Fine the volume of each rectangular prism.

1 1/2 in. 1 1/2 in. 1 1/2 in.

Answer:

Step-by-step explanation:

In the Intermediate Phase of mathematics education, one topic that demonstrates a hierarchical and logical progression in patterns, functions, and algebra is the concept of "Linear Equations."

The topic of Linear Equations in the Intermediate Phase builds upon the foundation laid in earlier grades and serves as a stepping stone towards more advanced algebraic concepts. Here is an overview of the topic sequence and content area spread for Linear Equations:

Introduction to Variables and Expressions:

Students are introduced to the concept of variables and expressions, learning to represent unknown quantities using letters or symbols. They understand the difference between constants and variables and learn to evaluate expressions.

Solving One-Step Equations:

Students learn how to solve simple one-step equations involving addition, subtraction, multiplication, and division. They develop the skills to isolate the variable and find its value.

Solving Two-Step Equations:

Building upon the previous knowledge, students progress to solving two-step equations. They learn to perform multiple operations to isolate the variable and find its value.

Writing and Graphing Linear Equations:

Students explore the relationship between variables and learn to write linear equations in slope-intercept form (y = mx + b). They understand the meaning of slope and y-intercept and how they relate to the graph of a line.

Systems of Linear Equations:

Students are introduced to the concept of systems of linear equations, where multiple equations are solved simultaneously. They learn various methods such as substitution, elimination, and graphing to find the solution to the system.

Word Problems and Applications:

Students apply their understanding of linear equations to solve real-life word problems and situations. They learn to translate verbal descriptions into algebraic equations and solve them to find the unknown quantities.

The content area spread for Linear Equations includes concepts such as variables, expressions, equations, operations, graphing, slope, y-intercept, systems, and real-world applications. The progression from simple one-step equations to more complex systems of equations reflects a logical sequence that builds upon prior knowledge and skills.

By following this hierarchical progression, students develop a solid foundation in algebraic thinking and problem-solving skills. They learn to apply mathematical concepts and procedures in a systematic and logical manner, paving the way for further exploration of patterns, functions, and advanced algebraic topics in later phases of mathematics education.

Answer:

Banks charge fees to help make a profit.

Step-by-step explanation:

Bank fees allow financial institutions to recoup operating expenses. Banks also make money on loans, via interest and other fees.

f(x) = 5x²- 2

To calculate f(2) replace the value of x by 2:

f(2)= 5(2)^2-2

f(2)= 5(4)-2

f(2)= 20-2

f(2)= 18

Answer:

False

Step-by-step explanation:

10x3=30

30-20=10

10=20

These equations dont match.

Hence, the equation is false

Answer: This equation is FALSE. The left side 10 does not equal to the right side which is 20.

Step-by-step explanation:

Answer:

.77

Step-by-step explanation:

the 7 is repeating so you can put a dash above the second 7

Answer:

(x + i) (x - i)

Step-by-step explanation:

The expression x^2 + 1 is a sum of squares, which means that it cannot be factored using real numbers. However, it can be factored using complex numbers.

To factor x^2 + 1, we can use the fact that i^2 = -1, where i is the imaginary unit.

We can rewrite x^2 + 1 as:

x^2 + 1 = x^2 - (-1)

Now, we can use the difference of squares formula to factor x^2 - (-1):

x^2 - (-1) = (x + i)(x - i)

Therefore, the factored form of x^2 + 1 is:

(x + i)(x - i)

Answer:

9, 18, 27, 54, 63.

Step-by-step explanation:

A composite number has factors other than 1 and itself.

For example 6 = 2 * 3.

y = 2 sin x cos x

dy/dx =

2[sin x . d (cos x)/dx + cos x . d(sin x)/dx]

dy/dx = y' =

2[ sin x . (-sin x) + cos x . cos x]

y' = 2 [cos² x - sin² x]

y' = 2 cos 2x [cos²x - sin²x = cos 2x]

Hence, option C is correct!

Hope it helps...!!

Answer:

Nobody would save the most money. This is because everyone chipped in the same amount.

Step-by-step explanation:

Kala spun the spinner 1000 times and got the following results:

- Yellow: 400 times

- Red: 300 times

- Blue: 300 times

1. Calculate the amount of sales tax:

  - The item costs $350 before tax.

  - The sales tax rate is 14%.

  - To find the sales tax amount, multiply the cost of the item by the tax rate:

    Sales tax = $350 * 0.14 = $49.

2. Determine the total cost of the item including tax:

  - Add the sales tax amount to the original cost of the item:

    Total cost = $350 + $49 = $399.

3. Analyze the spinner results:

  - The spinner has 10 equal-sized slices.

  - There are 4 yellow slices, 3 red slices, and 3 blue slices.

  - Kala spun the dial 1000 times.

4. Calculate the frequency of each color:

  - Yellow: Kala got 400 yellow results out of 1000 spins.

  - Red: Kala got 300 red results out of 1000 spins.

  - Blue: Kala got 300 blue results out of 1000 spins.

5. Calculate the probability of landing on each color:

  - Yellow: Probability = Frequency of yellow / Total spins = 400 / 1000 = 0.4.

  - Red: Probability = Frequency of red / Total spins = 300 / 1000 = 0.3.

  - Blue: Probability = Frequency of blue / Total spins = 300 / 1000 = 0.3.

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Answer:

1/6 that's the answer

Step-by-step explanation:

so you do 43/6-7=43/6-42/6=1/6

Answer:

Actually the answer is -⅙

Step-by-step explanation:

43/6 written differently is 7 ⅙, because the fraction 42/6 is the same as 7 (42÷6=7). But since your number is 43/6 you get

7 1/6.

your original number is larger than 7 but the question was what number you have to "add" to get to 7. so they number has to be a negative number.

like this:

43/6 + (-1/6) = 42/6. which you rewrite now as

43/6 - 1/6 = 42/6. and I explained that 42/6 is the same as 7.

Answer:

X= 2, -5

Step-by-step explanation:

Take the root of both sides

Answer:

-5

Step-by-step explanation:

The fence in dead center is about 399 feet from the third base.

The Pythagorean Theorem states that in the case of a right triangle, the square of the length of the hypotenuse, which is the longest side,  is equals to the sum of the squares of the lengths of the other two sides.

Hence the equation for the theorem is given as follows:

c² = a² + b².

In which:

For the triangle in this problem, we have that:

Hence the distance is obtained as follows:

d² + 90² = 409²

\(d = \sqrt{409^2 - 90^2}\)

d = 399 ft.

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Proportionately, the dollar amount of the Gentrys' annual transportation and taxes combined is $11,004.70.

Proportion refers to the relative value of a number compared to another amount.

Proportions are ratios equated to one another.

Multiplying the proportional percentage of the combined transportation and taxes to the total budget of the Gentrys gives the dollar amount.

Yearly income for the Gentrys = $29,742.42

Percentage of income that is taxes = 28%

Percentage of income that is transportation = 9%

Combined percentage of taxes and transportation = 37% (28 + 9)

Combined transportation and taxes in dollars = $11,004.70 ($29,742.42 x 37%)

Thus, based on their proportional percentages, the Gentrys' combined annual transportation and taxes are $11,004.70.

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1) The probabilities are given as follows:

a) More than 75: 0.0301 = 3.01%.

b) Between 60 and 73: 0.4484 = 44.84%.

c) Less than 50: 0.1057 = 10.57%.

2) The proportion of students who fail the module is of: 0.0062 = 0.62%.

3) The measures are given as follows:

The z-score of a measure X of a variable that has mean symbolized by \(\mu\) and standard deviation symbolized by \(\sigma\) is obtained by the rule presented as follows:

\(Z = \frac{X - \mu}{\sigma}\)

The mean and the standard deviation in this problem are given as follows:

\(\mu = 60, \sigma = 8\)

The probability that an score is more then 75 is one subtracted by the p-value of Z when X = 75, hence:

Z = (75 - 60)/8

Z = 1.88

Z = 1.88 has a p-value of 0.9699.

1 - 0.9699 = 0.0301 = 3.01%.

The probability of an score between 60 and 73 is the p-valeu of Z when X = 73 subtracted by the p-value of Z when X = 60, hence:

Z = (73 - 60)/8

Z = 1.63

Z = 1.63 has a p-value of 0.9484.

Z = (60 - 60)/8

Z = 0

Z = 0 has a p-value of 0.5.

Then:

0.9484 - 0.5 = 0.4484 = 44.84%.

The probability of an score less than 50 is the p-value of Z when X = 50, hence:

Z = (50 - 60)/8

Z = -1.25

Z = -1.25 has a p-value of 0.1057.

The proportion who might fail the test is the p-value of Z when X = 40, hence:

Z = (40 - 60)/8

Z = -2.5

Z = -2.5 has a p-value of 0.0062.

Then the statistical measures are obtained as follows:

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Answer: Themba needs a total of 7.5  cups of yogurt to make 5 bowls of fruit dip, so 0.75 cup(s) will be needed

Step-by-step explanation:

your welcome.

The algebraic expression for the given phrase is: 45 - 2n.

What is algebraic expression ?

An algebraic expression is a mathematical phrase that consists of variables, constants, and operators, but does not have an equal sign. Algebraic expressions are used to represent a wide range of mathematical concepts and relationships, and are commonly used in algebra, calculus, and other branches of mathematics. Examples of algebraic expressions include "3x + 4y," "2a - b/5," and "\(7x^2 + 2x - 1\)."

According to the question:

The phrase "45 decreased by twice a number" can be translated into the algebraic expression:

45 - 2n

The variable n represents the unknown number. The expression is formed by taking twice the value of n (2n) and subtracting it from 45. This expression can be simplified by performing the subtraction to get:

45 - 2n = -2n + 45

This represents a linear function where the output (or value of the expression) depends on the input (the value of n). For example, if n = 5, then the expression would evaluate to:

-2(5) + 45 = 35

If n = 10, then the expression would evaluate to:

-2(10) + 45 = 25

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Answer:

AC+ CD = ACD

X+1 + 2X + 2 = 30

3X+3 =30

3X=30–3

3X=27

X= 27/ 3

X= 9

I'm not sure of the solution, but I solved it according to a straight line (Line segment) .

I hope I helped you^_^

Answer:

it's exchanging values of x and y

Answer:

44

Step-by-step explanation:

Answer: 4(p - 7) = 44

First distribute the 4 over the parentheses

4p - 28 = 44

Add 28 to both sides:-

4p = 44 + 28

4p = 72

Divide both sides by 4:-

p = 72/4

p = 18

Answer:

55 full bags

Step-by-step explanation:

Answer:

55 bags

Step-by-step explanation:

Answer:

Yes, No, No, Yes

Step-by-step explanation:

The perfect squares are

Step-by-step explanation:

1.

\( \sqrt{25} \\ \sqrt{ {5}^{2} } \\ = 5\)

2.

\( \sqrt{2} = 1.41421 \\ \)

3.

\( \sqrt{99} \\ = \sqrt{9 \times 11} \\ = \sqrt{ {3}^{2} \times 11 } \\ 3 \sqrt{11} \)

4.

\( \sqrt{100} \\ = \sqrt{10 \times 10} \\ = \sqrt{ {10}^{2} } \\ = 10\)

The total area of the three triangles is square units is 36 and the area of the figure is square units is 60.

The triangle can be defined as a three-sided polygon in geometry, and it consists of three vertices and three edges. The sum of all the angles inside the triangle is 180°.

From the figure, the area of triangles can be calculated using the:

Area = (1/2)height×base length

Area of three triangle = 1/2(4×6) + 1/2(6×4) + 1/2(4×6)

Area of three triangle = 1/2(24×3) = 36 square units

Area of the figure = area of three triangle + area of the rectangle

= 36 + 6×4

= 60 square units

Thus, the total area of the three triangles is square units is 36 and the area of the figure is square units is 60.

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The additive inverse of the polynomial is +7y²-x²y+3xy+7x².

The additive inverse can be defined as when we add a number to some number and get result as zero.

Given polynomial:

-7y²+x²y-3xy-7x²

As, the value of additive inverse is same as of the number but the sign of the additive inverse is opposite.

So,

=  +7y²-x²y+3xy+7x²

Check:

-7y²+x²y-3xy-7x² + 7y²-x²y+3xy+7x²

= -7y²+  7y² +x²y -x²y -3xy +3xy -7x² +7x²

=0

Hence, the additive inverse of the polynomial is +7y²-x²y+3xy+7x².

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The equations of the composite functions are (h o h)(x) = (x² + 3)² + 3 and (f o f)(x) = x

From the question, we have the following equations that can be used in our computation:

h(x) = x² + 3

f(x) = 3/4x

From the above, we have

(h o h)(x) = h(h(x))

So, we have

(h o h)(x) = (x² + 3)² + 3

Also, we have

(f o f)(x) = 3/[4(3/4x)]

Evaluate

(f o f)(x) = x

Hence, the composite functions are (h o h)(x) = (x² + 3)² + 3 and (f o f)(x) = x

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Answer:-1.25

Step-by-step explanation: First you add -3 and -7 it is -10/8 then you devide -10/8 and it is -1.25

The answers are:

27. P(6) = 0.2 , 28. P(even number) = 0.6 , 29. P(6) = 1/10 , 30. P(even number) = 5/10 = 0.5

The experimental probability of getting a 6 is 0.2, because 2 out of 50 displays were 6s.

The experimental probability of getting an even number is 0.6, because 30 out of 50 displays were even numbers.

The theoretical probability of getting a 6 is 1/10, because there is 1 chance out of 10 that the calculator will display a 6.

The theoretical probability of getting an even number is 5/10, because there are 5 chances out of 10 that the calculator will display an even number.

As you can see, the experimental probabilities are close to the theoretical probabilities. This is because the calculator was programmed to randomly display a digit from 0 to 9, so the results should be evenly distributed. However, there is always some chance of variation, so the experimental probabilities may not be exactly equal to the theoretical probabilities.

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