a³ = 125
Each edge of the cube is
feet long.

Since the percent grade in period 1 was 92% and in period 2 was 96%, then the percent change from period 1 to 2 was 4%.

Since the percent grade in period 2 was 96% and in period 3 was 99%, then the percent change from period 2 to 3 was 3%.

Since 4% is 1% greater than 3%, then the percent change from grading period 1 to 2 was 1% greater than the percent change from grading period 2 to 3.

Therefore, the answer is: 1.0%.

• Solution

To solve for x, we take the logarithm of both sides.

Applying the law of logarithm to the equation above;

Therefore, the approximate value of x is 3.562

The correct option is E.

Based on the given linear equation of y = - 3/4x + 5, the graph is shown attached.

When given a linear equation, you graph it by coming up with x values and then using the equation to find the corresponding y values.

The linear equation is y = - 3/4x + 5.

If the value x = -1, then y would be:

y = - 3/4x + 5

= -3/4(-1) + 5

= 5.75

If the value x = 0, then y would be:

y = -3/4(0) + 5

= 5

If the value x = 1, then y would be:

= -3/4(1) + 5

= 4.25

If the value x = 2, then y would be:

= -3/4(2) + 5

= 3.5

If the value x = 3, then y would be:

= -3/4(3) + 5

= 2.75

The points would be:
(-1, -5.75) (0, 5) (1, 4.25) (2, 3.5) (3, 2.75)

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Answer: measure of the third angle is 55 degrees

Step-by-step explanation: the sum of all interior angles in a triangle is always 180 so, 96+29+x=180.

125+x=180

x=55

Given:

There is a density curve given in the question

Required:

We need to find for

Explanation:

Part a

We want to find P(X<1.6)

For this we just need to find the area below the curve until x=1.6, since we have a triangle we can do this:

Part b

For this case we want to find this probability:

P(X>4.8)

and we can complement rule and we got

Final answer:

0.04

0.64

First, graph the rhombus:

Area of a rhombus = Product of diagonals / 2

Find the length of the diagonals:

Distance between points:

Diagonal AC

AC= 10√2

Diagonal BD

BD=6√2

Area= AC x BD / 2

Area = [(10√2) x (6√2)]/2

Area = 60

The possible values of the expression 1/a = 1/2 is 2

The expression is the simple fraction form = 1/a

The expression is the defined as the a sentence with a minimum of two  variables and at least one math operation.

The simple fraction is fraction that contains the numerator and denominator as whole number. The term one the top of the simple fraction called as the numerator and bottom term is called as the denominator.

Here it is given that

1/a = 1/2

Therefore the value of a = 2

Hence, the possible values of the expression 1/a = 1/2 is 2

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The equation that has the same solution as x = 5 are as follows:

An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.

In other words, an equation is a mathematical statement that is made up of two expressions connected by an equal sign.

The equation can be solved as follows:

The equation will have the same solution as x = 5.

Therefore,

25 / x + 4 = 9

subtract 4 from both sides of the equation

25 / x + 4 = 9

25 / x + 4 - 4 = 9 - 4

25 / x  = 5

cross multiply

5x = 25

divide both sides by 5

x = 25 / 5

x = 5

x / 5 +  5 = 6

x / 5 = 6 - 5

x / 5 = 1

cross multiply

x = 5

32 - 4x = 12

- 4x = 12 - 32

- 4x = - 20

divide both sides of the equations by - 4

x = -20 / - 4

x = 5

Therefore, the equation with same solution are 25 / x + 4 = 9, x / 5 +  5 = 6 and  32 - 4x = 12

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Answer:

Step-by-step explanation:

Step 1: Simplify both sides of the inequality.

12x+36>4x−8

Step 2: Subtract 4x from both sides.

12x+36−4x>4x−8−4x

8x+36>−8

Step 3: Subtract 36 from both sides.

8x+36−36>−8−36

8x>−44

Step 4: Divide both sides by 8.

8x/8 > -44/8

Therefore your answer will now equal  [tex]x > \frac{-11}{2}[/tex]

[tex]{ \boxed{ \pink{ \sf{x > - \frac{11}{2}}}}}[/tex]

Step-by-step explanation:

The given inequality is, [tex]{ \green{ \sf{12(x + 3) > 4x - 8}}}[/tex]

[tex]{ \star}[/tex]Step 1: Simplify both the sides of inequality.

[tex]{ \green{ \sf{12x + 36 > 4x - 8}}}[/tex]

[tex]{ \star}[/tex]Step 2: Now Subtract 4x from both sides.

[tex]{ \purple{ \sf{12x+36−4x> { \cancel{4x}−8{ \cancel{−4x}}}}}}[/tex]

[tex]{ \purple{ \sf{8x+36>−8}}}[/tex]

[tex]{ \star}[/tex]Step 3: Subtract 36 from both sides.

[tex]{ \blue{ \sf{8x+{ \cancel{36}{ \cancel{−36}}}>−8−36}}}[/tex]

[tex]{ \blue{ \sf{8x>−44}}}[/tex]

[tex]{ \star}[/tex]Step 4: Divide both sides by 8.

[tex]{ \orange{ \sf{ \frac{ \cancel8}{ \cancel8} x > - \frac{ \cancel{44^{ \blue{ \tt{11}}}} }{ \cancel8_{ \blue{ \tt{2}}} }}}} [/tex]

[tex]{ \boxed{ \red{ \sf{x > - \frac{11}{2}}}}} [/tex]

Sarah has hopped for 160ft when Will finished the race.

What is basic arithmetic?

Specific numbers and their computations employing a variety of fundamental arithmetic operations are at the center of arithmetic mathematics. Algebra, on the other hand, deals with the limitations and guidelines that apply to all other types of numbers, including whole numbers, integers, fractions, functions, and so on. Arithmetic math serves as the foundation for algebra, which always adheres to its definition. A large range of subjects fall within the broad definition of mathematics, which encompasses a very broad range of topics. Beginning with the fundamentals like addition, subtraction, and division of numbers, they then move on to more complicated topics like exponents, variations, sequence, progression, and more. This part does touch on some of the mathematical formulas and mathematical sequence. Four essential mathematical operations—addition, subtraction, multiplication, and division—are covered in basic arithmetic.

For Will

5 × 40

= 200 feet

For Sarah

4 × 40

= 160 ft

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Distance between two coordinates:

Given point: b) (10, -5) and ( -6, 7)

Substitute the value in the expression of distance formula

The distance between coordinates (10,-5) & (-6,7) is 20 unit

ANSWER:

13.35 hours

EXPLANATION:

Given:

Time Kristen takes to harvest = 10.2 hours

Time Kayla takes to harvest = 16. 5 hours

Let X represent the time it would take them to work together.

Here, to find the time it would take them if they worked together, let's find their mean time, using the formula below:

It would take them 13.35 hours if they worked together.

The empty boxes of the numerators for the given rational expression is to be filled with 4x and 2 respectively.

Rational expression is a division of two polynomials. Which implies that the numerator and denominator of the fraction consists of polynomials.

To solve this, we will first factorise the expression of the denominator as follows;

x² - 9x + 8 = x² - 8x - x + 8

x² - 9x + 8 = x(x - 8) -1(x - 8)

x² - 9x + 8 = (x - 1)(x - 8)

Hence, we can rewrite the rational expression as:

(4x + 2)/[(x - 1)(x - 8)]

we can break the expression further by dividing each term of the numerator with the expression (x - 1)(x - 8) as follows;

(4x + 2)/[(x - 1)(x - 8] = [4x/(x - 1)(x - 8)] + [2/(x - 1)(x - 8)]

Therefore, 4x and 2 will be the appropriate values to be filled in the empty boxes equated to the rational expression.

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By taking x as a common factor we get:

2x - 1 + 3x = 0

(2 + 3)*x - 1 = 0

5x - 1 = 0

Let's start with equation A, it is:

2x - 1 + 3x = 0

If we group like terms, we will get:

(2x + 3x) - 1 = 0

Now we can take x as a common factor in the left term, so we get:

(2x + 3x) - 1 = 0

(2 + 3)*x - 1 = 0

Now we simplify the sum in the left term:

(2 + 3)*x - 1 = 0

5x - 1 = 0

This is equation B.

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The initial amount that was deposited by Clare is $725.

The equation for the amount of money in Clare's bank account after x months will be 725 + 175x

An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.

Let the amount deposited initially be x.

Based on the information, this will be illustrated as:

x + 175(10) = 2475

x + 1750 = 2475

Collect like terms

x = 2475 - 1750

x = 725

The initial amount is $725.

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(1) The system of inequalities that can be used to represent this situation is 1.25x + 2y > 375  and x+y ≤ 500 .

(2) The least number of chocolate covered almonds that must be sold to cover the cost of attending Beta convention is 126 .

In the question ,

Part(1)

let the number of chocolates be "x" .

let the number of chocolates with covered almonds be "y"

price of each chocolate bar = $1.25

price of each chocolate covered almonds = $2

Beta club needs more than $375

So , according to the question

1.25x + 2y > 375

and also the students can sell up to 500 bars and covered almonds altogether.

So , x+y ≤ 500 .

Part(2)

Given , the club sells 100 chocolate bars.

substituting x= 100 in the inequality 1.25x + 2y > 375  , we get

1.25(100) + 2y > 375

125 + 2y > 375

2y > 375-125

2y > 250

y > 125

least number of chocolate covered almonds to be sold is 126 .

Therefore , (1) The system of inequalities that can be used to represent this situation is 1.25x + 2y > 375  and x+y ≤ 500 .

(2) The least number of chocolate covered almonds that must be sold to cover the cost of attending Beta convention is 126 .

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Answer:

Explanation:

To evaluate the difference:

First, rewrite the expression in the form below:

Next, factor out the powers of 10.

Thus, the difference written in scientific notation is:

Note: A number is in scientific notation if it is expressed as a product of a number (between 1 and 10) and a power of 10.

Answer: 3x-4

Step-by-step explanation: First Simplify, add the numbers 2x-9+x+5=2x-4+x Then combine like terms, 2x-4+x= 3x-4

√2 and -√3 belong to the set of Irrational Numbers.

1 belong to the following sets:

• Rational

• Whole

• Natural

• Integers

0 belongs to the following sets:

• Rational

• Whole

• Integers

Answer:

Negative Correlation:

Linear relationship

Explanation:

We can draw the line of best fit through the points given, and this indicates that the relationship is linear. Furthermore, the line of best fit has a negative slope (which tells us that if one variable increases, the other decreases); therefore, the data set has a negative correlation

Answer:

The answer is 8.27×10^4

Answer: 8.27×10^4

Step-by-step explanation:

Answer: -14

Step-by-step explanation:

[tex]\frac{1}{8}|x+6| \leq 1\\\\|x+6| \leq 8\\\\-8 \leq x+6 \leq 8\\\\-14 \leq x \leq 2[/tex]

Answer:

Rewrite using the commutative property of multiplication.

2

(

2

x

0

y

2

)

−

3

y

x

3

Anything raised to

0

is

1

.

2

(

2

⋅

1

y

2

)

−

3

y

x

3

Multiply

2

by

1

.

2

(

2

y

2

)

−

3

y

x

3

Rewrite the expression using the negative exponent rule

b

−

n

=

1

b

n

.

2

1

(

2

y

2

)

3

y

x

3

Simplify the denominator.

Tap for more steps...

2

1

8

y

6

y

x

3

Simplify terms.

x

3

4

y

5

The probability that the first card is a king and the second card is not a king is 0.0045

Suppose two cards are drawn sequentially so that one random circumstance is the result of the first card drawn and the second random circumstance is the result of the second card drawn. To find the probability that the first card is a king and the second card is not a king.

In the first case let's find the probability of drawing a king from the deck of cards,

A = ( 4/52 )

In the second case the probability of drawing a card that is not a king from the deck is,

B = ( 3/51 )

At last, to get the final probability to draw that the first card is a king and the second card is not a king we need to multiply the above two cases as,

A x B = ( 4/52 ) ( 3/51 )

         = 1/221

         = 0.0045

The probability that the first card is a king and the second card is not a king is 0.0045

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Order of the operations: parentheses, exponentials, division and multiplication, addition and subtraction.

1. Solve operations in parentheses:

2. Solve exponentials:

3. Solve division:

4. Solve multiplication:

5. Solve subtraction:

Answer: Answer is 20( please make me brainliest i just did this all in my head)

Step-by-step explanation: soo (14-2) =12  12divided by 3=4 so (2*3)= 6 so 4x6=24 24-2*2 =20 (2*2)=4 so 24-4=20 well this is confusing but i tried my best so hope my answer wasn't toooo confusing lol :)

The angle bisector theorem states that a triangle's opposite side is divided into two halves by an angle bisector that is proportional to the triangle's other two sides.

A point on a perpendicular bisector is equidistant from the endpoints of the segment it intersects, therefore if mACD = 90°, point D is equidistant from points A and B.

Any point on the perpendicular bisector is simply equal distance from both endpoints of the line segment on which it is drawn, according to the perpendicular bisector theorem.

The answer is that point  is equidistant from points A and B because a point on a perpendicular bisector is equidistant from the endpoints of the segment it makes up. Therefore, if a pillar is stationed at the middle of a bridge at an angle, all the points on the pillar will be equidistant from the end points of the bridge intersects.

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The values of the functions is  ,

(a) f(2) = -6

(b) f(4) = -2

(c) f(-3) = 19

In the question ,

it is given that the function is f(x) = x² - 4x - 2

we have to find the value of f(2) , f(4) , f(-3)

Part(a)

to find f(2) , we substitute x = 2 in the function

On substituting , we get

f(2) = 2² - 4*2 - 2

= 4 - 8 - 2

= 4 - 10

= -6

Part(b)

to find f(4) , we substitute x = 4 in the function f(x)

On substituting , we get

f(4) = 4² - 4*4 - 2

= 16 - 16 -2

= 0 - 2

= -2

Part(c)

to find f(-3) , we substitute x = -3 in the function

On substituting , we get

f(2) = (-3)² - 4*(-3) - 2

= 9 + 12 -2

= 9 + 10

= 19

Therefore , The values of the functions is  , (a) f(2) = -6  , (b) f(4) = -2 ,  (c) f(-3) = 19

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Speed of light = 300,000 km/sec

Rocket's speed = 63,000 km/hr or 6.3 x 10⁴ km/hr

Alpha Centauri distance from Earth = 4.11 x 10¹³ km

One light year (distance) = 9.46 x 10¹² km

To solve for the time it takes it travel, we can manipulate the speed formula.

We already have the distance of Alpha Centauri from Earth written above. We also have the speed of the rocket written above too. We will substitute those values to the formula.