50 POINTS .....................

Answer:

2 sqrt(2)

Step-by-step explanation:

To simplify a square root

sqrt(8)

sqrt(4*2)

sqrt(4) sqrt(2)

2 sqrt(2)

Answer:

2√2

Step-by-step explanation:

√8 =[tex]\sqrt{4 \times 2}[/tex]

= 2√2 (√4 = 2)

Hence, 2√2 is the required answer.

(a) 10% of x = 9

x = 9 ⋅ (100/10)

x = 90 kg

(b) 12% of x = 12/100 of 90

Weight she lost = 10.8

Her new weight = 90 - 10.8

= 79.2kg

Yes, they can be added and simplified further. 2√3 + 5√3 = 7√3 .

Take √3 as common factor:

2√3 + 5√3

(2 + 5)√3

7√3

The two irrational numbers sums to form another irrational number 7√3 . In decimals that is 12.12435...

[tex] \sf{\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Yes, The terms assigned above are alike so they can be added easily by simple algebric method where root number can be treated as a variable.

[tex]\qquad \sf  \dashrightarrow \: 2 \sqrt{3} + 5 \sqrt{3} [/tex]

[tex]\qquad \sf  \dashrightarrow \: (2 + 5) \sqrt{3} [/tex]

[tex]\qquad \sf  \dashrightarrow \: 7 \sqrt{3} [/tex]

Answer:

22.5 hours

Step-by-step explanation:

One cubic foot of water contains 7.48 gallons, so 40 cubic feet of water would equal 7.48 × 40, or 299.2 gallons. So the pumping rate is 299.2 gallons per minute. Multiplying 299.2 by 60, we have

299.2 × 60, or 17952 gallons per hour. Finally, divide 403,920 by 17,952 to find the number of hours to remove all the water: 403,920 ÷ 17,952 = 22.5 hours

Step-by-step explanation:

see photo for detailed analysis

Answer:

x = 10

Step-by-step explanation:

5(2x - 12) + 21 = 2x + 41 ← distribute parenthesis and simplify left side

10x - 60 + 21 = 2x + 41

10x - 39 = 2x + 41 ( subtract 2x from both sides )

8x - 39 = 41 ( add 39 to both sides )

8x = 80 ( divide both sides by 8 )

x = 10

Answer: C. 7.5%

Solve as decimal

0.5*0.15=0.075

Move two decimal points over

0.075 -> 7.5

Change back to percent

7.5%

The length and width of this rectangle are 15 cm respectively

The perimeter is given as:

Perimeter, P = 60

The greatest area is calculated as:

Greatest = (P/4)^2

Substitute 60 for P

Greatest = (60/4)^2

Evaluate the quotient

Greatest = 15^2

Evaluate the exponent

Greatest = 225 square centimeters

Hence, the greatest area is 225 square centimeters

We understand that the area is the greatest.

In such a scenario;

Length = Width

This means that:

Area =Length^2 =Width^2

So, we have:

Length^2 =Width^2 = 225

Take the square root

Length =Width = 15

Hence, the length and width of this rectangle are 15 cm respectively

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Answer:

1) -
2) +

3) -
4) +

Step-by-step explanation:

сумма внутренних углов треугольника не должна превышать 180 градусов

The real number of the given expression is a=-2.

Given that the expression is [tex]\frac{1}{a^3+7}-7=\frac{-a^3}{a^3+7}[/tex]

Real numbers is known as the union of both rational and irrational numbers. Real numbers can be both positive or negative and are denoted by the symbol “R”.

To compute the value of a.

In the given expression multiply both sides with (a³+7) as

[tex]\frac{(a^3+7)}{a^3+7}-7=\frac{-a^3(a^3+7)}{a^3+7}[/tex]

Simplify the expression as,

1-7(a³+7)=-a³

Expand out terms of the left hand side

1-7a³-49=-a³

-7a³-48=-a³

Taking out minus common from both sides and cancel them

-(7a³+48)=-(a³)

7a³+48=a³

Add -a³-48 on both sides

7a³+48-a³-48=a³-a³-48

6a³=-48

Divide both sides with 6

(6÷6)a³=(-48÷6)

a³=-8

write -8 in the expansion form which is (-2)×(-2)×(-2)=-8

a³=(-2)³

From above it says that

a=-2

Hence, real number that satisfy [tex]\frac{1}{a^3+7}-7=\frac{-a^3}{a^3+7}[/tex] is a=-2.

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A ratio shows how many times one number contains another.

Hence, the sand is in the ratio [tex]\frac{1}{6}[/tex] of the mixture is

[tex]\frac{1}{6}[/tex]×[tex]1800=300kg[/tex]

The Gravel is in the ratio [tex]\frac{2}{6}[/tex]×[tex]1800=600kg[/tex]

And the cement is in ratio [tex]\frac{3}{6}[/tex]×[tex]1800=900kg[/tex]

What is the ratio ?

A ratio is an ordered pair of numbers [tex]a[/tex] and [tex]b[/tex], written [tex]\frac{a}{b}[/tex] where [tex]b[/tex] does not equal [tex]0[/tex]. A proportion is an equation in which two ratios are set equal to each other.

Here the given ratio is [tex]1:2:3[/tex].

Here given that,

The dry concrete is   [tex]1800kg[/tex].

And the multiplication of the ratio is [tex]1[/tex]×[tex]2[/tex]×[tex]3=6[/tex]

Hence, the sand is in the ratio [tex]\frac{1}{6}[/tex] of the mixture is

[tex]\frac{1}{6}[/tex]×[tex]1800=300kg[/tex]

The Gravel is in the ratio [tex]\frac{2}{6}[/tex]×[tex]1800=600kg[/tex]

And the cement is in ratio [tex]\frac{3}{6}[/tex]×[tex]1800=900kg[/tex]

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d) 5x ≥ 15

Let's solve your inequality step-by-step.

5x≥15

Step 1: Divide both sides by 5.

[tex]\frac{5x}{5} \geq \frac{15}{5}[/tex]

[tex]x\geq 3[/tex]

(Attachment #1)

e) 3(2x + 1) ≤ 15

Let's solve your inequality step-by-step.

3(2x+1)≤15

Step 1: Simplify both sides of the inequality.

6x+3≤15

Step 2: Subtract 3 from both sides.

6x+3−3≤15−3

6x≤12

Step 3: Divide both sides by 6.

[tex]\frac{6x}{6} \leq \frac{12}{6}[/tex]

[tex]x\leq 2[/tex]

(Attachment #2)

The probability of selecting a jack, replacing the card, and then selecting a king is 1/169

In a standard deck of cards, we have:

Total = 52

Jack = 4

King = 4

The probability of each is:

P(Jack) = 4/52

P(King) = 4/52

So, we have:

P = 4/52 * 4/52

Simplify

P = 1/13 * 1/13

Evaluate

P = 1/169

Hence, the probability is 1/169

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Answer:

Each point (or pair) in a proportional relationship must share the same difference is the false statement.

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \:m\overbrace{DB}= 90 \degree[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex] \qquad \tt \rightarrow \: m \overbrace{DB} + m \overbrace{TB} = 180 \degree[/tex]

[ linear pair ]

[tex] \qquad \tt \rightarrow \: m \overbrace{DB} + 90 \degree = 180 \degree[/tex]

[tex] \qquad \tt \rightarrow \: m \overbrace{DB} = 180 \degree - 90 \degree[/tex]

[tex] \qquad \tt \rightarrow \: m \overbrace{DB} = 90 \degree[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

By finding the probability, we can expect that 2 out of the 30 students will win the prize.

First, we should get the probability of winning this game.

Here the students select two numbers out of 6, just to make the calculations let's say that these numbers are 1 and 2.

Now, we need to get these two numbers in two balls. The probability of getting the ball with the number 1 out of the 6 balls is:

p = 1/6

The probability of getting the ball with the number 2 out of the remaining 5 balls (because we already got one) is:

q = 1/5

The joint probability is then:

P = 2*(1/6)*(1/5) = 1/15.

Where the factor 2 comes to take in account the permutations, for the case where we first draw the number 2 and then the number 1.

Then the expected number of students that will win is equal to the probability times the total number of students:

(1/15)*30 = 2

So out of the 30 students, we can expect that 2 will win.

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Answer:

x=1/5

Step-by-step explanation:

You have to isolate x. First, add the one to the sider to give you 5x=1. In order to get the x by itself, you have to divide the 5 into both sides. In the end, this gives you x=1/5.

Based on the amount of cash that Elias Rubio brings, we can calculate that his total cash deposit is $1,323

This can be found as:

= (75 x 1) + (78 x 5) + (83 x 10) + (80 x 0.25) + (32 x 0.10 or 10 cents) + (95 x 0.05 or 5 cents) + (5 x 0.01 or 1 cent)

Solving gives:

= 75 + 390 + 830 + 20 + 3.20 + 4.75 + 0.05

= $1,323

Remaining part of the question:

How much did he deposit in cash?

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The molar heat of fusion for substance X , given the data is 775.6 cal/mol

Mole = mass / molar mass

Mole = (326 / 58.45) moles

Q = n × ΔHf

4325.8 = (326 / 58.45) × ΔHf

4325.8 = (326 × ΔHf ) / 58.45

Cross multiply

326 × ΔHf = 4325.8 × 58.45

Divide both sides by 326

ΔHf = (4325.8 × 58.45) / 326

ΔHf = 775.6 cal/mol

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The value of sin x in Q II is 0.86 .

This the field in Maths which deals with a right angled triangle and the other angles in the triangle.

It is given that cot = -0.59

cot x = cos x / sin x

Using online trigonometric calculator

sin x in Q II is 0.86 .

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Answer: $3.5

Step-by-step explanation:

If a product cost $1.50 and you paid $5, the change will be equal to

$5 - $1.50 = $3.5 for change

Answer:

[tex] \frac{18}{12} = \frac{24}{x - 2} [/tex]

Answer:

Your classmate says that there is not enough information to determine whether the two triangles below are congruent. Is your classmate correct?

yes it is

The two triangles are congruent triangles by RHS theorem of congruent triangles

Transformations change the size or position of shapes. Congruent shapes are identical, but may be reflected, rotated or translated. Scale factors can increase or decrease the size of a shape. Congruent Triangles simply mean the triangles that possess the same size and shape

The three sides are equal (SSS: side, side, side)

Two angles are the same and a corresponding side is the same (ASA: angle, side, angle)

Two sides are equal and the angle between the two sides is equal (SAS: side, angle, side)

A right angle, the hypotenuse and a corresponding side are equal (RHS, right angle, hypotenuse, side)

Given data ,

Let the first triangle be represented as ΔMLJ

Let the second triangle be represented as ΔLJK

Now , the measure of ∠MLJ = 90°

The measure of ∠LJK = 90°

The measure of side MJ = measure of side LK

So , the two sides of the triangles are similar and they have a common hypotenuse

Therefore , the triangles are congruent by right angle, the hypotenuse and a corresponding side are equal (RHS, right angle, hypotenuse, side)

Hence , the triangles are congruent

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If the subset y is the empty set, then the statement is false. That is the counterexample.

We know that for an invertible function, we always have that:

[tex]f(x) = y\\f^{-1}(y) = x[/tex]

Now, the range of f(x) is the set b. This means that the domain of the inverse is the set b. Such that:

f^{-1} is defined on b→a

Now we want to work on a subset y ⊆ b.

And here comes the problem.

The empty set {∅} is a subset of ay other set. So, if y is the empty set, there are no elements where we can evaluate the inverse function. From that counterexample, we conclude that the statement is false.

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Answer:

4,300

Step-by-step explanation:

total cost of the shipment of tile cost =$64,500

each tile cost =$15

how many pieces will now be the total cost of shipment tile divided by the cost of each tile

which will be

64500/15

=4,300 tiles are there

i am glad I helped

The 24 walls must paint by each volunteer if the work is divided evenly and the club has 36 volunteers.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

We have:

As part of a community-service project, a local club has decided to paint 864 walls across town. The club has 36 volunteers.

Total number of volunteers = 36

Number of walls = 864

The number of walls each volunteer paint can be expressed as a fraction:

= 864/36

= 24

Thus, the 24 walls must paint by each volunteer if the work is divided evenly and the club has 36 volunteers.

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Answer:

a. 42 g

b. 2.8 g

Step-by-step explanation:

a. Since the entire thing weighs 56g and gold is 75% of the mass you simply find 75% of the mass. This is done by converting the 75% into decimal form by dividing it by 100 to get 0.75 and then multiply it by the 56 g to get (0.75 * 56 g) = 42 g

b. same thing here as the previous answer. 5%/100 = 0.05. (0.05 * 56 g) = 2.8 g

Answer:

C

Step-by-step explanation:

1.75n = 7 ( to isolate n divide both sides by 1.75 )

n = [tex]\frac{7}{1.75}[/tex] = 4

Answer:

c.)  Divide by 1.75

Step-by-step explanation:

Given equation:

⇒ 1.75n = 7

Here the coefficient of n which is 1.75 needs to be removed. There is only one way of doing that - by dividing both sides by 1.75.

When done so:

⇒ 1.75n/1.75 = 7/1.75

⇒ n = 4