"The product of a six and a number increased by four is equal to
the product of twelve and the same number decreased by twenty."

[tex]\bold{\huge{\underline{ Solution }}}[/tex]

Here,

The dimension of larger cuboid are

We know that,

Lateral surface area of cuboid

[tex]\bold{\red{ = 2( lb + bh + hl)}}[/tex]

Subsitute the required values,

[tex]\sf{ = 2[(7)(7) + (7)(12) +(7)(12) ]}[/tex]

[tex]\sf{ = 2[ 49 + 84 ]}[/tex]

[tex]\sf{ = 2[ 49 + 168 ]}[/tex]

[tex]\sf{ = 2[ 217 ]}[/tex]

[tex]\bold{ = 434 cm^{2}}[/tex]

We have to find the lateral surface area of smaller cuboid

Therefore,

Lateral surface area of smaller cuboid

[tex]\sf{ = 2[(2)(7) + (7)(2) +(2)(2) ]}[/tex]

[tex]\sf{ = 2[ 14 + 14 + 4 ]}[/tex]

[tex]\sf{ = 2[ 28 + 4 ]}[/tex]

[tex]\sf{ = 2[ 32]}[/tex]

[tex]\bold{ = 64 cm^{2}}[/tex]

The common base area of both the cuboids

[tex]\sf{ = lb }{\sf{ + lb}}[/tex]

[tex]\sf{ = 14 + }{\sf{ 14}}[/tex]

[tex]\bold{ = 28 cm^{2}}[/tex]

The total surface area of the given composite figure

= SA of larger cuboid + SA of smaller cuboid - common base area

Subsitute the required values,

[tex]\sf{ = 434 + 64 - 28 }[/tex]

[tex]\sf{ = 498 - 28 }[/tex]

[tex]\bold{ = 470cm^{2}}[/tex]

Hence, The surface area of composite figure is 470 cm² .

Answer:

470cm²

Step-by-step explanation:

SA= (12*7)*4+(7*7)*2+(2*2)*2+(7*2)*2

=336+98+8+28

= 470 cm²

Therefore, the surface ares is 470 cm².

~

The constant terms are 12, -16, -10.

Look at the attached image for an example of how to identify constants!

Hope that helped!

Answer:

[tex]\huge\boxed{\sf{12, -16, -10}}[/tex]

Step-by-step explanation:

Hello.

Please remember that a constant is a number without any variables next to it.

Let's search for constants in this expression.

The first term is 12. It has no variables, thus, it's a constant.

The second term is 15x. It does have a variable, thus, it's not a constant.

The third term is -16. It has no variables, thus, it's also a constant.

The 4th term is -4x (not a constant)

The last term is -10 (a constant)

I hope it helps & have an outstanding day.

[tex]\boxed{imperturbability}[/tex]

Answer:

$20

Step-by-step explanation:

The large ones cost $4 more so what you would do is to subtract that $4 from the $24.

24-4=20

You circled b and i would agree. Because Francesca is doing a living room, it would natuarly start at $25. So it cant be c. And Because x represents the walls, the graph would be a possitive corrolotion so i would say it is b

The graph b shows the adequate information for painting cost of living room. Option b is correct.

Graph that shows adequate information for cost of painting for living room to be determine.

The graph is a demonstration of curves  which gives the relationship between x and y axis.

Here, equation for the painting of living room can be given as y = 1x+25.
This relation ship clearly seen in graph b.

Thus, the graph b shows the adequate information for painting cost of living room.

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Answer:

bjc hnfj yn yt NV ubf. giving! y NV,

Answer:

x= 45°

x+10=55°

2x-10=80°

Step-by-step explanation:

According to ASP,

x+x+10+2x-10=180°

4x=180°

Therefore, x=180/4

                    =45°

x+10=45+10

        =55°

2x-10=90-10

         =80°

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Answer:

Step-by-step explanation:

The formula for calculating the volume of a right triangular prism is:

Let's use the formula to calculate the volume of the right triangular prism.

Answer:

60

Step-by-step explanation:

east and north are two axis that are perpendicular to each other, so if we use Pythagorean rule, sqr60^2+20^2=20sqr10, approximately 63.24555

Answer:

36 Minutes

Step-by-step explanation:

150/8=18.75

675/18.75=36

So hence, your answer is 36 Minutes

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Answer:

I don't know-how to answer that

The graph of both plots would be the one graph in option C.

Combined area = 2(area of one rectangular plot) = 720 sq. yds.

Area of a rectangular shape = length × width

From the graph given, 1 unit represents 20 yards. Therefore:

Therefore, the graph of both plots would be the one given in option C.

The plot is rectangular in shape having 60 yards × 60 yards. Therefore:

Area of 1 plot = length × width = 60 × 60 = 360 square yards.

Combined area = 2(area of one rectangular plot) = 2(360) = 720 sq. yds.

Learn more about area of rectangular shapes on:

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The volume of the rectangular prism with the dimensions given are as follows:

v = 72 inches³

v = 36 inches³

v =  80 inches³

v = 54 inches³

where

l = length

w = width

h = height

Therefore,

a.  

b.

c.

d.

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Answer:

I think it is x is equals to 5/6.

Step-by-step explanation:

5/x = 25/6

x/5 * 5/x = 25/6 * x/5

x = 5/6

▪ Answer:

x = 5/6

▪ Step-by-step explanation:

Hi there !

5/x = 25/6

x = 5×6/25

x = 30/25

simplist 5

x = 6/5

Good luck !

Answer:

1110 g

Step-by-step explanation:

Here is the fastest way to solve this problem: (5 x 186) + (2.5 x 72)

However, if you want a step-by-step explanation, here it is:

The total mass of the coins in the bag is the mass of the nickels plus the mass of the pennies.

Let's start by finding the mass of the nickels in the bag.

We know that one nickel has a mass of 5 g, and that there are 186 nickels. So, the total mass of all the nickels in the bag will be 186 x 5 = 930 g.

Now, let's find the mass of the pennies in the bag.

We know that one penny has a mass of 2.5 g, and that there are 72 pennies in the bag. So, the total mass of all the pennies in the bag will be 2.5 x 72 = 180.

We now add these two masses (930 + 180) to get our final answer, 1110 g.

Answer:

125 and 55

Step-by-step explanation:

180=8x+20

160=8x

x=20

6(20)+5                            2(20)+15=

120+5=125 degrees           40+15=55 degrees

Answer:

1:4

Step-by-step explanation:

To represent 14:56 as a simplified ratio, we need to reduce it by finding the GCF (greatest common factor) and dividing it by both terms.

The GCF of 14 & 56 is 14.

14 / 14 = 1

56 / 14 = 4

Thus we are left with our new simplified ratio, 1:4.

Answer:

-1

Step-by-step explanation:

5-2=3

2-3=-1

For the integral ∫asin(x)dx, use integration by parts ∫udv=uv−∫vdu.

Let u=asin(x) and dv=dx.

Then du=(asin(x))′dx=[tex]\rm \dfrac{dx}{ \sqrt{1 - {x}^{2} } } [/tex] and v=∫1dx=x

So,

[tex] \rm{\int{\operatorname{asin}{\left(x \right)} d x}}=\color{h}{\left(\operatorname{asin}{\left(x \right)} \cdot x-\int{x \cdot \frac{1}{\sqrt{1 - x^{2}}} d x}\right)}=\color{h}{\left(x \operatorname{asin}{\left(x \right)} - \int{\frac{x}{\sqrt{1 - x^{2}}} d x}\right)} \\ [/tex]

Let u=1−x2.

Then du=(1−x2)′dx=−2xdx and we have that xdx=−du/2.

The integral can be rewritten as

[tex] \rm x \operatorname{asin}{\left(x \right)} - \color{g}{\int{\frac{x}{\sqrt{1 - x^{2}}} d x}} = x \operatorname{asin}{\left(x \right)} - \color{j}{\int{\left(- \frac{1}{2 \sqrt{u}}\right)d u}} \\ [/tex]

Apply the constant multiple rule ∫cf(u)du=c∫f(u)du with c=-1/2 and f(u)=[tex] \frac{1}{ \sqrt{u} } [/tex]

[tex] \rm x \operatorname{asin}{\left(x \right)} - \color{h}{\int{\left(- \frac{1}{2 \sqrt{u}}\right)d u}} = x \operatorname{asin}{\left(x \right)} - \color{h}{\left(- \frac{\int{\frac{1}{\sqrt{u}} d u}}{2}\right)} \\ [/tex]

Apply the power rule

[tex] \rm\int u^{n}\, du = \frac{u^{n + 1}}{n + 1} \\ [/tex]

with n=−1/2

[tex] \rm x \operatorname{asin}{\left(x \right)} + \frac{\color{h}{\int{\frac{1}{\sqrt{u}} d u}}}{2}=x \operatorname{asin}{\left(x \right)} + \frac{\color{j}{\int{u^{- \frac{1}{2}} d u}}}{2}=x \operatorname{asin}{\left(x \right)} + \frac{\color{j}{\frac{u^{- \frac{1}{2} + 1}}{- \frac{1}{2} + 1}}}{2}=x \operatorname{asin}{\left(x \right)} + \frac{\color{j}{\left(2 u^{\frac{1}{2}}\right)}}{2}=x \operatorname{asin}{\left(x \right)} + \frac{\color{h}{\left(2 \sqrt{u}\right)}}{2} \\ [/tex]

[tex] \rm Recall \: that  \: u=1− {x}^{2} [/tex]

[tex] \rm x \operatorname{asin}{\left(x \right)} + \sqrt{\color{re}{u}} = x \operatorname{asin}{\left(x \right)} + \sqrt{\color{rd}{\left(1 - x^{2}\right)}} \\ [/tex]

Therefore,

[tex] \rm\int{\operatorname{asin}{\left(x \right)} d x} = x \operatorname{asin}{\left(x \right)} + \sqrt{1 - x^{2}}+C \\ [/tex]

Answer:

the slope is −12

Step-by-step explanation:

The equation of a perpendicular line to y=−x2+5 y = - x 2 + 5 must have a slope that is the negative reciprocal of the original slope.

-1/2

That would be the answer

Answer:

For number question #8 its 8/3

Step-by-step explanation:

One way i do is multiply the denominator by the whole number and then add the numerator . For example 2 2/3

2x3=6     6+2=8

Do NOT change the numerator, it stays the same.

Answer:

=−148

     3

(Decimal: -49.333333)

Step-by-step explanation:

−364

9

−(

−102

9

)−

182

9

Answer: 0.29

Step-by-step explanation:

The probability of the first being blue is 6/17, the second is 5/16 and the third is 4/15.  Multiply these together to get the total probability:

6/17 x 5/16 x 4/15 = .029

[tex]f(x) = \sqrt{7 + x} [/tex]

[tex]7 + x \geqslant 0[/tex]

[tex]x \geqslant - 7[/tex]

[tex]domain \: - 7 \leqslant x \leqslant \infty [/tex]

[tex]range \: \: 0 \leqslant f(x) \leqslant \infty [/tex]

Answer:

a

             [tex]P(K = k ) = \  ^nC_x * p^k  *  (1-p)^{n-k}[/tex]

Here  k is the random number of number of pairs of shoes that will be returned for refund, which can be  k = 0,1 ,2,3,4 ..., 120

b

The mean is   [tex]E(K) =  np =  13.2[/tex]  

The  standard deviation is  [tex]\sigma =  3.43[/tex]

c

The mean is  [tex]E(C) =   E(105 K) =  1386[/tex]

The standard deviation is   [tex]\sigma  =  381.48 [/tex]  

Step-by-step explanation:

From the question we are told that

   The  cost to dealer for each refund is  [tex]C =  \$105[/tex]

   The  probability  that a shoe will refunded is  [tex]P(x) =  0.11[/tex]

   The number of shoes purchased is  n  =  120 pairs

Generally the probability distribution of the number of pairs of shoes that will be returned for refunds is

          [tex]P(K = k ) = \  ^nC_x * p^k  *  (1-p)^{n-k}[/tex]

Here  k is the random number of number of pairs of shoes that will be returned for refund, which can be  k = 0,1 ,2,3,4 ..., 120

Generally the mean is mathematically represented as

     [tex]E(K) =  np =  120 * 0.11[/tex]

=>    [tex]E(K) =  np =  13.2[/tex]  

Generally the  standard deviation is mathematically represented as

     [tex]\sigma  =  \sqrt{ n*  p  (1-p)}[/tex]

=>    [tex]\sigma  =  \sqrt{ 120* 0.11  (1-0.11)}[/tex]

=>    [tex]\sigma =  3.43[/tex]

Generally the total refund cost is mathematically represented as

     [tex]C =  105 K[/tex]

Here K denotes the number of shoes returned

Generally the mean of the total refund cost is mathematically represented as

           [tex]E(C) =   E(105 K) =  105 E(K)[/tex]

=>         [tex]E(C) =   E(105 K) =  105 * 13.2[/tex]

=>         [tex]E(C) =   E(105 K) =  1386[/tex]

Generally the variance of the total refund cost is mathematically represented as

       [tex]Var(K) =  105^2 *  E(K)[/tex]

=>     [tex]Var(K) =  105^2 *  13.2[/tex]

=>    [tex]Var(K) =  145530[/tex]  

=>      [tex]\sigma =  \sqrt{145530 }[/tex]

=>    [tex]\sigma  =  381.48 [/tex]  

Answer:

Probability of drawing a yellow candy: 10/36= 5/18

Something besides a yellow candy: for ecample: the red candies: 8/36= 2/9

Step-by-step explanation:

Probability of drawing yellow candies equals the sum of candies over yellow candies.

Answer:

40

Step-by-step explanation:

Angles opposite congruent sides in a triangle are congruent, so the other base angle is also 70 degrees.

This means that the interior angles are 70, 70, and x

Since the sum of the measures of the angles of a triangle is 180 degrees,

70+70+x=180

140+x=180

x=40

common denominator = 7x11 = 77

5/7 = (5x11) / (7x11) = 55/77

and

8/11 = (8x7) / (11x7) = 56/77

5/7 and 8/11 can be rewritten as 55/77 and 56/77, respectively, so that they have a common denominator of 77.

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

To rewrite 5/7 and 8/11 with a common denominator:

We can find the least common multiple (LCM) of the denominators 7 and 11, which is 77.

Then, we can multiply each fraction by the appropriate form of 1 so that the denominators are equal to 77.

Here are the steps:

5/7 = (5/7) x (11/11) = 55/77 (multiply the numerator and denominator of the first fraction by 11)

8/11 = (8/11) x (7/7) = 56/77 (multiply the numerator and denominator of the second fraction by 7)

Therefore, 55/77 and 56/77 are the required fractions.

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