hich is true about the solution to the system of inequalities shown?

y > 3x + 1

y < 3x – 3

On a coordinate plane, 2 solid straight lines are shown. The first line has a positive slope and goes through (negative 2, negative 5) and (0, 1). Everything to the left of the line is shaded. The second line has a positive slope and goes through (0, negative 3) and (1, 0). Everything to the right of the line is shaded.
Only values that satisfy y > 3x + 1 are solutions.
Only values that satisfy y < 3x – 3 are solutions.
Values that satisfy either y > 3x + 1 or y < 3x – 3 are solutions.
There are no solutions.

Based on the simulations from parts (A) thru (E), the shape of the distribution of "heads" is bell-shaped. Therefore, the correct answer is B. Bell-shaped.

What is the most probable distribution's shape?

Bell-shaped distributions, sometimes referred to as normal or Gaussian distributions in math and science, are the most significant probability distribution shapes since they are typically the result of sufficiently big data sets from naturally occurring random variables.

The mathematical idea known as the normal distribution, and also referred to as the Gaussian distribution, is commonly defined by the mound form.

When data points are utilized to plot a line for a particular item that satisfies the requirements of the normal distribution, a form called a mound is produced.

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Answer:

52 tickets cost $10 and 18 tickets cost $12

Step-by-step explanation:

10x+12y=804. (1)

x+y=70. (2)

From (2)

x=70-y

Substitute x=70-y into (1)

10x+12y=804

10(70-y)+12y=804

700-10y+12y=804

700+2y=804

2y=804-700

2y=104

y=104/2

y=52

Recall

x+y=70

x+52=70

x=70-52

x=18

52 tickets cost $10 and 18 tickets cost $12

By solving a system of equations we will see that the correct option is A.

First, let's define the variables:

First, we know that 70 tickets were sold, so:

x + y = 70

And we know that they reached $804, then we have:

x*$10 + y*$12 = $804

Then our system is:

x + y = 70

x*$10 + y*$12 = $804

To solve this, we first need to isolate one of the variables in one of the equations, I will isolate x on the first equation:

x = 70 - y

Now we can replace that in the other equation to get:

(70 - y)*$10 + y*$12 = $804

$700 - y*$10 + y*$12 = $804

$700 + y*$2 = $804

y*$2 = $804 - $700 = $104

y = $104/$2 = 52

So, 52 $12 tickets were sold, then the other 18 tickets were $12, so the correct option is A.

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The absolute maximum and minimum values of the function f(x, y) = x^2 + y^2 - 2y on the set R = {(x, y): x^2 + y^2 ≤ 9} can be found by analyzing the critical points and the boundary of the region R.

To find the critical points, we take the partial derivatives of f(x, y) with respect to x and y, and set them equal to zero. Solving these equations, we find that the critical point occurs at (0, 1).

Next, we evaluate the function f(x, y) at the boundary of the region R, which is the circle with radius 3 centered at the origin. This means that we need to find the maximum and minimum values of f(x, y) when x^2 + y^2 = 9. By substituting y = 9 - x^2 into the function, we obtain f(x) = x^2 + (9 - x^2) - 2(9 - x^2) = 18 - 3x^2.

Now, we can find the maximum and minimum values of f(x) by considering the critical points, which occur at x = -√2 and x = √2. Evaluating f(x) at these points, we get f(-√2) = 18 - 3(-√2)^2 = 18 - 6 = 12 and f(√2) = 18 - 3(√2)^2 = 18 - 6 = 12.

Therefore, the absolute maximum value of f(x, y) is 12, which occurs at (0, 1), and the absolute minimum value is also 12, which occurs at the points (-√2, 2) and (√2, 2).

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After one year of compounding at a 6% interest rate, you would have approximately $3,180 in your savings account.

To calculate the amount of money you will have in the savings account after one year with compound interest, we can use the formula:

A = P(1 + r/n)^(nt)

Where:

A is the final amount

P is the principal amount (initial deposit)

r is the annual interest rate (as a decimal)

n is the number of times the interest is compounded per year

t is the number of years

Let's solve it step by step:

Given:

P = $3,000 (principal amount)

r = 6% = 0.06 (annual interest rate as a decimal)

n = 1 (compounded annually)

t = 1 (one year)

Using the formula:

A = 3000 * (1 + 0.06/1)^(1*1)

A = 3000 * (1 + 0.06)^1

A = 3000 * (1.06)^1

A ≈ $3180

So, after one year of compounding at a 6% interest rate, you would have approximately $3,180 in your savings account.

It seems there was a discrepancy in the answer provided. Based on the given information, the correct calculation yields $3,180, not $5,372.54.

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Answer:

Hello!!! Princess Sakura here ^^

Step-by-step explanation:

The angles 2 and 3 are corresponding angles. So it's choice C.

Tip: Any pair of angles each of which is on the same side of one of two lines cut by a transversal and on the same side of the transversal.

The points in the plane (x, y) at which the functions g(x, y) and h(x, y) are continuous are as follows:a. g(x, y) = cos(xy)

The function is continuous everywhere in the plane, which means that the answer is any (x, y).b. h(x, y) = 8 + cos(x/(x+y)) - The function is discontinuous where the denominator of the argument of the cosine function is equal to 0. Because of this, the answer is every point in the plane (x, y) except those where x + y = 0. The function h(x, y) can be represented as follows:h(x, y) = 8 + cos(x/(x+y))

The domain of this function is R^2 \ {y = -x}, which means that the function is continuous in this domain.A continuous function is a function whose graph is a single unbroken curve or a surface. This indicates that as the input to a continuous function varies, the output changes continuously.In conclusion, the function g(x, y) is continuous everywhere in the plane, while the function h(x, y) is continuous in the domain R^2 \ {y = -x}.

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Q is not cyclic because it contains irrational numbers such as √2 that cannot be generated by any element in Q. R is not cyclic due to its uncountable nature and additional properties as a complete ordered field.

(a) To prove that Q (the set of rational numbers under addition) is not cyclic, we need to show that there is no element in Q that generates the entire group under the operation of addition.

Assume, for contradiction, that Q is cyclic and let q be a generator of Q. This means that every rational number can be expressed as an integral power of q. However, we can find a rational number r that cannot be expressed in this form.

Consider the square root of 2 (√2), which is irrational. If q is a generator of Q, then there exist integers m and n such that q = m/n. However, it is known that √2 is not rational, which means it cannot be expressed as a fraction of two integers. Therefore, √2 cannot be generated by any element in Q, which contradicts the assumption that Q is cyclic. Hence, Q is not cyclic.

(b) Since Q is not cyclic, we cannot deduce directly that R (the set of real numbers under addition) is not cyclic. However, there are other reasons to conclude that R is not cyclic. One such reason is that R is an uncountable set, whereas cyclic groups are countable. Another reason is that R is a complete ordered field, which means it has additional properties not present in cyclic groups. Therefore, we can deduce that R is not cyclic based on these additional characteristics.

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The required  cost of each shirt is $21.28.

A mathematical statement known as an equation is made up of two expressions joined together by the equal symbol. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the quantity x is 7.

The total cost of 3 identical shirts, including shipping, is $71.83. So we can write the equation as:

3s + 7.99 = 71.83

To solve for the cost of each shirt, we need to isolate the variable "s" on one side of the equation. We can start by subtracting 7.99 from both sides:

3s = 63.84

Then, we can divide both sides by 3:

s = 21.28

Therefore, the cost of each shirt is $21.28.

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Answer

x=5 y=2

Step-by-step explanation:

The solution to the expression 6x - 2x + 8y - 6y is 4x + 2y

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

6x - 2x + 8y - 6y

Collect the like terms in the expression

So, we have the following representation

6x - 2x + 8y - 6y = 6x - 2x + 8y - 6y

Evaluate the like terms in the expression

So, we have the following representation

6x - 2x + 8y - 6y = 4x + 2y

Hence, the simplified expression is 4x + 2y

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Answer:

\(15^4\)

Step-by-step explanation:

Given the following question:

\(15\times15\times15\times15\)

In order to find the exponent of the given expression we count how many times the number is being multiplied by itself, that number would then be the exponent.

\(15\times15\times15\times15\)
They're four 15's
\(15^4\)

To prove the answer:
\(15\times15\times15\times15=50625\)
\(15^4=50625\)
\(15^4\)

Hope this helps.

Answer:

3 by 4

Step-by-step explanation:

Given the dimension of the polygon as 6 by 8

If the scale factor is 1/2, the new side length is gotten by multiplying both dimensions by 1/2 as shown:

For the side length 6:

New length = 1/2 * 6 = 3

For the side length 8:

New length = 1/2 * 8

New length = 4

Hence the new side lengths in the copy is 3 by 4

Answer:

Ratio is 1:4 . 1 cup sugar and 4 cup flour.

1 : 4 is the ratio of sugar to flour.

A ratio exists as an ordered pair of numbers a and b, written a / b where b does not similar to 0. A proportion exists in an equation in which two ratios stand set equal to each other.

The demonstrated quotient of two mathematical expressions is called ratio.

cup of sugar = one
cup of flour = four

1 : 4 is the ratio of sugar to flour

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Answer:

$1.66 per foot

Step-by-step explanation:

3 yards=9 ft

14.94/9=$1.66 per foot

Answer:

$0.99

Step-by-step explanation:

15x0.066=0.99

the average speed of the plane in still air is s + 30.

Let's call the average speed of the plane in still air "s" (in miles per hour).

We can use the formula:

time = distance / speed

to find the time it takes the plane to travel from Salt Lake City to Oakland with the wind and against the wind.

With the wind:

time with wind = \(600 / (s + 30)\)

Against the wind:

time against wind =\(600 / (s - 30)\)

time against wind > time with wind

So we can set up an inequality:

\(600 / (s - 30) > 600 / (s + 30)\)

Multiplying both sides by \((s - 30)(s + 30)\), we get:

\(600(s + 30) > 600(s - 30)\)

Expanding and simplifying, we get:

\(600s + 18000 > 600s - 18000\)

Subtracting 600s from both sides, we get:

\(18000 > -18000\)

This inequality is true for all values of s. In other words, there are no restrictions on the value of s that would make the return trip take longer than the trip with the wind.

Therefore, we can use the average of the two speeds (with and against the wind) to find the average speed of the plane in still air:

Average speed = \(2s(s + 30) / (s + 30 + s - 30)\)

Simplifying, we get:

Average speed = \(2s(s + 30) / (2s)\)

Canceling the common factor of 2s, we get:

Average speed = s + 30

We know that the distance from Salt Lake City to Oakland is 600 miles, and we can use the formula:

time = distance / speed

to find the time it takes the plane to travel this distance:

time = \(600 / (s + 30)\)

We also know that the return trip (against the wind) takes longer, so we can set up another equation:

time return trip =\(600 / (s - 30)\)

We can use these two equations to solve for s:

\(600 / (s + 30) = 600 / (s - 30)\)

Cross-multiplying, we get:

\(600(s - 30) = 600(s + 30)\)

Expanding and simplifying, we get:

\(600s - 18000 = 600s + 18000\)

Subtracting 600s from both sides, we get:

\(-18000 = 18000\)

This is not a valid equation, so there must be no solution.

However, we can still find the average speed of the plane in still air by using the equation we derived earlier:

Average speed = s + 30

So the average speed of the plane in still air is s + 30. We don't have a specific value for s, but we can say that the average speed is equal to the speed with the wind plus 30 (which is the speed of the wind).

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Answer: x=+27

Step-by-step explanation:

\(\huge\qquad\underline{{\tt answer : - }} \)

\(x+12=2x-15 \\ x - 2x = - 12 - 15 \\ - x = - 27 \\ x = 27\)

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Answer:

7/10 is greater than 5/8

Step-by-step explanation:

Answer:

7/10

Step-by-step explanation:

Find the least common denominator or LCM of the two denominators:

LCM of 8 and 10 is 40

Next, find the equivalent fraction of both fractional numbers with denominator 40

For the 1st fraction, since 8 × 5 = 40,

5

8

=

5 × 5

8 × 5

=

25

40

Likewise, for the 2nd fraction, since 10 × 4 = 40,

7

10

=

7 × 4

10 × 4

=

28

40

Since the denominators are now the same, the fraction with the bigger numerator is the greater fraction

25/40 < 28/40

or

5/8 < 7/10

Answer:

10000 total possible PIN numbers.

The amount of money which Lamar should pay for the gas he bought as calculated is $2.36.

The amount which Lamar has to pay can be calculated by multiplying the amount of gas from the price of gas per gallon,

Price of gas = 2.95

Quantity which he bought = 0.8

Therefore ,

Price =2.95 x 0.8 = $2.36.

Therefore, he is suppose to pay $2.36 for 2.95 gallons of gas.

Multiplication is the process in which we multiply two numbers from each other , it can be performed between more than two numbers as well.

Other basic mathematical operations are addition , subtraction and division.

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The volume of the solid region is approximately 10.4109 cubic units.

To find the volume of the solid region lying below the surface z = f(x,y) and above the plane region R, we can use the formula:

V = ∬R f(x,y) dA

where dA is the area element in the xy-plane and the double integral is taken over the region R.

To evaluate this integral, we first need to perform a change of variables. Let u = x + y and v = x - y. Then the inverse transformations are x = (u + v)/2 and y = (u - v)/2. The Jacobian of this transformation is:

J = ∂(x,y) / ∂(u,v) = 1/2

Next, we need to express the surface z = f(x,y) in terms of u and v. Using the substitutions x = (u + v)/2 and y = (u - v)/2, we get:

f(x,y) = (x+y)ex-y = [(u+v)/2 + (u-v)/2]e(u-v)/2 = ueu/2

So the volume of the solid is:

V = ∬R f(x,y) dA

= ∬R ueu/2 dA

= ∫₂⁴ ∫₂⁶ (u/2)e^(u/2) du dv (using the limits of integration for R in terms of u and v)

= ∫₂⁶ [e^(u/2)u²/4] from 2 to 4 dv

= ∫₂⁴ [e^(u/2)u²/4] from u-2 to 6 du

= 16(e^3 - e^2)/3

Therefore, the volume of the solid region is approximately 10.4109 cubic units.

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Answer:

36

Step-by-step explanation:

The absolute value of a number is how far away the number is from zero. The absolute value is ALWAYS positive.

Answer:

36.

Step-by-step explanation:

absolute value is always zero or positive

3 Answers:

==========================================================

Explanation:

Let's go through the answer choices one by one.

In short, we can use choice A, choice D, choice F. We can't use the other three choices because we lack the info about any other pairs of angles.

The congruence theorem or postulate that we can use to show that triangle ABC is congruent to triangle LMN is LL (Side-Side-Side), the correct option is A.

Suppose it is given that two triangles ΔABC ≅ ΔDEF

Then that means ΔABC and ΔDEF are congruent. Congruent triangles are exact same triangles, but they might be placed at different positions.

The order in which the congruency is written matters.

For ΔABC ≅ ΔDEF, we have all of their corresponding elements like angle and sides congruent.

Thus, we get:

\(\rm m\angle A = m\angle D \: or \: \: \angle A \cong \angle D \angle B = \angle E\\\\\rm m\angle B = m\angle E \: or \: \: \angle B \cong \angle E \\\\\rm m\angle C = m\angle F \: or \: \: \angle C \cong \angle F \\\\\rm |AB| = |DE| \: \: or \: \: AB \cong DE\\\\\rm |AC| = |DF| \: \: or \: \: AC \cong DF\\\\\rm |BC| = |EF| \: \: or \: \: BC \cong EF\)

(|AB| denotes length of line segment AB, and so on for others).

We are given that;

Sides are equal

Now,

Based only on the information given in the diagram, we can use the following congruence theorems or postulates to show that triangle ABC is congruent to triangle LMN:

A. LL (Side-Side-Side): This theorem states that if three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent. In this case, we know that AB = LM, AC = LN, and BC = MN, so we can use LL to show that triangle ABC is congruent to triangle LMN.

B. ASA (Angle-Side-Angle): This theorem states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent. In this case, we do not know any angle measures, so we cannot use ASA to show that the triangles are congruent.

Therefore, by the  congruent triangles the answer will be LL (Side-Side-Side).

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When solving the multiplication of fractions by whole numbers, it's important to remember that a fraction is a number that represents the division of two quantities, and a whole number is a non-negative integer.

To multiply a fraction by a whole number, you need to multiply the numerator (the top number of the fraction) by the whole number and leave the denominator (the bottom number of the fraction) unchanged. For example, if you have the fraction 3/4 and you want to multiply it by 2, you would get 3/4 * 2 = 6/4 = 3/2.

Another way to think about it is that when multiplying a whole number by a fraction, you are essentially adding the fraction to itself that many times. For example, if you have 3/4 * 2, you can think of it as 3/4 + 3/4 = 3/2

It's important to note that when multiplying a fraction by a whole number, you are not changing the value of the fraction, you are only changing its representation.

It's also important to simplify the result if possible, check if both the numerator and denominator have a common factor, if they do, you can divide both by that factor. For example, if you have the fraction 6/8, you can simplify it to 3/4.

In summary, to multiply a fraction by a whole number, you need to multiply the numerator by the whole number and leave the denominator unchanged, and then simplify the result if possible. It's a simple operation but it is important to understand the concept behind it before solving the problem.

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we know that

The clock represent a complete circle

The circumference of a circle is giving by the formula

C=2pi r

where

r is the radius of the circle

In this problem

The radius of the circle is equal to the length of the minute hand

so

r=6 in

C=2pi(6)

C=12pi in

The length of the complete circle subtends a central angle 0f 360 degrees

Find out what is the central angle for 10 minutes (6:35 to 6:45)

we know that

6 hours represent 90 degrees

so

1 hour represent 15 degrees

1 hour represent 60 minutes so

divide by 6

15/6=2.5 degrees

therefore

using proportion

12pi/360=x/2.5

solve for x

x=12pi(2.5)/360

use 3.14 as pi

x=12(3.14)(2.5)/360

x=0.26 inches

The answer is 0.26 inches

The exponent property that supports this technique is given as follows:

a^(m/n) = nth root of a^m.

The expression that is equals to 4^(5/2) is given as follows:

A. square root of 4^5.

The exponential expression for this problem is defined as follows:

4^(5/2).

The fraction in the exponent means that:

Then the equivalent expression to 4^(5/2) is given as follows:

square root of 4^5.

Because:

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Answer:

It's ASA, AAS,

Step-by-step explanation:

AAS- If two angles and a non-included side in one triangle are congruent to two angles and the corresponding non-included side in another triangle, then the triangles are congruent.

ASA-The ASA criterion for triangle congruence states that if two triangles have two pairs of congruent angles and the common side of the angles in one triangle is congruent to the corresponding side in the other triangle, then the triangles are congruent.

y intercept: 80, it means that peyton sells 0 dollars worth of computer on a day, she just makes a base pay amount that day.

A mathematical declaration that two mathematical expressions are equal is the definition of an equation in algebra in its most basic form. An equation where the components 3x + 5 and 14 are separated by the equal sign, such as 3x + 5 = 14, is an illustration of this.

In the equation ,

y=mx+b, m is the slob and b is the y intercept

For, P = 0. 025x+80p=0. 025x+80

The y intercept is 80.

it means that peyton sells 0 dollars worth of computer on a day, she just makes a base pay amount that day.

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After 3 hours Dylan and Sam will be exactly 15 miles apart .

In the question ,

it is given that ,

the speed at which Dylan is jogging in east = 4 miles per hour .

the speed at which Sam is jogging in south = 3 miles per hour .

the distance covered by Dylan is = 4t

the distance covered by Sam is = 3t

we have to find the time when they are 15 miles apart .

Since Dylan walks in east and Sam walks in South  , it forms a right triangle , so , it will satisfy the Pythagoras Theorem ,

(3t)² + (4t)² = 15²

9t² + 16t² = 225

225 = 25t²

t² = 225/25 = 9

t = 3

Therefore , the time taken will be 3 hours .

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