Round the numbers to the highest place value.

2 398-
56 254-
71 563-
33 021-
9 645-​

Answer:

Step-by-step explanation:

The surface area of a rectangular prism calculator gives us the answer: A = 2 * l * w + 2 * l * h + 2 * w * h = 2 * 8 ft * 6 ft + 2 * 8 ft * 5 ft + 2 * 6 ft * 5 ft = 236 ft² .

Answer:

074°

Step-by-step explanation:

the bearing of Y from X is the measure of the angle from the north line (N) at X in a clockwise direction to Y , that is ∠ NXY

∠ NXY = 180° - 106° = 74°

the 3- figure bearing of Y from X is 074°

Answer:

Clark can type 40 words in one minute

Step-by-step explanation:

I hope this helps!

Answer:

3. a. 10:35= 2:7

b.35:45=7:9

c.40:50=4:5

a) The height of the cuboid is; 5 cm

(b) The volume of metal not used in making these spheres is; 172.5 cm³

The volume of a cuboid is the space that is enclosed within a cuboid. For example, in order to fill water in an aquarium, we must know its volume.

The volume of a cuboid is found by multiplying the length by the breadth by the height.

The formula for the volume of a cuboid is;

V = l * w * h

Where;

l is length

w is width

h is height

a) We are given;

Volume = 600 cm³

Length = 12 cm

Width = 10 cm

Thus;

Height = 600/(12 * 10)

Width = 5 cm

b) Formula for volume of a sphere is;

V = ⁴/₃πr³

where r is radius

Thus;

V = ⁴/₃ * π * 0.45³

V = 0.3817 cm³

Volume of 1120 spheres = 1120 * 0.3817 cm³ = 427.5 cm³

Volume of metal not used = 600 - 427.5 = 172.5 cm³

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Answer:

8 of the 11

Step-by-step explanation:

4+4=8 of the 11

Part of oranges usef from the orange packet used on 1st day = 4/11

Part of oranges used from the orange packet used on 2nd day = 4/11

Total part of oranges used from the orange packet

= (4/11) + (4/11)

= 8/11

So, Sipho's dad used 8 elevenths of the oranges.

The measure of angle B is approximately equal to 56.31 degrees, rounded to two decimal places.

An angle measure is a numerical value that represents the amount of rotation between two intersecting lines, line segments or rays. It is typically measured in degrees, although other units of measurement such as radians and grads may also be used. The size of an angle can range from 0 degrees (corresponding to no rotation or a straight line) to 360 degrees (corresponding to a full rotation). In geometry, angles are used to describe the relationships between lines and shapes, and are an important concept in fields such as trigonometry and calculus.

To find the measure of angle B given cot B = 0.57736, we can use the inverse tangent function.

The tangent of an angle is the ratio of the opposite side to the adjacent side,

So cot B = adjacent side / opposite side.

By taking the inverse tangent of both sides and substituting cot B for adjacent side / opposite side, we arrive at the equation

B = arctan(cot B).

Evaluating arctan(cot B) using a calculator gives us the measure of angle B as,

B = arctan(cot B) = 56.31° (rounded to two decimal places)

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The complete question is: "Given cot B = 0.57736, determine the measure of angle B".

Answer:

a = 3

Step-by-step explanation:

ok so first you do the reciprocal of division which is multiplication. So its gonna be 3/4 x 1/a = 1/4

you multiply the fractions 3/4 x 1/a and get 3/4a = 1/4

then you cross multiply and you get 12=4a

swap sides so its going to be 4a = 12

divide both sides by 4 and you get a = 3

You would expect to pay $90 each month for electricity based on an average usage of 120 KWHs per month.

To calculate the monthly cost of electricity, you can multiply the average number of kilowatt-hours (KWH) used per month by the cost per KWH.

Given:

Cost per KWH: $0.75

Average monthly usage: 120 KWHs

To find the monthly cost, you can multiply the cost per KWH by the average monthly usage:

Monthly Cost = Cost per KWH * Average monthly usage

Plugging in the values, we have:

Monthly Cost = $0.75/KWH * 120 KWHs

Calculating the result:

Monthly Cost = $90

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Answer:

9

Step-by-step explanation:

You don't need to pass through each edge once.

If we name the top vertex 1 and the bottom vertex 2 then here are the possible combinations:

A-1-B

A-B

A-2-B

A-1-B-A-2-B

A-2-B-A-1-B

A-B-1-A-2-B

A-B-2-A-1-B

A-1-B-2-A-B

A-2-B-1-A-B

Some people say 6 because they think you need to pass through all the edges. But the only restriction with travelling on the edges is you can't pass one twice. The point is read the wording and it becomes easy.

Hope this helps!

Answer:

27 and 28

Step-by-step explanation:

x+x+1=55

2x+1=55

2x=55-1

2x=54

divide each side by 2

x=27

x+1=28

check your answer adding the two integers

27+28=55

Answer:

2/3

Step-by-step explanation:

1 and 2 are taken away, therefore you have 3, 4, 5, and 6 left as options to roll. So the answer is 4/6 since there's 4 numbers, but simplified it's 2/3.

Answer:

There are six possible outcomes when rolling a die, each of which is equally likely. Of these six outcomes, three are greater than 2 (3, 4, 5) and three are not (1, 2, 6). Therefore, the odds in favor of rolling a number greater than 2 are 3 to 3, or simply 1 to 1. Alternatively, we could express this as a probability: the probability of rolling a number greater than 2 is 3/6, or 1/2, since there are three favorable outcomes out of a total of six possible outcomes.

Step-by-step explanation:

Answer:

Height of rectangle = 5x feet

Step-by-step explanation:

Given:

Area of rectangle = 10x² feet

Base of rectangle = 2x feet

Find:

Height of rectangle

Computation:

Area of rectangle = Length x width

Area of rectangle = Base of rectangle × Height of rectangle

10x² = 2x × Height of rectangle

Height of rectangle = 10x² / 2x

Height of rectangle = 10x / 2

Height of rectangle = 5x feet

Answer:

All the correct statements are,

The vertex of the graph is (5, -37).

The parabola has a minimum.

The parabola opens up.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The function g(x) = 10x² - 100x + 213 written in vertex form is,

⇒ g(x) = 10(x – 5)² – 37.

Since, General equation is,

y = a (x - h)² + k

Where, (h, k) is vertex of parabola.

Hence, We get;

The vertex of the graph is (5, -37)

Since, the coefficient of x² is positive

Hence, The parabola has a minimum

And, The parabola opens up.

Thus, All the correct statements are,

The vertex of the graph is (5, -37).

The parabola has a minimum.

The parabola opens up.

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Answer:

13 cm

Step-by-step explanation:

We can use the Pythagorean Theorem to find the length of the hypotenuse. The Pythagorean Theorem is used to find a missing side to a right triangle.

The theorem states that \(a^2 + b^2 = c^2\), where a and b are the legs, and c is the hypotenuse.

The legs of this triangle are already states - 5 and 12, so we can plug it's values into the formula.

\(5^2 + 12^2 = c^2\\\\25 + 144 = c^2\\\\169 = c^2\\\\c = \sqrt{169}\\\\c=13\)

So the hypotenuse of this triangle is 13 cm.

Hope this helped!

Answer:

-64/5

Step-by-step explanation:

Basically, the word "quotient" means the answer to a division problem. Therefore, its a division problem, so you have to work backwards with multiplication. -8 times a number is 5/8, so the other number is going to be negative.

The number is -64/5

Answer:

n = -5

Step-by-step explanation:

Form this quotient, representing the number by n:  n / (-8) = 5/8.

Solve this equation for n by multiplying both sides by 8:  -n = 5.  Then n = -5

a. The interval of time between eruptions if the previous eruption lasted 4 minutes is 86.51 minutes.

b. The residual for this cycle is 2.07 minutes.

c. The interval of time between eruptions lasted for 2.07 minutes than the regression line equation predicted.

d. The slope of the regression line means that the interval of time between eruptions increases by 13.29 minutes for every additional minute of the previous eruption.

e. No, the value of the y-intercept doesn't have meaning in the context of the problem.

Based on the information provided above, the relationship between the duration of the previous eruption (x in minutes) and the interval of time between eruptions (y in minutes) is modeled by this regression line equation:

ÿ = 33.35 + 13.29x

Part a.

When x = 4 minutes, the value of is given by:

ÿ = 33.35 + 13.29(4)

ÿ = 86.51 minutes.

Part b.

The residual for the given cycle can be calculated as follows;

Residual = y - ÿ

Residual = 62 - (33.35 + 13.29(2))

Residual = 62 - 59.93

Residual = 2.07 minutes.

Part c.

Based on the calculation above, we can logically deduce that the interval of time between eruptions lasted for 2.07 minutes than the equation of regression line predicted.

Part d.

The slope of the regression line is equal to 13.29 and it implies that the interval of time between eruptions increases by 13.29 minutes for every additional minute of the previous eruption.

Part e.

In the context of the problem, we can logically deduce that the value of the y-intercept doesn't have any meaning because the duration of the previous eruption cannot be equal to 0 minutes.

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Answer:

\(\\(x- -1)^{2} + (y- -1)^{2} = 13\)

so, -1, -1 and 13

Answer:

C

Step-by-step explanation:

cot²θ = 1/tan²θ

plug this in to get

1/(1/tan²θ + 1)

1/tan²θ + 1 = 1/tan²θ + tan²θ/tan²θ = (1+tan²θ)/tan²θ

we then have

1/((1+tan²θ)/tan²θ)

1/(x/y) = y/x, so this is equal to

tan²θ/(1+tan²θ)

tan²θ = sin²θ/cos²θ, so plug this in to get

(sin²θ/cos²θ)/(1+sin²θ/cos²θ)

1+sin²θ/cos²θ = cos²θ/cos²θ + sin²θ/cos²θ

sin²θ + cos²θ = 1, so we have

(cos²θ+sin²θ)/cos²θ = 1/cos²θ. plug this in to get

(sin²θ/cos²θ)/(1/cos²θ)

(a/b)/(c/d) = (d/c) * (a/b), so we have

(sin²θ/cos²θ)/(1/cos²θ)  = cos²θ/1 * sin²θ/cos²θ = sin²θ

ES LA B

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

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.

The exponential function will be equal to y = 20ˣ.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Carter shared his post with 10 friends, who each share with only 2 people each day.

The exponential function will be written as,

y = abˣ

y = 10(2)ˣ

y = 20ˣ

Therefore, the exponential function will be equal to y = 20ˣ.

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Answer:

f(x) = 10(2)^x

Step-by-step explanation:

Rule for solving: The first number is the first part of the equation, and the second number is in parenthesis.

The constant differences between the consecutive terms are 2 (a); 2 (b), -3 (c), 7 (d), 1(e), and 6(f).

In math, the constant difference can be defined as the number that defines the pattern of a sequence of numbers. This means that number that should be added or subtracted to continue with the sequence.

Due to this, to determine the constant difference it is important to observe the pattern and find out the number that should be added. For example, if the sequence is 2, 4, 6, 8, there is a difference of 2 between each of the numbers and this is the constant difference.

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we have the expression

In the exponential form we have

in the given problem

y represents the base of the exponential equation

r represents the exponent of the base

a is the result of the base elevated to the exponent

general form

If you have

Answer: Solving two-step linear equations using distributive property: a (x+b)=c;aleft ( {x + b} ight) = ca (x+b)=c Solving linear equations using multiplication and division Solving two-step linear equations: ax+b=cax + b = cax+b=c, xa+b=c {x over a} + b = cax​+b=c

Step-by-step explanation:

Answer:

solving equations using distributive property. We'll guide you through two ways that the following question can be solved.

Question: 11.32 = 8(0.61 + x)

Solution 1:

11.32 = 8(0.61+x)

Divide both side by 8, you get 1.415 = 0.61 +x

Minus both side by 0.61, 0.805 = x

In this solution, we first try to move all the non-x terms over to one side. The first step of dividing both sides by 8 helps us move the 8 from the right side to the left side. This allows us to get rid of the parentheses too as the terms no longer have to be multiplied out (there's nothing to multiply them with). Then, in order to move 0.61 to the left side, we'll minus it from both sides. In the end, we'll get that x ultimately equals 0.805.

Solution 2:

11.32 = 8(0.61+x)

Open up the right side, you get 11.32 = 4.88+8x

Minus both side by 4.88, you get 6.44 = 8x

Divide both side by 8, you get 0.805 = x

In solution 2, we're truly using the distributive property. We're going to distribute 8 into the terms in the parentheses, which are "+0.61" and "+x". This gives us 4.88 + 8x on the right side of the equation. Then we can move over 4.88 to the left side with the rest of the non-x terms by minusing it from both sides. Lastly, divide both sides by 8 to move the 8 over to the left side and you'll find that x = 0.805. Both methods will bring you to the same correct answer.

it would be option D

Answer:

c. 42 1/12

Step-by-step explanation:

sorry if it's wrong. this was an educated guess