round 67,103 and 1,273 to nearest hundred​

Answer:

Step-by-step explanation:

As RS is a straight line sin ∠RUT = sin ∠SUT

line UT bisects ∠RTS

Let θ be ∠UTR and ∠UTS

Law of sines

Left side triangle

3x/sinθ = 40/sinRUT

sinRUT = 40sinθ / 3x

Right side triangle

(x + 2) / sinθ = 16 / sinSUT

(x + 2) / sinθ = 16 / (40sinθ / 3x)

(x + 2)(40sinθ / 3x)  = 16sinθ

(x + 2)(40sinθ)  = 48xsinθ

40xsinθ + 80sinθ = 48xsinθ

40x + 80 = 48x

80 = 8x

x = 10

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:

d = 8

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Step-by-step explanation:

Step 1: Define

6d = 8(12 - 6)

Step 2: Solve for d

Answer:

\(Z = 3.33\)

Step-by-step explanation:

Z-score:

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

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

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question:

\(\mu = 13, \sigma = 1.2\)

You listen to the radio station for 1​ hour, at a randomly selected​ time, and carefully observe that the amount of advertising time is equal to 17 minutes. Calculate the​ z-score for this amount of advertising time.

We have to find Z when X = 17. So

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

\(Z = \frac{17 - 13}{1.2}\)

\(Z = 3.33\)

B

Step-by-step explanation:

because the figure is based on the graphic law

Answer:

Yes, any whole number (positive OR negative) is an integer

Hope this helps :)

Enseñanza Básica is the term used to describe the first level of education in the Chilean education system, which includes the first to eighth grades. A teacher of Enseñanza Básica asked his students to choose three-digit mixed numbers that can be formed.

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The difference between the greatest and the least mixed numbers is 9.87 - 6.0789 ≈ 3.7911.

The three digits different from {1, 2, 3, 4, 5} can be chosen from {0, 6, 7, 8, 9}.

The greatest mixed number is formed by placing the largest digit as the whole number and the remaining two digits as the fraction in descending order, i.e., 9 87/100 or 9.87.

The smallest mixed number is formed by placing the smallest non-zero digit as the whole number and the remaining two digits as the fraction in ascending order, i.e., 6 07/90 or 6.0789.

The difference between the greatest and the least mixed numbers is 9.87 - 6.0789 ≈ 3.7911.

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The Question in English

A Basic Education teacher tells his students to choose three digits

different from the set {1, 2, 3, 4, 5} and form mixed numbers by placing the digits

in the locker It also reminds them that the fractional part has to be

less than 1, for example

2

3

5

. What is the difference between the greatest and the least of the

mixed numbers that can be formed?

The loss percentage is 91%.Given that Venessa bought 80 apples for 4$, out of these apples, 25% were rotten and had to be thrown away. Venessa sold the remaining apples at 6 cents per apple.To calculate the profit or loss percentage, we need to determine the cost price, selling price, and the number of apples sold.

Cost price (CP) = 4 $.Selling price (SP) = 80 × 0.75 × 6 cents= 36 cents = 0.36 $.Now, let's calculate the profit.Profit = SP – CP= 0.36 $ – 4 $= – 3.64 $Loss = CP – SP= 4 $ – 0.36 $= 3.64 $.

Therefore, Venessa incurred a loss of $3.64 when she sold 80 apples at 6 cents per apple.Now let's calculate the loss percentage Loss Percentage = (Loss / CP) × 100= (3.64 / 4) × 100= 91%.

Therefore, the loss percentage is 91%.Note: If the result obtained after the subtraction of SP from CP is negative, it means there is a loss, and the percentage of loss can be calculated by (loss/CP) × 100.

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The alternate interior angles theorem states that, when two parallel lines are cut by a transversal, the resulting alternate inferior angles are congruent.

In this case:

The nth term of the given sequence is 4n - 1.

So,

Therefore, the nth term of the given sequence is 4n - 1.

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Answer:

?=8

Step-by-step explanation:

I substituted the ? for x

-3=x-11

first we want to isolate the x to do that, you have to find a way to move -11 to the other side. Well, x+0=x right? So all we have to do is find a way to go from -11 to 0! In this case you add 11 to both sides. This is very important so don't forget.

-3=x-11

+11    +11

-3+11=8

x=8

If you check your work, this should also go back in perfectly.

-3=8-11

or

-3=-11+8

I hope this helps!

Have a good day!

The model predicts a negative population (-843) if the hunting season lasts the entire year.

To find the maximum amount of deer predicted by the quadratic model, we need to determine the vertex of the quadratic function. The vertex of a quadratic function in the form of \(y = ax^2 + bx + c\) can be found using the formula x = -b / (2a). In this case, the quadratic model is \(P = -10h^2 + 30h + 237.\)

Using the formula, we can calculate the value of h at the vertex:

\(h = -30 / (2\times(-10)) = 1.5\)

Substituting this value back into the equation, we can find the maximum population of deer:

\(P = -10(1.5)^2 + 30(1.5) + 237\\P = -22.5 + 45 + 237\\P = 259.5\)

Therefore, the model predicts that the maximum population of deer would be 259.5 at the end of the year if the hunting season duration is optimized based on the quadratic model.

If the government allowed year-round hunting, we can assume the hunting season duration (h) would be 12 months. Substituting this value into the equation, we can find the predicted population of deer:

\(P = -10(12)^2 + 30(12) + 237\\P = -1440 + 360 + 237\\P = -843\)

However, in practical terms, a negative population is not meaningful. It suggests that the quadratic model might not accurately represent the population dynamics in the case of a year-round hunting season. This could be due to various factors, such as migration patterns, breeding habits, or the influence of other ecological factors not considered in the model.

Further research and data analysis would be needed to develop a more accurate model or understand the population dynamics under different hunting scenarios.

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Answer:

√38

Step-by-step explanation:

√38

step 1: Check which squared numbers can be multiplied by another number to get 38.

Start with these numbers: 4, 9, 16, and 25

Step 2: Testing out the numbers

√25 × __ = 25 can't be divided by 38

√16 × ___ = 16 can't be divided by 38

√9 × ____ = 9 can't be divided by 38

√4 × ____= 4 can't be divided by 38

Step 3: Answer

After trying the square root numbers that could possibly work with √38 none work; which means √38 can't be simplified. So the answer is √38

I hope this helps!

Solution :

Given data :

Total number of books sold each month= 700

The charts in the display attached below shows the most popular books category by percentages.

Percentage of romance books sold each = 8.5%

Therefore, the number of romance books sold in each month is given by :

\($=8.5 \% \text{ of }\ 700$\)

\($=\frac{8.5}{100}\times 700$\)

= 59.5

≈ 60 books (rounding off)

You can use the fact that total amount is taken as 100%.

The number of romance books in the given Streets Books is 60

Suppose the value of which a thing is expressed in percentage is "a'

Suppose the percent that considered thing is of "a" is b%

Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).

Thus, that thing in number is \(\dfrac{a}{100} \times b\)

Since the total amount of books is 700, and its 8.5% books are romance books, thus we have:

\(\text{Number of Romance books} = \dfrac{700}{100} \times 8.5 = 59.5 \approx 60\)

The number of romance books in the given Streets Books is 60

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y-intercept: (0, -4)

x-intercept: (0, 2)

Sorry if this wasn't what you were asking for, I'm not sure if I understood your question correctly. I don't know if you asking just to graph it or if you were asking for the x and y intercepts too, along with the graph. Either way, hope this helped!

Answer: 9

Step-by-step explanation:

took the k12 quiz

Answer:a box and whisker plot

Step-by-step explanation:

Just took the quiz

Answer:

(4 2/7) x (11 1/4) = 48 3/14

Step-by-step explanation:

6.928 units is the apothem of a hexagon with a radius of 8.

The apothem of a regular hexagon is the distance from the center to the midpoint of a side. For a regular hexagon with a radius of 8, the apothem can be found using the formula:

apothem = radius x √3/2

Substituting the given value of the radius, we get:

apothem = 8 x √3/2

apothem = 8 x 1.732/2

apothem = 6.928

Therefore, the apothem of the hexagon is 6.928 units.

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Answer:

For the points (0, 0) and (5, 3), the numerical expression 3 − 0 gives the rise and the numerical expression 5 − 0 gives the run.

Step-by-step explanation:

Answer:

Starting with the point on the left, sketch a right triangle, going from the first point to the second point.

Step-by-step explanation:

Answer:

n = 2

Step-by-step explanation:

Since ∆A is similar to ∆B, therefore, the ratio of their corresponding sides would be equal.

Thus:

\( \frac{10}{n + 2} = \frac{6}{3} \)

\( \frac{10}{n + 2} = 2 \)

Multiply both sides by (n + 2)

\( \frac{10}{n + 2}(n + 2) = 2(n + 2) \)

\( 10 = 2n + 4 \)

Subtract 4 from each side

\( 10 - 4 = 2n + 4 - 4 \)

\( 6 = 2n \)

Divide both sides by 2

\( \frac{6}{2} = \frac{2n}{2} \)

\( 3 = n \)

n = 2

For the given equation, the values of X and Y are X=4 and Y=-2, respectively.

What is equation?

In mathematics, an equation is a statement that asserts the equality of two expressions. It consists of two expressions separated by an equal sign (=).

To find the values of X and Y, we need to separate the real and imaginary parts of the complex number on the right-hand side of the equation.

We have:

X + Yi = 3Y - 2Xi + 4i

Separating the real and imaginary parts, we get:

X = -2Y + 0

Y = 3Y + 4

Simplifying the second equation, we have:

-2Y = 4

Dividing by -2, we get:

Y = -2

Substituting this value of Y into the first equation, we have:

X = -2(-2) = 4

Therefore, the values of X and Y are X=4 and Y=-2, respectively.

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Answer:

G and J

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

Notice: we do not have to solve for x, and y. All we really have to do is to subtract the two equations.

(-10x + 3y) - (-4x + 7y) = 9 - 1.

Taking off the parentheses, we get:

-10x + 3y + 4x - 7y = 8.

Simplifying, we get:

-6x - 4y = 8.

So, the answer is 8.

The value of the mutual fund of Tom after 15 deposits will be $5197.320   .

In the question ,

it is given that , Tom invested $2500 in mutual fund for 15 years ,

So,

the investment amount(P) = $2500 .

time for investment(x) = 15 years

rate of increase(r) = 5% = 0.05

The amount of fund  after 15 deposits can be calculated using the formula

amount = P*(1+r)ˣ

Substituting the values of  P, x and r , we get

amount = 2500*(1 + 0.05)¹⁵

= 2500*(1.05)¹⁵

= 5197.320

Therefore , The value of the mutual fund of Tom after 15 deposits will be $5197.320   .

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Answer:

Step-by-step explanation:

the estimated time to lay the shingles and underlayment

The Estimation cost of the shingles chosen for the roof.

Estimation cost is the process of predicting how much a project or task will cost. It is used to help make decisions about the feasibility of the project and to plan for its budget. Estimation cost is based on past experiences, the current market and expected future conditions. The accuracy of an estimate can be improved by gathering detailed information about the project and its components. This information can include the cost of materials, labor and time needed to complete the project. Estimation cost is an important part of project management and is used in combination with other project management tools and methods such as scheduling, budgeting and risk management.

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The time take to fill the pool will be 494 hours.

Inlet pipe fills in  38 hours = 1 pool

Inlet pipe fills in 1 hours = 1/38

Drain pipe empty in 39 hours = 1 pool

Drain pipe empty in 1 hour = 1/39

If both pipes are opened together then in pool fills in 1 hour =  1/38 - 1/39

= 1/1482

Therefore, 1/1482 fills in 1 hour.

. Therefore, 1/3 will be:

= 1/3 × 1482

= 494 hours.

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Answer:

52

Step-by-step explanation:

(2x3 = 6

4x5 = 20)

(6+20) = (26)

(26)2 = 52

=52