white ball without replacement (W)] = 25 / 110

Probability[Selected ball is a white ball without replacement (W)] = 5 / 22

Answer:

Water is a compound. One molecule of water is made up of H2O or 2 hydrogen atoms and 1 oxygen atom. Water is colorless, tasteless, shapeless, and sizeless.

Step-by-step explanation:

Water is a compound made up of two hydrogen and one oxygen.

Compounds are chemical substances formed by the combination of two or more different elements.

Here consider the compound Water.

A Water molecule is made up of two hydrogen atoms and one oxygen atom.

The molecular formula is H₂O.

Consider the element hydrogen from water.

Hydrogen is an element which does not have any smell and does not have color.

In the room temperature, hydrogen exists in gaseous state. It will turn in to liquid at low temperature and high pressure.

Hence water is a compound made up of two hydrogen and one oxygen.

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Answer:

You have 44$, your brother has 11$.

Step-by-step explanation:

Let [tex]x[/tex] be the amount of money your brother has.

Since you have four times the amount of money your brother has, we can call the amount of money you have [tex]4x[/tex].

[tex]x+4x=55,\\5x=55,\\x=\boxed{\$11}[/tex]

Thus, you have:

[tex]4(11)=\boxed{\$44}[/tex]

Answer:

he has 11 you have 44 dollars

Answer:

I don't know what the answer choices are because this question is used twice But if im guessing correctly you mean the one where the answer choices are 6, 8, 12, and 24. The Correct answer is 6

a2 + 8a + 12 = (a + 2)(a + )

The answer is 6

Step-by-step explanation:

Answer: TRY E

IF WRONG TRY E, D, F

Step-by-step explanation:

Answer number 3

Step-by-step explanation:

Answer:

hey, i answered in the wrong place last time, so i'm answering here again, it's letter c or d

Step-by-step explanation:

Answer:

24 tiles^2

Step-by-step explanation:

Length = 6

width = 4

Area = Length x width

        = 6 x 4

        = 24 tiles^2

Answer:

$34.04

Step-by-step explanation:

The dimensions of a slab is 11 feet by 11 feet by 2 inches or 3.67 yards, 3.67 yards and 0.055 yards

We need to find the cost to pour a slab.

We know that the volume of a cuboid shape is given by :

V = lbh

Put all the values,

V = 3.67 × 3.67 × 0.055

V = 0.74 yards³

Cost,

C = $46 × 0.74

C = $34.04

Hence, the required cost is equal to $34.04.

Answer:

Step-by-step explanation:

I think it’s z. The angles made are less than 90 degrees. The remaining letters all have right angles.

Answer:

B

Step-by-step explanation:

Figure A

2(8*4 + 4*4 + 4*8)

160

Figure B

6*4^2

96

Answer:

A = $1,871.77

Step-by-step explanation:

A = P(1 + r/n)nt

Where,

A = Total money in the bank

P = principal = $1,600

r = interest rate = 4% = 0.04

n = number of periods = 1 year

t = time = 4 years

A = P(1 + r/n)^nt

A = 1,600(1 + 0.04/1)^1*4

A = 1,600(1 + 0.04)^4

= 1600(1.04)^4

= 1600(1.16985856)

= 1,871.773696

Approximately,

A = $1,871.77

Answer:

sas ofc

side angle side

Step-by-step explanation:

Answer: 2 hr and 13 min

Step-by-step explanation:

Given

Bilal starts at 3 PM and finishes at 5:38 PM

He took a rest of 25 min

Total time spent 2 hr and 38 min

time spend in cycling is given by

[tex]\Rightarrow 2\ hr\ 38\ min-25\ min\\\Rightarrow 2\ hr\ 13\ min\ or\\\Rightarrow 120\ min+13\ min=132\ min\ or\\\Rightarrow 2+0.21=2.21\ hr[/tex]

Answer:

2/3

Step-by-step explanation:

There are 6 different letters and 4 of them are consonants, so:

4/6 simplify it by 2:

2/3