25% of the students in a school are in sixth grade.A. How many sixth graders are there if the school has160 students?B. How many sixth graders are there if the school has28 students?C. If the school has x students, write an expression for the number of sixth graders in terms of x. D. How many students are in the school is 42 of them are sixth graders.

Answer:

The answer is the first option

Step-by-step explanation:

Tan is opposite over adjacent

so its 24/10

simplify

12/5

hope this helped

The equations of the two lines are y=2 (the horizontal one) and y=x (the diagonal line).

The region is 'under' y=x without including such line, and 'above' y=2 without including that line.

Therefore, the system of inequalities whose solution is the shaded region is

Answer:

tan y = a/b = 1

(.tan 45° = 1)

a=b

Areas a=1/2 a * b = 1/2 =1/2 * 7√2 * 7√2 cm

b = 7√2 cm

= 49cm²

Step-by-step explanation:

12 words is 3/4 or 75% of the list

How many words are=

Find 100- 75=25%

25%= 1/4 = 3/4÷3

Then divide 75%/3= 12/3= 4

Now add 12words + 4 words = 16 words

Then answer is, there are 16 words

The Equivalent numbers are

5.812 × 10⁻⁷ and 0.0000005812

5.46 × 10¹¹ and 546,000,000,000

What is the meaning exponent of 10?

A power of 10 is the sum of all the tens that the exponent indicates. As a result, a power of 10 is represented in long form as the number 1 followed by n zeros, where n is the exponent and is bigger than 0; for instance, 10⁶ is represented as 1,000,000.

Given numbers are:

4.836 × 10⁶ and 4,836,000,000

5.812 ×  10⁻⁷ and 0.0000005812

5.46 × 10¹¹ and 546,000,000,000

The equivalent form of 4.836 × 10⁶ is

4.836 × 1000000 = 4,836,000

The equivalent form of 5.812 ×  10⁻⁷  is

5.812 ×  10⁻⁷  = 5.812/ 10000000 = 0.0000005812.

The equivalent form of 5.46 × 10¹¹ is

5.46 × 10¹¹  = 5.46 × 100000000000 = 546,000,000,000

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The slope-intercept form of a line equation is given by:

Where m is the slope of the line and b is the y-intercept. From the problem, we identify:

To find b, we use the fact that when x = 20, y = 13:

Finally, for x = 16 (the corresponding y is the height of the candle after 16 hours):

Answer:

• Point A

• Triangle ABC

• Triangle ADE

Explanation:

From the diagram

The center of dilation is point A.

We know this because the center of dilation is a fixed point in the plane about which all points are expanded or contracted.

Point A does not change in the two triangles.

The original triangle is triangle ABC.

We know this because it is the larger of the two triangles. A scale factor of 1/2 will reduce the size of the original image.

The dilation is triangle ADE.

The graph rises parabolically. The rise in the value is not perfectly parabolic, but the increase can be structured as parabolic.

The general equation of a parabola is given by a quadratic equation as-

y = ax² + bx + c. It has a degree of [2] and has two possible roots.

We have the following table -

Days after posting [x] →    1     2     3     4    5    6

Unique daily views [y] →   5    8   13   20  29  40

Refer to the graph attached. It can be seen that, the graph is a parabola. Although the rise in the value is not perfectly parabolic, but the increase can be structured as parabolic. Mathematically, the equation of the parabola can be written as -

y = ax²

The parabola is wide open {not close to y - axis}, this signifies that the value of [a] is in decimals. If we make a estimate, it would be almost [a] = 1/88 for the mentioned data.

Therefore, the graph rises parabolically. The rise in the value is not perfectly parabolic, but the increase can be structured as parabolic.

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For the given graph , piecewise function for the given graph is as follow:

f(x)  =  1  ,                if x < -2

        2x ,              if -2 < x ≤ 0

       (- x / 2) + 2     if x > 0

As given in the question,

Given is the graph of the function f( x )

Now to find the piecewise function for the given graph is as follow:

For   x < -2 it is given that f ( x) = 1

Now consider two points for  -2 < x ≤ 0

( x₁ , y₁ ) = ( 0 , 0 )

( x₂ , y₂ ) = ( -2 , -4 )

Equation of f(x) is given by :

( y - 0 )/ ( x -0 ) = ( -4 - 0)/ (-2 - 0 )

⇒ y = 2x

Now consider two points for  x > 0

( x₁ , y₁ ) = ( 0 , 2 )

( x₂ , y₂ ) = ( 2 , 1 )

Equation of f(x) is given by :

( y - 2 )/ ( x -0 ) = ( 1 - 2)/ ( 2 - 0 )

⇒ y - 2 = -x / 2

⇒ y = ( -x / 2 ) + 2

Therefore, for the given graph , piecewise function for the given graph is as follow:

f(x)  =  1  ,                if x < -2

         2x ,              if -2 < x ≤ 0

       (- x / 2) + 2      if x > 0

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The formula of a slope:

[tex]\huge\begin{array}{ccc}m=\dfrac{y_2-y_1}{x_2-x_1}\end{array}[/tex]

We have two points:

[tex](0,\ 3)\to x_1=0,\ y_1=3\\\\(5,\ 13)\to x_2=5,\ y_2=13[/tex]

Substitute:

[tex]m=\dfrac{13-3}{5-0}\\\\m=\dfrac{10}{5}\\\\\boxed{m=2}[/tex]

Answer:

Slope = 2

Step-by-step explanation:

Now we have to,

→ find the slope of the line.

Formula we use,

→ Slope(m) = (y2 - y1)/(x2 - x1)

Then the slope will be,

→ m = (y2 - y1)/(x2 - x1)

→ m = (13 - 3)/(5 - 0)

→ m = 10/5

→ [ m = 2 ]

Hence, the slope is 2.

The linear equation to model the situation of water when Baxter begins to drain it is 55 + 2x = y.

The initial amount is 55 gallons and will not change.

The amount of water in the tank is increasing by 2 gallons per minute.

The minutes are the independent variable, which we can represent with the x.

The amount just at end of the minutes is the dependent variable, which we can represent with the y.

The linear equation;

55 + 2x = y

Thus, the linear equation to model the situation of water when Baxter begins to drain it is 55 + 2x = y.

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In 2years time, Lamar will be 18years old by application of an algebraic expression x for the unknown value.

Algebra is the branch of mathematics that helps to represent problems or unknown values in the form of mathematical expressions.

Algebraically, let us represent the age of Malcolm with the unknown value x

then the age of Lamar will be 4x

In 2years time;

Malcolm's age = x + 2

Lamar's age = 3(x + 2) {3times as old as Malcolm}

Also

Lamar's age = 4x + 2 {Lamar's age plus 2years}

So

4x + 2 = 3(x + 2)

open bracket by expansion

4x + 2 = 3x + 6

collect like terms

4x - 3x = 6 - 2

x = 4

Hence, substituting the known value of x in the algebraic expressions of x for Malcolm's age and 4x for Lamar's age, we have 4years and 16years respectively. And in 2years time Lamar will be 18years

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Answer:

is a way to express the definition of a circle on the coordinate plane. The formula is ( x − h) 2 + ( y − k) 2 = r 2. h and k are the x and y coordinates of the center of the circle. ( x − 9) 2 + ( y − 6) 2

Step-by-step explanation:

Hope it helped the answer is up there☝

Answer: 9.7 seconds

Step-by-step explanation:

[tex]16t^2 =1503\\\\t^2 =1503/16\\\\t=\sqrt{1503/16} \text{ } (t > 0)\\\\t \approx 9.7[/tex]

Answer:

A incorrect

Step-by-step explanation:

the degree is a optional request

The triangle is an Corollary 1 to the isosceles triangle theorem.

Given that,

In the picture we have a triangle,

We have to find which triangle is it.

From the triangle,

The 2 sides are equal and the 2 angles are also equal.

So, The triangle is an Corollary 1 to the isosceles triangle theorem.

According to the isosceles triangle theorem, if two triangle sides are congruent, then the angles across from those sides are likewise congruent.

An isosceles triangle is one with two sides that are the same size and a third side that is a different size.

Therefore, The triangle is an Corollary 1 to the isosceles triangle theorem.

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The time that it took Raj's older brother to complete his homework was 1 ¹ / ₄ hours

The time that it would take for Raj to complete the homework is 5/6 hours. His older brother would do it in 1 1/2 times as long.

The first thing to do is to convert this to an improper fraction:

= 1 1/2

= (2 x 1 + 1) / 2

= 3 / 2

The time it would take Raj's brother is therefore:

= Time it took Raj x Multiple

= 3 / 2 x 5 / 6

= 15 / 12

= 1 .25

1.25 in mixed fractions is:

= 1 ¹ / ₄ hours

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The correct order of the steps in a trial from first to last, include the following:

A trial court can be defined as a court of original jurisdiction where issues of fact, evidence, laws, and testimony for a litigation are first received, considered and decided, based on the deliberation by the jury.

Generally speaking, the citizen jury are legally empowered by the constitution to perform the following actions and activities:

In conclusion, a trial court is saddled with the responsibility of persuading the citizen jury before giving its verdict and sentencing a guilty offender, as the case may be.

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The solution of the given equation is 1. Therefore, option B is the correct answer.

The given equation is 6+7(b-1) = 5+b.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The given equation can be solved as follows:

Now, 6+7b-7 = 5+b

⇒ 7b-1=5+b

⇒ 7b-b=5+1

⇒ 6b=6

⇒ b=1

The solution of the given equation is 1. Therefore, option B is the correct answer.

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Given data:

The principal is

The time is

The interest is

Concept:

The formula to calculate interest rate (R) is given below as

By substituting the values in the formula above, we will have

Hence,

The final answer is 5%

The required measure of side y = 8

Given : Triangle TUV and triangle XWV are similar

Thus [tex]\frac{UV}{VW} = \frac{6}{21}[/tex]

this is further equal to [tex]\frac{2}{7}[/tex]

Thus the ratio UV : VW = 2 : 7

this implies that the ratio TV : VX should also be equal to the ratio of UV : VW = 2 : 7 because of cpst or also called corresponding parts of similar triangles.

Given  UV : VW = 2 : 7

thus TV : VX = [tex]\frac{y}{28 }[/tex] which on equation will give y as 8

because [tex]\frac{8}{28}[/tex] when divided by 4 will give us the required ratio that is 2 : 7

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x=-1, y =2 S { -1,2}

1) Solving that linear system

x + 2y = 3 x -5 To eliminate x

5× +5y = 5​

-5x -10y = -15

5x +5y = 5​

---------------------

-5y = -10

y =2

1.2 Plugging into the I equation:

x +2(2)= 3

x +4=3

x=-1

in irder to solve this problem

we need to now that the probability to win one coin toss is 0.5

so other thing we need to know is

there all these possible scenarios that will happen

w= win

L=lose

WWW

WWL

WLW

LWW

LLW

LWL

LLW

LLL

as you can see only in 3 scenarios when the cougar win exactly 2

so the correct answer is B

Answer

They should deposit $7710.99

Explanation

Using compound interest formula,

Where:

A = Amount = $20,000

P = Principal = ?

r = Interesr rate = 10% = 0.1

n = 1

t = 10

Given:

We have the graph below:

The value of the radius that minimizes the amount of Aluminium is 4.64 cm and it gives the local minimum of the function

From the question, the volume of the aluminium is given as

Volume = 200pi cm^3

Rewrite this volume properly using the correct symbols and units

So, we have the following representation

Volume = 200π cm³

Solving further, we make use of the volume of a cylinder (i.e. a can)

The volume of a sphere is represented as

V = πr²h

Substitute Volume = 200π cm³ in

πr²h = 200π

Make h the subject in the above equation

This gives

h = 200π/πr²

Cancel the common factors

h = 200/r²

The surface area of a can is

A = 2πr(h + r)

So, we have

A = 2πr(200/r² + r)

This gives

A = 400π/r + 2πr²

Differentiate the function

This gives

A' = -400π/r² + 4πr

Set the differentiated function to 0

-400π/r² + 4πr = 0

So, we have

-400π/r² = -4πr

Cross multiply

-400π = -4πr³

Divide through by -4π

r³ = 100

Take the cube roots

r = 4.64

Hence, the radius that given minimum material is 4.64 cm

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The theorem that states that the sampling distribution of the sample mean is approximately normal when the sample size n is reasonably large is known as the Central Limit Theorem

The Central Limit Theorem is a statistical theorem that states that, given a sufficiently large sample size, the distribution of the mean of any sample will be approximately normal, regardless of the shape of the distribution from which the sample was drawn.

In other words, the theorem states that the mean of a large sample will be close to the mean of the population, and that the standard deviation of the distribution of the sample mean will be small.

The theorem is important because it provides a way to approximate the distribution of any sample statistic, as long as the sample size is large enough. This is useful because many statistical tests, such as hypothesis tests and confidence intervals, require that the data be normally distributed.

The theorem is also important because it provides a way to quantify the amount of error that is introduced when a sample is used to estimate a population parameter. This is known as the standard error, and it is equal to the standard deviation of the distribution of the sample mean divided by the square root of the sample size.

The Central Limit Theorem is one of the most important theorems in statistics, and it is widely used in many different fields.

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Answer:

$14.70

Step-by-step explanation:

If she get paid the time and a half you would first divide $9.80 by 2 which is $4.90. Now that you have the half price you add the original time to it. $9.80+$4.90= 14.70 so that’s the answer

Answer:

Given that,

Margie is 4.25 feet tall

The maple tree in her backyard is 5.5 times taller than her.

To find the height of the maple tree.

we get,

Height of the maple tree is,

Maple tree is 23.375 feet tall.